www.materialstoday.com Available online at www.sciencedirect.com Cloaking devices New opportunities with metamaterials DECEMBER 2009 | VOLUME 12 | NUMBER 12www.materialstoday.com DECEMBER 2009 | VOLUME 12 | NUMBER 12 Solartron Analytical provides a range of solutions that enable researchers to measure the electrical properties of materials. Testing at both high and low temperatures is simplified using the tightly integrated temperature control capability, while our comprehensive data acquisition / materials analysis software completes the picture and helps build a winning hand for your research. See how our products are used in your application by searching our extensive online applications reference library, or book a demo or sales call, via our website at: www.solartronanalytical.com/stacksofapps Stacks of apps. US: Tel: 1-865-425-1360 UK: Tel: +44 (0)1252 556800 solartron.info@ametek.com Superconductors SUPERCONDUCTORS Displays DISPLAYS Polymers POLYMERS Dielectrics DIELECTRICS Ceramics CERAMICS Semiconductors SEMICONDUCTORS Power curvePOWERCURVE I P V Mott Schottky MOTTSCHOTTKY V 1 C2 Impedance IMPEDANCEZ real Zimag Biomaterials BIOMATERIALS Nanotechnology NANOTECHNOLOGY Solar cells SOLARCELLS EDITORIAL DECEMBER 2009 | VOLUME 12 | NUMBER 12 1 Editorial Advisory Panel Growing numbers of students are electing to take science based subjects More students than ever before are opting to take science related degrees at university ­ and this trend is also filtering through to our nations schools which are also recording a surge in interest between 5 ­ 18 year olds. These results were announced by the University and Colleges Admissions Service (UCAS). The Engineering and Physical Sciences Research Council (EPSRC) Chief Executive Dave Delpy welcomes this news and comments: "This strengthens the case for supporting our future scientists and engineers" Dave Delpy goes on to say, "With the increase in undergraduate interest in science and engineering, we anticipate greater numbers of PhD students applying for research funding over the years to come. It is therefore more vital than ever to create a support network for school children to encourage them to engage with science and engineering at an early stage to help them become career scientists and engineers." I feel this presents a challenge incumbent on all of us; to help educate and promote, a challenge I am sure we will all embrace with enthusiasum. Many schemes and initiatives are already evident in every day life, and just scanning the national news you will find numerous events from industrial and entreprenureal challenges to polls such as the recent Science Museums poll to vote for the most important invention in science. From a shortlist of inventions such as the Apollo capsule, DNA double helix and the X-ray machine, it attracted an unprecedented number of votes. To find out which invention was voted the most significant visit www.sciencemuseum.org.uk. We still face a number of worrying issues and claims over poor levels of science literacy and teaching levels in our schools; the Chief executive of the Royal Society of Chemistry, Dr Richard Pike claims some exam papers contain absolutely no maths in them and some questions even no science. We have heard many arguments and discussions about the fears of dumbing down science, Dr Pike fears if we do not appoint a rigorous regulator soon then overall standards (even though we are witnessing a surge in interest) will suffer. Ofqual have responded and said it was taking steps to improve science. This renewed interest in science is an opportunity to bring our best brains to the fore and discuss and engage with our next generation of scientists the challenges facing both the environment and industry at large. We must not only inform but also encourage debate, this will ensure we build on the growing interest in science and tackle head-on some of the disconnect between the quality of teaching and resources open to our young students. The future can be a bright one for science providing we continue to build the infrastructure in our communities, and awareness and interest in our schools and colleges. Science is the new cool? Gabriel Aeppli University College London, UK Caroline Baillie Queens University, Canada Zhenan Bao Stanford University, USA Franco Cacialli University College London, UK Martin Castell University of Oxford, UK Peter Goodhew University of Liverpool, UK Ulrich Gösele Max Planck Institute of Microstructure Physics, Germany Hermann Grimmeiss Lunds Universitet, Sweden Alan Heeger University of California, Santa Barbara, USA Mark Johnson Naval Research Laboratory, USA Richard A. L. Jones University of Sheffield, UK Neil McKeown Cardiff University, UK Tae Won Noh Seoul National University, Korea Stephen Pearton University of Florida, USA Marshall Stoneham FRS University College London, UK Helena Van Swygenhoven Paul Scherrer Institute, Switzerland Richard Vaia Air Force Research Laboratory, USA George Whitesides Harvard University, USA Jackie Yi-Ru Ying Institute of Bioengineering and Nanotechnology, Singapore Published by Elsevier Ltd. The Boulevard, Langford Lane, Kidlington, OX5 1GB, UK Editorial Commercial Editor Jonathan Agbenyega E-mail: J.Agbenye@elsevier.com Production Controller Lin Lucas E-mail: materialstoday@elsevier.com Advertising Advertisements Manager Kevin Partridge E-mail: k.partridge@elsevier.com Advertisement Sales Guy Plowman E-mail: g.plowman@elsevier.com Free circulation enquiries Materials Today, Tower House, Sovereign Park, Market Harborough LE16 9EF, UK Tel: +44 (0)1858 439 601 Fax: +44 (0)1858 434 958 E-mail: elsevier@subscription.co.uk Subscription orders & payments Materials Today (ISSN 1369-7021) is published 10 times per year by Elsevier Ltd. The Boulevard, Langford Lane, Kidlington, OX5 1GB, UK Price: 209 / US$234 / 27900 Europe/ROW Tel: +31 20 485 3757 USA Tel: +1 212 633 3730 Elsevier Ltd. 2009 All material published in Materials Today is copyright Elsevier Ltd. Annual subscription price in the USA US$ 234 (valid in North, Central and South America), including air speed delivery. Periodical postage paid at Rahway NJ and additional mailing offices. USA POSTMASTER: Send change of address: Materials Today, Elsevier, 6277 Sea Harbor Drive, Orlando, FL 32887-4800. AIRFREIGHT AND MAILING in USA by Mercury International Limited, 365, Blair Road, Avenel, NJ 07001. This journal and the individual contributions contained in it are protected under copyright by Elsevier Ltd, and the following terms and conditions apply to their use: Photocopying: Single photocopies of single articles may be made for personal use as allowed by national copyright laws. Permission of the Publisher and payment of a fee is required for all other photocopying, including multiple or systematic copying, copying for advertising or promotional purposes, resale, and all forms of document delivery. Special rates are available for educational institutions that wish to make photocopies for non-profit educational classroom use. Permissions may be sought directly from Elsevier Global Rights Department, P.O. Box 800, Oxford OX5 1DX, UK; phone: (+44) 1865 843830, fax: (+44) 1865 853333, e-mail: permissions@elsevier.com. You may also contact Global Rights directly through Elsevier's homepage (http:// www.elsevier.com), by selecting `Obtaining Permissions'. In the USA, users may clear permissions and make payments through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA; phone: (+1) (978) 7508400, fax: (+1) (978) 7504744, and in the UK through the Copyright Licensing Agency Rapid Clearance Service (CLARCS), 90 Tottenham Court Road, London W1P 0LP, UK; phone: +44 (0)20 7631 5555; fax: +44 (0)20 7631 5500. Other countries may have a local reprographic rights agency for payments. Derivative Works: Subscribers may reproduce tables of contents or prepare lists of articles including abstracts for internal circulation within their institutions. Permission of the Publisher is required for resale or distribution outside the institution. Permission of the Publisher is required for all other derivative works, including compilations and translations. Electronic Storage or Usage: Permission of the Publisher is required to store or use electronically any material contained in this journal, including any article or part of an article. Except as outlined above, no part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior written permission of the Publisher. Address permissions requests to: Elsevier Global Rights Department, at the mail, fax and e-mail addresses noted above. Notice: No responsibility is assumed by the Publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made. Although all advertising material is expected to conform to ethical (medical) standards, inclusion in this publication does not constitute a guarantee or endorsement of the quality or value of such product or of the claims made of it by its manufacturer. Printed by Headley Brothers Ltd, Kent, UK ISSN 1369-7021 Journal number: 03069 Jonathan Agbenyega | Editor, Materials Today | j.agbenye@elsevier.com Stability ˇ Performance ˇ Productivity www.jeolusa.com ˇ salesinfo@jeol.com 978-535-5900 Another Extreme Imaging SolutionKFPM AtomicResolutionMicroscope The Power of -12* * TEM 80 picometers, or 80 trillionths of a meter The best atomic level imaging and chemical mapping available today. Seeing is believing. jeolusa.com/ARM200F Contents www.materialstoday.com CONTENTS DECEMBER 2009 | VOLUME 12 | NUMBER 12 3 Cite of special scientific interest Materials Today is covered by Thomson Scientific products and services; beginning with Volume 9 (2006) articles and abstracts have been indexed in SciSearch, Materials Science Citation Index, Current Contents/Physical Chemical and Earth Sciences, and Journal Citation Reports. Our 2008 listing was recently published and after many months of speculation and anticipation the long wait was over and we were delighted to hear our first impact factor of 12.9. This figure represents an amazing achievement for our magazine and also for all those who have contributed to the content over the years both internally and within the greater research community. Regulars Editorial 1 Science is the new cool? Growing numbers of students are electing to take science based subjects. Research News 8 Synthetic cells help research and provide battery power | Danish nanowires capture the sunlight | New approach produces stimuli-responsive assemblies of nanoparticles | Casting a new light on chromophores | Processing nanotube fibers goes mainstream | A hard X-ray interferometer | Graphene speeds up computers | Innovative metallic glass shows promise for bone surgery | Neuronal nanotubes | Magnetricity is taken for a spin. Updates Tools and Techniques 70 Diary 72 8 PbS nanoparticles arranged in a hexagonal grid 12 A perfect quasi-free standing graphene layer and nanodomes 14 Neurons firing and communicating with nanotubes DECEMBER 2009 | VOLUME 12 | NUMBER 124 CONTENTS www.materialstoday.com Cloaking devices Next issue Materials Today will feature the current state of play in the design, performance, and viability of the biomaterials in research and clinical application of artificial organ development and regeneration. Contents to include: Resorbable biomaterials as bone graft substitutes Marc Bohner looks at presenting a concise, accessible overview of the field of resorbable bone graft substitute materials. Biological and biomimetic materials in tissue engineering Patterson, et al., reviews the biomaterial matrices which are being developed that mimic the key characteristics of the extracellular matrix. Ultra hard biomineral in the radular teeth of Cryptochiton stelleri Weaver, et al., describe the architectural and mechanical properties of the radular teeth from Cryptochiton stelleri and explain how the unique multiphasic design of these materials contributes not only to their functionality, but also highlights some interesting design principles that might be applied to the fabrication of synthetic composites. Review 26 Anisotropic metamaterial devices This paper reviews the recent progress on the parametric design of transformation devices. Wei Xiang Jiang, Jessie Yao Chin and Tie Jun Cui Review 34 Phononic crystals and acoustic metamaterials Phononic crystals have been proposed about two decades ago and some important characteristics have stimulated practical studies in acoustic materials and devices since then. Ming-Hui Lu, Liang Feng and Yan-Feng Chen Review 44 Electromagnetic wave in 2D photonic crystals This paper reviews recent progresses on the negative refraction and the abnormal transmission of electromagnetic wave in twodimensional photonic crystals. Xiangdong Zhang Review 52 Resonance properties of metallic ring systems Lei Zhou et al., review their recent efforts in understanding the resonance properties of metallic ring systems using a rigorous mode-expansion theory. Lei Zhou, Xueqin Huang, Yi Zhang, Siu-Tat Chui Review 60 Mie resonance-based dielectric metamaterials Qian Zhao et al., review the recent progresses of Mie resonance-based metamaterials by providing a description of the underlying mechanisms to realize negative permeability, negative permittivity and double negative media. Qian Zhao, Ji Zhou, Fuli Zhang, Didier Lippens Lead story 16 Optical nano-antennas and metamaterials Sailing He et al., review some recent approaches to transmission enhancement and light harvesting based on optical nanoantennas and metamaterials. Nano-cavity antennas are used to enhance the extraordinary transmission of TM-polarized light through vertical nano-slits in a metal film. Sailing He, Yanxia Cui, Yuqian Ye, Pu Zhang, and Yi Jin X-Max TEM BIG performance at the NANO scale New Large Area Silicon Drift Detector now offers Maximum Productivity from your TEM www.oxford-instruments.com/xmaxtem For further information contact us directly: Email: nanoanalysis@oxinst.com ce at the NANO sca X-Max TEM * Maximum efficiency * larger solid angle for maximum count rate * Maximum performance * best analytical performance for elements from beryllium upwards * Maximum sensitivity * obtain meaningful data from nanostructures and nanoparticles * Maximum convenience of LN2 free operation * improved safety and reduced life cost Semconductor image. Sample courtesy M. Phaneuf, Fibics Inc. Ottawa Improved collection efficiency produces X-ray maps and linescans in shorter times at higher count rates 80mm2 DECEMBER 2009 | VOLUME 12 | NUMBER 126 RESEARCH NEWS Synthetic cells help research and provide battery power BIOMATERIALS Scientists have discovered a technique for using artificial cells to explore the function of molecules in actual biological cells. The new approach can help the measurement of biological systems and show how cell nanomachinery interacts within cells, which could have a major impact in the development of new medical procedures and drug discovery. The team, from Yale University and the National Institute of Standards and Technology (NIST), have developed a highly simplified model cell that includes only a few chemical processes which reproduce cell function, to help them understand how real cells can generate electric voltages and act as tiny batteries. This research shows how such cells could provide an alternative to conventional solid-state energy-generating devices and other new energy technologies. Published online in [Xu et al., Advanced Materials, doi: 10.1002/adma.200901945], the methodology used allows the study of cellular machinery in terms of some basic properties, such as the size of the droplets, the concentration of the aqueous solutions and the number of ion channels in the barrier between the two cells, simplifying the process of examining how biological cells work, and enabling them to examine biological energy conversion processes. The study found that a tiny battery with two droplets, each containing just 200 nanoliters of solution, could deliver electricity for almost 10 minutes, while a bigger system, with a total volume of almost 11 microliters, lasted more than four hours. Although the biological battery is not as effective as a conventional lead-acid battery, it is efficient in terms of its ability to convert chemical into electrical energy. The synthetic cells have a droplet of a waterbased solution containing a salt ­ potassium and chloride ions ­ enclosed within a lipid wall, a molecule with one end that is attracted to water molecules while the other end repels them. If the solutions in the two cells start with different salt concentrations, then poking thin metal electrodes into the droplets creates a small electric battery. They then inserted into the bilayer a modified form of a protein, alpha-hemolysin, which create pores that act as channels for ions, mimicking the pores in a biological cell. As David LaVan points out, "This preferentially allows either positive or negative ions to pass through the bilayer and creates a voltage across it. We can harness this voltage to generate electric current." The study has effectively demonstrated that synthetic cells can be a key method for making cell measurements, and a means to isolate and study individual components in cell systems. Laurie Donaldson Image of two artificial cells that can act as a tiny battery. Danish nanophysicists have developed a new method for manufacturing nanowires. The discovery has great potential for the development of nanoelectronics and highly efficient solar cells. [Krogstrup, et al., Nano Lett. (2009) doi: 10.1021/n1901348d] We have improved the methodology for producing nanowires. This means we can produce nanowires that contain two different semiconductors, namely gallium indium arsenide and indium arsenide. It is an enormous breakthrough, because for first time on a nanoscale, we can combine the desirable characteristics of these two materials thus gaining new possibilities for the electronics of the future, explains Peter Krogstrup. Incredibly even today only 1 % of the world's electricity comes from solar energy. This is because we are still experiencing difficulty in efficiently converting solar energy into electricity. This latest breakthrough may change this statistic. Different materials capture energy from the sun in different and quite specific absorption areas. When we manufacture nanowires of gallium indium arsenide and indium arsenide, which each have their own absorption area, they can collectively capture energy from a much wider area, therefore utilizing more solar energy. The nanowires of gallium indium arsenide and indium arsenide also have great potential in nanoelectronics. They can, for example, be used in the new OLED displays and LEDs. But it requires sharp transitions between the two materials in the nanowire. The cultivation of nanowires takes place in a vacuum chamber. The researchers lay a gold droplet on a thin disc comprising of the semiconductor and the nanowire grows from below. In the transition between the two semiconductor materials in the gold droplet there was previously a mixing between the materials in the gold droplet and there was a soft transition between the materials. With the new method both of the materials can go from the top of the gold droplet or from the underside of the gold droplet. When the material comes from the underside, there is no mixing of the semiconductor materials. There is therefore a sharp transition on the atomic level between the gallium indium arsenide and indium arsenide. This sharp transition between the two semiconductors is necessary for the current ­ in the form of electrons, to be able to travel with high efficiency between the two materials. If the transition is soft, the electrons can easily get caught in the border area. The new mixed nanowire can be beneficial for many areas of nano research around the world, comments Peter Krogstrup. Jonathan Agbenyega Danish nanowires capture the sunlight NANOTECHNOLOGY Nanowire made of the two semiconductors courtesy Peter Krogstrup. RESEARCH NEWS DECEMBER 2009 | VOLUME 12 | NUMBER 128 Researchers from Harvard University in Massachusetts have devised a method to study non-fluorescent molecules using a technique called stimulated emission microscopy, an approach based upon a phenomenon first described by Albert Einstein in 1917 [Min et al., Nature (2009) 461, 1105]. Most molecules absorb parts of white light, allowing us to see them with the naked eye. However, absorption contrast is not widely used for optical imaging of molecules because of the poor sensitivity involved. On the other hand, fluorescence microscopy, which is based upon emission rather than absorption, is a much more sensitive technique. When molecules or atoms absorb energy they enter an excited state then spontaneously decay back to lower energy levels, in some cases giving rise to fluorescence. The problem is, not all chromophores fluoresce upon decay and instead they may take a non-radiative pathway. Such molecules must either be studied using the low sensitivity optical techniques or they need to be tagged using a fluorescent marker. In a new technique, molecules of the sample are subjected to a pulse with the right energy and timing to enable another form of emission known as stimulated emission. In this case, emission competes with nonradiative decay such that it becomes the dominant energy pathway back to lower, more stable energy levels. Stimulated emission offers a sensitivity that is several orders of magnitude higher than normally seen for molecules that do not fluoresce. Team leader Xiaoliang Sunney Xie explains the technique's potential in the future of medicine. "It allows spectroscopic identification of molecules in living organisms and is free from the complication of light scattering by the sample. This opens many new possibilities for biomedical imaging, such as label free mapping of drug distributions and blood vessels in tissues." In fact, the team has already demonstrated proof-ofprinciple by imaging the delivery pathway of a drug that is normally difficult to study because its fluorescence is quenched on binding with tissues. The images obtained show the drug at different depths of the skin and can also confirm the hypothesis that the drug binds to cytoplasmic RNA to initiate cell death in cancerous cells. Katerina Busuttil Casting a new light on chromophores CHARACTERIZATION Ex vivo stimulated emission image of microcapillaries of a mouse ear (Image courtesy of Wei Min and Sijia Lu, Harvard University. 2009 Nature Publishing Group.) New approach produces stimuli-responsive assemblies of nanoparticles POLYMERS New research has demonstrated how a blend of polymers and nanoparticles that react to different stimuli, such as heat and light, can be made by adding small molecules to the mixture. This straightforward approach could be a key development in applying such materials industrially, and could have potential for energy harvesting and storage, as well as optical devices and catalysis. The group of scientists, from the University of California, Berkeley, the Berkeley National Laboratory, Kyoto Institute of Technology and Tohoku University, used small molecules that are attracted to the nanoparticles and certain parts of polymers. This combination orders the nanoparticles into complex shapes within the polymer material. Small molecules that change either their affinity for the polymers or their own shape in response to heat or light were then used, allowing the nanoparticle ordering within the polymers to be altered on demand. Published online in [Xu et al., Nature Materials, doi: 10.1038/nmat2565], the study shows how this approach can be used with a variety of different blends to order the nanoparticles at different length scales with high precision. It also simplifies the material fabrication because the nanoparticles can be used without further chemistry. The main significance of the work can be seen in the use of small molecules to mediate particle-polymer interactions to selectively incorporate nanoparticles within block copolymer microdomains, the use of molecular ordering of small molecules to direct spatial arrangement of nanoparticles within copolymer microdomains, and the external stimuli-responsiveness ­ that is, using non-covalent interactions to direct the assembly. The team worked on the basis that non-covalent interactions are both important and powerful, and that sophisticated structures can be obtained by blending various components and directing inter-molecular interactions. As the team's approach is essentially plug-and-play and each component can be readily switched, it may enable relatively rapid advances in these studies. The research also aids an understanding of multi-length assemblies in multi-component systems, how to measure various contributions from different components, and how to manipulate nanoscopic building blocks in a confined geometry. The team are now examining the structure/ property relationship of these nanocomposites in bulk, and are looking at how to manipulate the nanoparticle assemblies in thin films with control over their macroscopic alignment and inter-particle ordering, which should enable them to fabricate devices in a thin film setting. In addition, further research into the properties of nanoparticle assemblies may lead to some functional devices on a larger scale, especially as process used here is compatible with existing fabrication process in the microelectronic industry. Laurie Donaldson A blend of PS(40)-b-P4VP(5:6)(PDP)3 and 85:4nm PbS (87 vol%) nanoparticles, showing the PbS nanoparticles arranged in a hexagonal grid. Renewable and Alternative Energy Web Portal sigma-aldrich.com Have you seen these Material MattersTM issues on Alternative Energy? Get your complimentary subscription today: sigma-aldrich.com/mm3 The Portal offers a comprehensive set of links about environmentally benign production, storage and conversion of energy. Solar Energy Hydrogen Economy Batteries Supercapacitors Alternative Fuels Relevant events and conferences are also highlighted. We focus on materials, so you can focus on results. For more information, visit sigma-aldrich.com/renewable DECEMBER 2009 | VOLUME 12 | NUMBER 1210 RESEARCH NEWS A novel type of hard X-ray interferometer employing a bilens system with two parallel arrays of compound refractive lenses has been developed by scientists from France and Russia. Under coherent illumination, the bilens generates two diffraction limited mutually coherent beams. When the beams overlap they produce an interference pattern with a fringe spacing ranging from tens of nanometres to tens of micrometres. This simple way to create a X-ray standing wave in a paraxial geometry opens up the opportunity to develop new X-ray interferometry techniques to study natural and advanced man-made nanoscale materials, such as selforganised biosystems, photonic and colloidal crystals, and nanoelectronic materials. [Snigirev et al., Phys. Rev. Lett. (2009), 103] present a new and simple way to generate an X-ray periodic interference field such as a standing wave with variable period ranging from tens of nanometres to tens of micrometres. The proposed interferometer thus occupies the place between crystal and grating interferometers. The silicon bilens can generate standing waves with a 40 nm period above 50 keV. If diamond lenses were employed, then we could expect the smallest pitch to be 30 nm at energies E less than 12 keV. Contrary to Bonse-Hart interferometers and X-ray standing wave techniques, the bilens interferometer generates an interference pattern without the requirement of additional optics like crystals or multilayers. The interference occurs in air at a reasonable distance from the device itself allowing great flexibility in sample size and environment. Such coherent spatially harmonic illumination can be used for new diffraction and imaging methods to study mesoscopic materials. A phase contrast imaging technique is feasible whereby a sample is inserted into one of the beams while they are separated, as in the case of a classical interferometer. Any interaction with that beam will induce significant changes in the interference pattern, allowing the extraction of high resolution information on the sample from the new phase pattern produced. A second technique would be Moiré imaging whereby the sample is placed behind the bilens within the interference field. Standing wave techniques are evident: a sample could be scanned across the periodic interference field and secondary processes (fluorescence, secondary electrons, etc.) would be detected by a detector placed to one side of the beam. In addition to imaging applications, the bilens interferometer could also be used for coherence diagnostics at existing synchrotrons. Silicon bilenses are stable under extremely powerful beams and relatively insensitive to mechanical vibrations. We expect that they will also be widely used for beam characterisation for future free electron X-ray laser sources. Jonathan Agbenyega A hard X-ray interferometer CHARACTERIZATION SEM of a bilens interferometer. Rice University scientists today unveiled a method for the industrial-scale processing of pure carbon-nanotube fibers that could lead to revolutionary advances in materials science, power distribution and nanoelectronics [Rice et al., Nature nanotech. (2009) doi:10.1038/ nnano.2009.302 ].The result of a nine-year program, the method builds upon tried-and-true processes that chemical firms have used for decades to produce plastics. "Plastics is a $300 billion U.S. industry because of the massive throughput that's possible with fluid processing," said Rice's Matteo Pasquali, a paper co-author and professor in chemical and biomolecular engineering and in chemistry. "The reason grocery stores use plastic bags instead of paper and the reason polyester shirts are cheaper than cotton is that polymers can be melted or dissolved and processed as fluids by the train-car load. Processing nanotubes as fluids opens up all of the fluid-processing technology that has been developed for polymers." The new process builds upon the 2003 Rice discovery of a way to dissolve large amounts of pure nanotubes in strong acidic solvents like sulfuric acid. The research team subsequently found that nanotubes in these solutions aligned themselves, like spaghetti in a package, to form liquid crystals that could be spun into monofilament fibers about the size of a human hair. "That research established an industrially relevant process for nanotubes that was analogous to the methods used to create Kevlar from rodlike polymers, except for the acid not being a true solvent," said Wade Adams, director of the Smalley Institute and co-author of the new paper. "The current research shows that we have a true solvent for nanotubes chlorosulfonic acid ­ which is what we set out to find when we started this project nine years ago." Following the 2003 breakthrough with acid solvents, the team methodically studied how nanotubes behaved in different types and concentrations of acids. By comparing and contrasting the behavior of nanotubes in acids with the literature on polymers and rodlike colloids, the team developed both the theoretical and practical tools that chemical firms will need to process nanotubes in bulk. "Kevlar, the polymer fiber used in bulletproof vests, is about five to 10 times stronger than the strongest nanotube fibers today, but in principle the Rice scientists should be able to make their fibers about 100 times stronger. If they can realize even 20 percent of their potential, they will have a great material, perhaps the strongest ever known. Jonathan Agbenyega Processing nanotube fibers goes mainstream NANOTECHNOLOGY Moving science forward Now Anyone Can Have the Raman Touch Announcing a Breakthrough in Raman Spectroscopy 2009ThermoFisherScientificInc.AllRightsreserved. Enjoy all the benefits of Raman spectroscopy without a big investment in time, money or effort. The all-new Thermo Scientific DXR Raman systems make it possible. DXR Raman systems allow you to focus on your own particular discipline, and not on mastering the instrument itself. Patented optics, revolutionary sampling accessories, and smart software work together to give you an intelligent analytical tool ­ one that eliminates the obstacles to applying Raman to everyday situations. So, if you want Raman spectroscopy that's easy and affordable, don't compromise with trade-offs. Trade up instead, to the Thermo Scientific DXR. Visit www.spectroscopysimplified.com or call call 1-800-532-4752 or e-mail: analyze@thermo.com The Thermo Scientific DXR Raman Microscope and DXR SmartRaman Spectrometer DECEMBER 2009 | VOLUME 12 | NUMBER 1212 RESEARCH NEWS A team of scientists at the Swiss Federal Institute of Technology Zurich (ETH Zurich, www.ethz.ch), Switzerland, has developed an innovative biodegradable metallic glass that might one day replace the metal implants currently used to repair bone fractures [Zberg et al., doi:10.1038/nmat2542]. The new material would make it unnecessary to undergo a second implant-removal surgery; it would also eliminate the side-effects of permanent implants by dissolving into the body, once the healing process of the bones has been achieved. For several years, scientists have been working on the development of biodegradable implants that would exhibit strength, flexibility, durability and the ability to dissolve harmlessly in the body. Magnesium-based alloys have been found to be the most promising candidates for that purpose due to their mechanical stability, favorable dissolution properties and their ability to be absorbed by the human body without any toxicity. However, they present one major drawback: as they dissolve, they produce hydrogen gas bubbles that linger around the implant and hinder the bone healing process. The new metallic glass synthesized by Dr. Zberg and his colleagues, under the leadership of Prof. Jorg Löffler at the EHT Zurich, shows a fundamentally different behavior from previous materials synthesized in the past, and appears to eliminate the problem of hydrogen-forming gas. By producing a metallic glass structure, the researchers were able to develop a magnesium-zinc-calcium alloy containing a high proportion of zinc (35%), far superior to the usual percentage used in traditional metals. Indeed, in traditional metals, undesirable crystalline phases precipitate in the magnesium matrix above a maximum amount of 2.4% zinc atoms. On the other hand, the amorphous structure of metallic glass, produced by rapid cooling of the combined mixture of molten materials, does not present such limitation. By producing a magnesium (60%)-zinc (35%)-calcium (5%) glass, the researchers were able to dramatically alter the corrosion behavior of the magnesium contained in the alloy, and therefore significantly reduce the formation of undesirable hydrogen gas in the body. In fact, animal studies performed by Zberg et al., reported no clinically observable production of hydrogen-forming bubbles during the degradation process of the implant. Further studies and clinical tests will be needed to determine whether the new metallic glass fulfills all criteria for actual implementation in patients. Elisabeth Lutanie Graphene speeds up computers CARBON New research has shown how graphenelike structures designed on the nanoscale level ­ geodesic systems shaped like the Eden Project building in Cornwall, UK ­ could be used as building blocks for a new generation of electronic circuits, giving rise to faster computers, or mobile phones that send data at much higher rates. Although graphene sheets are difficult and expensive to produce, their use is on the increase, especially in nanoelectronics, electrochemistry and gas sensing. Graphene, a sheet of carbon that is only one atom thick, is the thinnest known and strongest material ever measured, is thought to be about 200 times stronger than steel, and has the ability to carry one million times more electricity than copper. While there are various methods for fabricating graphene films, such as through epitaxial growth or self-assembly procedures where graphene oxide films are transferred to a substrate and reduced to graphene by chemical reaction or heating, the approach that was taken by the research team was that of chemical vapor decomposition. This involves the deposition of hydrocarbon molecules onto an iridium surface that is heated between room temperature and 1,000 degrees. The scientists, from the University of Trieste, the Synchrotron light laboratory in Trieste and the University College London, whose study has been published in [Lacovig et al., Physical Review Letters, doi: 10.1103/PhysRevLett.103.166101], have shown how mechanisms of graphene growth have been found depending on the metal substrate, very different from those observed for two-dimensional metal islands on metals. When these molecules hit the surface they lose their hydrogen atoms, leaving the remaining carbon atoms sticking to the iridium, where they start to self-assemble in small "nano-structures". The nano-structures eventually develop into fully formed graphene sheets; the researchers are now starting to understand how the process takes place, and therefore how it might be controlled. The study is concentrating on how the mechanism moves from a carbon-covered surface to the formation of a fully formed highquality graphene sheet. As Alessandro Baraldi points out, "The growth of graphene starts with the formation of small islands of carbon with an unusual dome structure, in which only the atoms at the perimeter are bound to the iridium substrate while the central atoms detach from it, making the island bulge upwards at the centre." The team also found that the size of these geodesic carbon nanodomes depended on the temperature of the metallic substrate, and the manipulation procedure, suggesting a number of possible ways of controlling the size of graphene sheets at the nanoscale. Laurie Donaldson A perfect quasi-free standing graphene layer and our nanodomes. The new metallic glass produces no hydrogen bubbles in tissue (left). Traditional alloys form undesirable gas bubbles (right). (Image credit: LMPT/ETH Zurich.) Innovative metallic glass shows promise for bone surgery BIOMATERIALS think forward Bruker AXS Unique TWIN optics for primary and secondary beam path Push-button switch between Bragg-Brentano and parallel-beam geometries Superb LYNXEYE detector XRD The new D8 ADVANCE with TWIN/TWIN setup Ultimate flexibility and push-button ease of use www.bruker-axs.com DECEMBER 2009 | VOLUME 12 | NUMBER 1214 RESEARCH NEWS At long last there is experimental evidence that magnetic charges exist and that they have measurable currents or magnetricity, just like an electric charge [Bramwell et al., Nature (2009) 461, 956]. A team from the UK and France used Dy2Ti2O7, a material known as a spin ice, to test the new technique. Spin ices are predicted to have sharply defined magnetic point charge (magnetic monopole) excitations, making them good test materials. In their recent paper, the researchers explained how they applied Onsager's theory of electrolytes, which describes the conductivity of liquid and lattice electrolytes, to set up an experiment that can detect the magnetic monopoles in spin ice. They replaced the electrical quantities described in Onsager's theory with magnetic quantities, based on the assumption that there is equivalence between electricity and magnetism. A spin ice sample was cooled to temperatures close to zero and then probed using muons, negatively charged elementary particles. Single crystals of spin ice were aligned parallel to the muon spin direction and a magnetic field was applied at right angles to this axis. The asymmetry of muon beta decay was then measured as a function of time, leading to information on internal magnetic fields. Results so far have yielded a value of 5 B -1 for the elementary unit of magnetic charge. The technique has not only been used to prove the existence of magnetic charges in spin ice but is also capable of measuring relative changes in magnetic conductivity. While the new technique is a good proof of theory, can be used to determine deviations from Ohm's law, and demonstrates good correlation between electricity and magnetism, it may also lead the way to controlling magnetic charges in the future. Katerina Busuttil Magnetricity is taken for a spin MAGNETISM Could nanotechnology be the key to developing an interface between nerve cells and microelectronic circuitry? US scientists have recently demonstrated that signals can be recorded from rat neurons using conducting polymer nanotubes. The research carried out at the University of Michigan might one day help in the development of sensors and treatments for neurological disorders including Parkinson's disease and paralysis. Conventional neural electrodes can have operational times of hours or even years but all of them trigger an initial in inflammatory response once they are inserted into the brain. After that, the brain settles into a chronic, wound-healing process, which can isolate the electrode from surrounding neurons as new tissue encapsulates it. Metal electrodes are obviously conducting but lack the biocompatibility that precludes this chronic wound-healing problem. Now, nanotubes coated with the polymer poly(3,4-ethylenedioxythiophene) (PEDOT) have been used to record neural signals [Abidian et al., Adv. Mater. (2009) 21, 3764-3770]. Mohammad Reza Abidian and colleagues explain that PEDOT is not only electrically conductive but is also biocompatible, which they hoped would prevent encapsulation. "Microelectrodes implanted in the brain are increasingly being used to treat neurological disorders," explains Abidian. "Moreover, these electrodes enable neuroprosthetic devices, which hold the promise to return functionality to individuals with spinal cord injuries and neurodegenerative diseases." The challenge is to find ways to make robust and reliable neural electrodes that could monitor symptoms and perhaps even deliver the appropriate medication automatically. The researchers have demonstrated the ability of PEDOT nanotubes to act as drug carriers previously. The team has now tested their PEDOT nanotube electrodes in laboratory rats. In the experiment, they implanted two neural microelectrodes in the brains of three rats. They then monitored the electrical impedance of the recording sites and measured the quality of recording signals over a seven-week period. They found that not only was the signal-tonoise ratio of the coated electrodes 30% higher than with uncoated electrodes, but the coated electrodes operated with less electrical resistance. This meant that the electrodes could communicate more clearly with individual surrounding neurons. "Conducting polymers are biocompatible and have both electronic and ionic conductivity," Abidian explains. "Therefore, these materials are good candidates for biomedical applications such as neural interfaces, biosensors and drug delivery systems." He adds that, "This study paves the way for smart recording electrodes that can deliver drugs to alleviate the immune response of encapsulation." David Bradley The image depicts neurons firing (green structures in the foreground) and communicating with nanotubes in the background. (Illustration courtesy of Mohammad Reza Abidian.) Neuronal nanotubes NANOTECHNOLOGY ISSN:1369 7021 Elsevier Ltd 2009DECEMBER 2009 | VOLUME 12 | NUMBER 1216 REVIEW Optical nano-antennas and metamaterials Optical nano-antennas and metamaterials Since its discovery1, extraordinary optical transmission (EOT) through subwavelength apertures including single apertures2-9 and aperture arrays10-19 in an opaque metal film have attracted considerable attention. These nanoscale metallic structures possess a wide variety of extraordinary optical properties including beaming20-22, local filed enhancement23, and total absorption24, 25. Surface plasmons polaritons (SPPs)26, 27 play an essential role in this phenomenon and have opened up potential applications in lithography28, 29, biophotonics30, 31, Raman effect32, and other areas33-35. Besides at visible frequencies, these intriguing phenomena have also been found and investigated at terahertz36-38, microwave39-43, acoustic frequencies44, 45 and matter-waves46. Here we review some different approaches to transmission enhancement and light harvesting through nano-apertures, namely, by utilizing optical nano-antennas9 (note that optical nano-antennas for many other applications have been studied very recently47-52) and metamaterials (including slow-light photonic crystal waveguides)53. In this article, we will also harvest light with an invisibility metamaterial cloak shell. Metamaterials are composites with subwavelength unit cells dominating some homogenized electromagnetic properties which can not be found in a naturally occurring material54-56. Historically, the introduction of this novel concept was initiated decades ago by pursuing the theory of left-handed materials57, 58. After the realization of metamaterials at microwave59 and optical frequencies60, 61, various predicted effects were demonstrated, such as evanescent wave amplification and subwavelength lensing62, 63. We have also studied some potential applications64-66. Electromagnetic metamaterials with theoretically arbitrary parameters could be exploited67. Similar methods and unit cells have also been developed to investigate single We review some recent approaches to transmission enhancement and light harvesting based on optical nano-antennas and metamaterials. Nano-cavity antennas are used to enhance the extraordinary transmission of TM-polarized light through vertical nano-slits in a metal film. The enhanced transmission of TE-polarized waves through an array of subwavelength-slits in a thin metal film at low frequencies (including microwave) is also investigated. Light harvesting with a metamaterial cloaking shell is also demonstrated. Sailing He1,2,*, Yanxia Cui1, Yuqian Ye1, Pu Zhang1,2, and Yi Jin1 1 Centre for Optical and Electromagnetic Research, State Key Laboratory of Modern Optical Instrumentation, Zhejiang University; JORCEP (Joint Research Centre of Photonics of the Royal Institute of Technology (Sweden) and Zhejiang University), Zijingang Campus, Zhejiang University, China 2 Division of Electromagnetic Engineering, School of Electrical Engineering, Royal Institute of Technology, S-100 44 Stockholm, Sweden * E-mail: sailing@kth.se Optical nano-antennas and metamaterials REVIEW DECEMBER 2009 | VOLUME 12 | NUMBER 12 17 negative, or zero-valued effective materials, where electric/magnetic plasmonic and perfect tunneling effects were observed68, 69. Using metamaterials, people have studied other promising applications such as perfect absorbers70, slow light71, polarization manipulation72, etc. The method of transformation optics73 has greatly enlarged the potential application areas of metamaterials, enabling us to design devices according to required characteristics. Invisibility metamaterial cloak is a successful example. The ability to reduce total scattering dramatically has been predicted and verified in various ways, including rigorous analytical solution74, numerical simulation75, and proof-ofprinciple experiment76, 77. Various simplified cloak designs78-80 have been proposed to avoid extreme material parameters. Similar to the widely studied electromagnetic cloaks, cloaks in other fields such as acoustics81 and matter-waves82, have also attracted considerable attention. Enhance transmission of light through metallic nano-slits by utilizing optical nano- antennas The EOT through a nano-slit in a metal film can be enhanced by introducing nano-antennas. By integration with some optical nanoantennas, the efficiency and spectral response of the EOT or a lightharvesting device could be greatly improved. Recently, Pillai et al.83 put gold nanospheres on the surface of a Si solar cell to increase the spectral response of the thin-film cell. A gold nanorod (GNR) can work as an optical antenna whose resonant frequency can be tuned over a very broad spectrum. A GNR has two surface plasmon resonance (SPR) bands, namely the transverse and longitudinal bands. The longitudinal band is a strong one corresponding to the electron oscillation along the long axis of the nanorod, and can be tuned from visible to near-infrared-red (NIR) region by increasing the aspect ratio (of the width to the length) of the nanorod. In our laboratory we have synthesized GNRs (see84, 85 and the references therein) according to the classic seed-mediated growth method and the TEM image of our synthesized GNRs is shown in Fig. 1a. GNRs with a SPR peak of 607 nm (corresponding to a GNR with an aspect ratio of 1.8), 650 nm (aspect ratio 2.4) and 710 nm (aspect ratio 2.8) were synthesized and their measured absorption spectra are shown in Fig. 1b (consistent with the results of our numerical simulation). From the photo of the three GNRs (inset in Fig. 1b), one sees that the colors of the three GNR solutions are distinct according to their different SPR resonant bands. We plan to utilize these GNRs to harvest light. Below we show how an appropriately designed plasmonic nanorod (or nano-strip in a 2D case) can be utilized to harvest light and improve the EOT. First, we present the case of transmission enhancement with a single optical nano-antenna. Fig. 2a shows the two-dimensional (2D) schematic diagram for a metallic rectangular nano-strip (with thickness Hp and width Wp) over a metallic nano-slit of width Ws in a metal film of thickness t (with a distance of d). A plane wave of TM polarization (with the magnetic field perpendicular to the x-z plane) with wavelength 0 = 1 m impinges normally on the top of the structure. Intuitively, the metallic nano-strip over the nano-slit seems to block the incident light. However, through the formation of a resonant nano-cavity antenna, the metallic nano-strip can assist to couple more incident light into the nano-slit and thus enhance the transmission. Both the film and the nano-strip are made of silver, and all the results are calculated with a 2D finite element method (FEM). The transmission efficiency is defined as the ratio of the integration Fig. 1 (a) Measured absorbance spectra of three different types of gold nanorods with SPR peaks at 607 nm, 650 nm, and 710 nm. (b) TEM image of our synthesized gold nanorods with an SPR peak of 650 nm. (b) (a) REVIEW Optical nano-antennas and metamaterials DECEMBER 2009 | VOLUME 12 | NUMBER 1218 of the z-component of the Poynting vector over the output opening (with or without the nano-strip) to that over the input opening of the bare slit (without the nano-strip). A nano-slit milled in a metallic thin film can form a vertical metal-insulator-metal (MIM) waveguide of finite length, which can give Fabry-Pérot (F-P) resonance in the narrow slit region3, 5. The transmission is maximal due to constructive interference for a length phase of even integer of /2 (related to the effective wavelength in the MIM waveguide) and is minimal for a length phase of odd integer of /2 (due to destructive interference)3. A horizontal MIM waveguide cavity can also be formed by putting a metallic nano-strip over a metal film with an air gap in-between. Fig. 3a shows the distribution of the magnetic field modulus (|Hy|) when we put a silver nano-strip (with Wp = 1 m and Hp = 300 nm) over the silver film (with d = 44 nm) to form constructive interference of three peaks in the horizontal F-P cavity (close to a 3 phase length waveguide). One sees obviously that the metallic nano-strip collects the incident light effectively due to the resonance in the cavity below the nano-strip, and localized field of high Fig. 3. Distributions of |Hy| for a horizontal resonant MIM cavity (Wp = 1 m) (a), and a horizontal resonant cavity over a non-resonant nano-slit (b) or a resonant nano-slit (c). The insets in (b) and (c) show the |Hy| distributions for the corresponding cases of a bare nano-slit. (d) Transmission spectrum for various Wp when Hp = 50 nm, d = 44 nm, Ws = 25 nm and t = 240 nm (dashed curve is for the bare nano-slit). Fig. 2 Configuration of a nano cavity antenna (a) or an array of nano cavity antennas (b) placed a certain distance away from the input surface of a nano-slit aperture milled in a metal film. (b) (a) (b)(a) (c) (d) Optical nano-antennas and metamaterials REVIEW DECEMBER 2009 | VOLUME 12 | NUMBER 12 19 magnitude is accumulated within the horizontal cavity. Then we make a nano-slit in the metal film at a position where the magnetic field in the horizontal resonant cavity is maximal and wish to enhance the extraordinary transmission through the nano-slit in the metal film. The influence of the nano-slit configuration to the field distribution in the horizontal cavity is small (large) when the vertical nano-slit is in a nonresonant (resonant) state. First we consider the case of a non-resonant vertical nano-slit with destructive interference. The inset of Fig. 3b shows the |Hy| distribution for a bare nano-slit with opening width Ws = 25 nm (same in all simulations below) milled in a silver film of 390 nm thickness (as a vertical waveguide of 3/2 phase length). To see clearly, we plot the field distribution with doubled magnitude in this inset. The transmission efficiency for this bare nano-slit is very low ( = 0.6) and the nano-slit causes little distortion of the field reflected by the silver film. Fig. 3b shows the field distribution when there is a silver nano-strip over this non-resonant nano-slit (opened at the center where the magnetic field is maximal in the horizontal resonant cavity). The resonant cavity antenna over the non-resonant nano-slit brings an enhanced transmission, and the energy flowing out of the nano-slit aperture is enhanced by a factor of 5 as compared with that for the non-resonant bare nano-slit in the inset of Fig. 3b. The inset of Fig. 3c shows the |Hy| distributions for a resonant bare nano-slit with t = 240 nm (corresponding to a vertical MIM waveguide of phase length). An output transmission efficiency = 7.8 is achieved, attributed to the constructive interference in the vertical MIM waveguide of finite length. When the silver nano-strip (same as Fig. 3a, b) is put over the resonant nano-slit as shown in Fig. 3c, the horizontal cavity can no longer keep its optimal internal field distribution for harvesting light and the cavity antenna does not work any more. Thus, the energy flowing into the nano-slit is small and is only 3.6, lower than in the inset of Fig. 3c. To achieve an efficient receiving antenna for harvesting light (from incident light to SPPs) and further enhancing transmission, the width of the metallic nanostrip should be carefully designed to form a resonant cavity and the height of the nano-strip should also be small enough. When we choose Wp = 1410 nm and Hp = 50 nm, the transmission for the resonant nano-slit can be greatly enhanced to = 17.5 (124% larger than = 7.8 for a resonant bare nano-slit). Fig. 3d shows the transmission spectrum for various antenna widths (Wp) when Hp = 50 nm and d = 44 nm. This illustrates the tunability of the optical nano-cavity antenna for harvesting light of desired wavelength. This is quite similar to the tunability of the absorption peak of GNRs for different aspect ratios as shown in Fig. 1b. Some other properties can be found in our recent work9. The light transmission enhanced by a single nano-antenna is still not high enough. This can be improved by replacing the single nanoantenna with an array of nano-antennas. Fig. 2b shows the schematic diagram for an array of nano-antennas formed by two metallic rectangular nano-strip arrays (of period P, width Wp, thickness Hp, and number N) on the left and right sides of the vertical nano-slit over a metal film. The distance between the nano-slit center and the nearest nano-strip center (slit-to-strip distance) is denoted by L. Fig. 4 shows the |Hy| distribution after the resonant nano-slit (t = 240 nm) is assisted by a nano-cavity antenna array with P = 900 nm, Wp = 700 nm, L = 450 nm, Hp = 60 nm, d = 50 nm and N = 6. The enhanced transmission through the nano-slit is quite high ( = 128.3), which is 16.4 times of that for the bare resonant nano-slit ( = 7.8) and 6 times larger than that for the single nano-cavity antenna case ( = 17.5). The array of nano-strips could generate some strong surface plasmon wave (SPW) on the input surface. The nano-slit cavity can also generate some reflected SPW near its input opening, whose intensity is much smaller compared to the nano-strip-generated SPW. Thus, the influence of the nano-slit can be considered as a disturbance to the light distribution on the input surface. The vertical nano-slit configuration will influence the field distribution on the input surface quite differently, depending on whether the vertical nano-slit is in resonance or not3, 9. Our numerical simulation results have shown that both the position of the nano-slit and distance L influence significantly Fig. 4 Distributions of |Hy| for the metallic nano-slit (Ws = 25 nm, t = 240 nm) assisted by an array of nano cavity antennas with P = 900 nm, Wp = 700 nm, L = 450 nm, Hp = 60 nm, d = 50 nm and N = 6. REVIEW Optical nano-antennas and metamaterials DECEMBER 2009 | VOLUME 12 | NUMBER 1220 the transmission of light through the nano-slit. Since non-resonant nano-slits give negligible influence to the local field distribution on the input surface, such an array of nano-cavity antennas can be combined easily with an array of non-resonant nano-slits and some potential applications can be envisaged. Enhance transmission of low frequency TE waves through subwavelength slits in a metallic thin film by utilizing an array of electric dipole antennas As mentioned before, many works have been carried out on enhanced transmission through subwavelength slits from optical frequencies to microwave frequencies39-43. However, most of them are for TM-polarized waves. Different from TM-polarized waves, transmission of a TE-polarized wave (with the electric field parallel to the slit wall) through a subwavelength slit has a cut-off frequency86, below which no propagating modes exist. Thus, one would not expect a large transmission of low frequency TE-polarized wave (below the cut-off frequency) through subwavelength slits in a thin metallic film. Here we show how to utilize electric dipole antennas (metallic wires of finite lengths) to enhance the transmission of TE-polarized microwaves through the subwavelength slits at a resonant point below the cut-off frequency. Fig. 5a shows the schematic diagram of a periodic array of subwavelength slits perforated in an aluminum film of thickness t. The slit width and the period of the slit array are denoted by g and p, respectively. Fig. 5b shows the cover layer composed of an array of broken metallic wires (electric dipole antennas) on a lossless dielectric layer with permittivity = 3.0 and thickness t'. The width and length of the broken wires are w and l, respectively. The period of the broken wire array in the x and y directions are p and D, respectively. Fig. 5c shows a unit cell of the combined structure when the thin cover layer is put on the top of the metal film to enhance the transmission through the subwavelength slits. By using the three-dimensional finite-difference time-domain (FDTD) method, the transmission spectrum of the slit array (without the cover layer) with g = 5.5 mm, p = 30 mm and t = 0.5 mm is calculated and shown by the dashed (blue) curve in Fig. 6a. Since the microwave wavelength we considered here ( > 30 mm, corresponding to frequencies below 10 GHz) is much larger than the slit width (g < /5), no propagating mode can be excited in these subwavelength slits for TE-polarized waves86. Thus the transmission can only rely on the evanescent tunneling process, and is quite low (<0.5%) even for such a thin metallic film at microwave frequencies (note that the dashed curve for the transmission is magnified by 50 times to improve the visibility in Fig. 6a). However, by adding a cover layer (the parameters for the broken wire array are l = 24 mm, w = 1.6 mm, D = 30 mm, and t' = 0.3 mm ) on this array of subwavelength slits, a resonant transmission peak appears at frequency = 4.88 GHz ( = 61.5 mm) with transmission up to 72% (see the blue curve in Fig. 6a), which is about 800 times larger than the transmission (at the same frequency) without the cover layer. The distribution of zcomponent electric field on a broken wire at the resonant frequency is shown in Fig. 6b, from which one sees charges of opposite signs accumulate at the two ends of the broken wire, indicating the excitation of a strong electric dipole resonance87 on the broken wire. Based on the strong localized electric field near the input apertures of the slits, the incident wave is effectively coupled into evanescent waves, and then squeezed through the subwavelength slits. Consequently, a striking resonant transmission is achieved. The distribution of the corresponding electric field magnitude on the y-z plane at the edge of the broken wire is shown in Fig. 6c, from which one sees a highly localized electric field around the broken wire due to the electric dipole-like resonance. In fact, the metallic structure (shown in Fig. 6b) of the cover layer with broken wires can be regarded as a layer of metamaterial with electric resonance (which may give a negative value of the effective permittivity at a microwave frequency). Some detailed analysis will be published elsewhere. Fig. 5 Schematic diagram of (a) an aluminum film with an array of subwavelength slits; (b) a cover layer with an array of broken metallic wires; (c) unit cell for transmission calculation when the cover layer is put on the aluminum film to enhance the transmission. (b)(a) (c) Optical nano-antennas and metamaterials REVIEW DECEMBER 2009 | VOLUME 12 | NUMBER 12 21 Enhance transmission and harvest light with a horizontal slow-light photonic-crystal waveguide As an example of enhanced transmission through an aperture in a dielectric material, we consider the resonant tunneling of a wide beam through a vertical subwavelength slow-light photonic-crystal (PC) waveguide53. As an important application of PCs88-99, a slow-light PC waveguide (SPCW) can be used to enhance drastically the lightmatter interactions93-96. In practice, efficient coupling of light into a subwavelength SPCW is an important subject98, 99. When a SPCW is of finite length, large reflection at the two open ports makes the waveguide behave like a F-P cavity94. At the resonance of a SPCW, a narrow beam can tunnel through the narrow vertical waveguide aperture efficiently. Such a resonance transmission is similar to the enhanced transmission of light through a subwavelength hole in a metal film. However, if the beam is quite wide, a large part of the beam will be directly reflected by the bulky PC (at the two horizontal side walls of the vertical SPCW) and the efficiency of the resonant tunneling is low. By utilizing an assistant horizontal SPCW, the resonant tunneling of a wide beam through the vertical SPCW can be enhanced drastically for light harvesting. The SPCWs considered here are based on a square-lattice PC, which consists of dielectric cylinders with permittivity = 12.96 and radius r = 0.3a (a is the period) in air. By removing an array of cylinders along the -M direction, a vertical single-line defect waveguide is formed as shown at the bottom part of the structure in Fig. 7a. Fig. 7b gives the dispersion curve of this waveguide. At the band edge edge = 0.26277(2c/a) (near the point), the dispersion curve is rather flat so that the group velocity vg = /k is very small and the waveguide becomes a SPCW with a very small propagation constant. Large reflection exists on the interfaces between the SPCW (of finite length) and free space, and some slow guide modes satisfying the F-P resonance condition may resonate strongly inside the waveguide. The resonant frequency of the F-P resonant mode closest to edge is = 0.26324(2c/a). Due to the slow propagation of light, the F-P resonant mode has a large quality factor (Q = 2.74 x 103) (the high intensity of light here can be utilized for e.g. some nonlinear applications). In our numerical simulation, we choose a wide beam with waist width w = 13a. From curve 2 in Fig. 7c, one sees the transmissivity is very low (only about 0.19) although the SPCW is in resonance at = 0.26324(2c/a). We can use an assistant horizontal SPCW to enhance drastically the transmission of the wide beam through the above vertical SPCW. To construct a horizontal asymmetric SPCW (of finite length), we put two finite-length lines of dielectric cylinders at distance d = a away from the top of the vertical SPCW as shown in Fig. 7a. The resonant frequency of the composite structure becomes = 0.26329(2c/a), shifting a bit away from that of the individual vertical SPCW due to the interaction of the two SPCWs. The Q value is reduced to 1.90 x 103. At = 0.26329(2c/a), a normally incident wide beam can be collected efficiently by the horizontal SPCW and then resonantly tunnels through the vertical SPCW. Curve 1 in Fig. 7c shows the drastically enhanced Fig. 6 (a) Transmission spectrum through the slit array without (red dashed curve) and with (blue solid curve) the cover layer. (b) Distribution of Ez on a broken wire at the resonant frequency. (c) Distribution of |E| near the aperture of the subwavelength slit on the y-z plane at an edge of the broken wire. (b)(a) (c) REVIEW Optical nano-antennas and metamaterials DECEMBER 2009 | VOLUME 12 | NUMBER 1222 REVIEW Optical nano-antennas and metamaterials transmissivity when the wide beam is normally incident on the top of the structure with the assistant horizontal SPCW (like the previous resonant cavity antenna in Fig. 2a). The largest transmissivity is about 0.80 at resonant frequency = 0.26329(2c/a). Fig. 7d shows the distribution of |Ez| at = 0.26329(2c/a). The largest |Ez| is about 28 times the amplitude of the incident beam. To harvest light more efficiently, we can use a periodic array of vertical resonant tunneling SPCWs (instead of a single SPCW) and make the horizontal SPCW infinitely long (practically several periods wider than the beam would suffice), as shown in Fig. 8a. It is found that the transmissivity becomes nearly unity when the interval between two adjacent vertical SPCWs is 9a. The periodic composite structure can act as a resonant cavity, and the resonant frequency and Q are 0.26311(2c/a) and 2.15 x 103, respectively. Fig. 8b shows the transmissivity curve (the largest transmissivity is about 0.95). Fig. 8c shows the corresponding distribution of |Ez| (the strongest |Ez| inside the air gaps of the vertical symmetric SPCWs is about 33 times of the amplitude of the incident plane wave). Without the horizontal SPCW, the transmissivity will be very small (less than 0.18, see curve 2 in Fig. 8b). Obviously light has been harvested efficiently with this dielectric structure. Some details can be found in our recent work53. Harvest light with a metamaterial cloaking shell A transformation-based metamaterial cloaking shell can receive incident light efficiently (even 100% when perfectly matched), and then transport the light along the shell toward the other directions. Thus, if the light is impinged on an elliptic cloaking shell (with a very large aspect ratio) from its longer side, a great amount of light could be harvested at the two far ends of the cloaking shell. In our design example, the metamaterial cloak shell has a quasi-uniform thickness (of one wavelength). The aspect ratio is 3:1 for the inner ellipse, and 2:1 for the outer ellipse. The material parameters for the cloaking shell are calculated through the standard procedure of transformation optics73, and shown in Fig. 9a. A down-going plane wave is used as an excitation in the FEM simulation. Magnetic field distribution (magnitude) in Fig. 9b shows that the light is harvested efficiently and concentrated at the two ends of the cloaking shell. One may use only the upper half of the cloaking shell and guide the harvested light to two vertical matched strips75. Outlook We have reviewed and described some approaches of optical nanoantennas and metamaterials for transmission enhancement and light Fig. 7 (a) Harvesting light with a horizontal asymmetric SPCW (like a cavity antenna) in front of a vertical SPCW. (b) Dispersion curve of the vertical SPCW. (c) The transmissivity of a down-going wide beam (with waist w = 13a) through the vertical SPCW with (curve 1) or without (curve 2) the horizontal SPCW. The lengths of the horizontal SPCW and the vertical SPCW are 19a and 20a, respectively. (d) Distribution of |Ez| at the resonant frequency of curve 1 in (b). (b)(a) (c) (d) Optical nano-antennas and metamaterials REVIEW DECEMBER 2009 | VOLUME 12 | NUMBER 12 23 harvesting. Enhanced transmission of light can be utilized in many near-field optics applications, whereas light harvesting is directly related to the efficiency of solar cells. In an organic solar cell, efficient light absorption in a thin film is crucial for efficiently converting sunlight to electricity. Optical antennas can be employed to harvest external propagating light to a highly confined space for absorption in an organic solar cell. Optimally designed nano-antenna structures may improve solar cells' performances in conversion efficiency and spectral responses. We foresee that metamaterials can also play an important role in these emerging areas. Fig. 8 (a) Harvesting light with a long horizontal asymmetric SPCW in front of a periodic array of vertical SPCWs. (b) The transmissivity of a down-going wide beam through the vertical SPCW with (curve 1) or without (curve 2) the horizontal SPCW. The length of the vertical SPCWs is 20a and the interval between two adjacent vertical SPCWs is 9a. (c) Distribution of |Ez| in a unit cell at the resonant frequency of curve 1 in (b). Fig. 9 (a) Non-vanishing components of the material parameters of the cloaking shell; (b) Distribution of the magnetic field magnitude (normalized) in the metamaterial cloaking shell. (a) (c) (a) (b) (b) REVIEW Optical nano-antennas and metamaterials DECEMBER 2009 | VOLUME 12 | NUMBER 1224 Acknowledgment This work is supported partially by the National Basic Research Program (973) of China (No. 2004CB719800), the National Science Foundation of China (90101024 and 60688401) and the Swedish Research Council (VR) under Project No. 2006-4048 and AOARD. References 1. Ebbesen, T. W., et al., Nature (1998) 391, 667. 2. Thio, T., et al., Opt. Lett. (2001) 26, 1972. 3. Xie, Y., et al., Opt. Express (2004) 12, 6106. 4. Takakura, Y., Phys. Rev. Lett. (2001) 86, 5601. 5. Hideki, T. M., and Yoichi, K., Phys. Rev. Lett. (2006) 96, 97401. 6. García-Vidal, F. J., et al., Phys. Rev. Lett. (2003) 90, 213901. 7. Thio, T., et al., Nanotechnology (2002) 13, 429. 8. Degiron, A., and Ebbesen, T. W., Opt. Express (2004) 12, 3694. 9. Cui, Y. X., and He, S. L., Opt. Lett. (2009) 34, 16. 10. Ghaemi, H. F., et al., Phys. Rev. B (1998) 58, 6779. 11. Porto, J. A., et al., Phys. Rev. Lett. (1999) 83, 2845. 12. Popov, E., et al., Phys. Rev. B (2000) 62,16100. 13. Xie, Y., et al., Opt. Express (2005) 13, 4485. 14. Gordon, R., et al., Nano Lett. (2005) 5, 1243. 15. Ruan, Z. C., and Qiu, M., Phys. Rev. Lett. (2006) 96, 233901. 16. Cao, Q., and Lalanne, P., Phys. Rev. Lett. (2002) 88, 57403. 17. Lezec, H. J., and Thio, T., Opt. Express (2004) 12, 3629. 18. Sturman, B., et al., Phys. Rev. B (2008) 77, 75106. 19. Liu, H., and Lalanne, P., Nature (2008) 452, 728. 20. Lezec, H. J., et al., Science (2002) 297, 820. 21. Martin-Moreno, L., et al., Phys. Rev. Lett. (2003) 90, 167401. 22. Yu, L. B., et al., Phys. Rev. B (2005) 71, 41405. 23. Perchec, J. L., et al., Phys. Rev. Lett. (2006) 97, 036405. 24. Teperik, T. V., et al., Nat. Photon. (2008) 2, 299. 25. Bonod, N., et al., Opt. Express (2008) 16,15431. 26. Raether, H., Surface Plasmons, Springer, Berlin, (1988). 27. Maier, S. A., Plasmonics: fundamentals and applications, Springer, New York, (2007). 28. Srituravanich, W., et al., Nano Lett. (2004) 4, 1085. 29. Shao, D. B., and Chen, S. C., Nano Lett. (2006) 6, 2279. 30. Levene, M. J., et al., Science (2003) 299, 682. 31. Capoulade, J., et al., Phys. Rev. Lett. (2005) 95, 117401. 32. Kahl, M., and Voges, E., Phys. Rev. B (2000) 61, 14078. 33. Liu, C., et al., Appl. Phys. Lett. (2005) 86, 143501. 34. Bahriz, M., et al., Opt. Express (2007), 15, 5948. 35. Laux, E., et al., Nat. Photon. (2008) 2, 161. 36. Pendry, J. B., et al., Science (2004) 305, 847. 37. Miyamaru, F., et al., Opt. Lett. (2006) 31, 1118. 38. Isaac, T. H., et al., Phys. Rev. B (2008) 77, 113411. 39. Yang, F., and Sambles, J. R., Phys. Rev Lett. (2002) 89, 63901. 40. Bravo-Abad, J., et al., Phys. Rev. E (2004) 69, 26601. 41. Hibbins, A. P., et al., Science (2005) 308, 670. 42. Ma, Y. G., et al., Phys. Rev. B (2007) 76, 85413. 43. Lockyear, M. J., et al., Appl. Phys. Lett. (2007) 91, 251106. 44. Lu, M. H., et al., Phys. Rev. Lett. (2007) 99, 174301. 45. Akimov, A. V., et al., Phys. Rev. Lett. (2008) 101, 33902. 46. Fernandez-Dominguez, A. I., et al., Phys. Rev. A (2008) 78, 23614. 47. Kuhn, S., et al., Phys. Rev. Lett. (2006) 97, 17402. 48. Schuck, P. J., et al., Phys. Rev. Lett. (2005) 94, 17402. 49. Muhlschlegel, P., et al., Science (2005) 308, 1607. 50. Tang, L., Nat. Photon. (2008) 2, 226. 51. Merlein, J., et al., Nat. Photon. (2008) 2, 230. 52. Taminiau, T. H., et al., Nat. Photon. (2008) 2, 234. 53. Jin, Y., and He, S. L., Opt. Express. (2008) 16, 19550. 54. Wood, B., Laser Photon. Rev. (2007) 1, 249. 55. Yu, K., et al., Rev. Mod. Phys. (2008) 80, 1201. 56. Soukoulis, C. M., et al., J. Phys.: Condens. Matter. (2008) 20, 304217. 57. Veselago, V. G., Sov. Phys. Usp. (1968) 10, 509. 58. Pendry, J. B., et al., IEEE Trans. Micr. Theory & Tech. (1999) 47, 2075. 59. Shelby, R. A., et al., Science (2001) 292, 77. 60. Linden, S., et al., Science (2004) 306, 5700. 61. Shalaev, V. M., et al., Opt. Lett. (2005) 30, 3356. 62. Pendry, J. B., Phys. Rev. Lett. (2000) 85, 3966. 63. Fang, N., et al., Science (2005) 308, 534. 64. Chen, L., et al., Phys. Rev. Lett. (2004) 92,107404. 65. He, S. L., et al., New J. Phys. (2005) 7, 210. 66. Liu, L., and He, S. L., Opt. Express (2004) 12, 4835. 67. Sihvola, A., et al., J. Comm. Tech. & Electron. (2007) 52, 986. 68. Alu, A., et al., IEEE Antenn. & Propag. Mag. (2007) 49, 23. 69. Silveirinha, M., and Engheta, N., Phys. Rev. Lett. (2006) 97, 157403. 70. Landy, N. I., et al., Phys. Rev. Lett. (2008) 100, 207402. 71. He, J. L., and He, S. L., IEEE Microw. & Wireless Compon. Lett. (2006) 16, 96. 72. Hao, J. M., et al., Phys. Rev. Lett. (2007) 99, 63908. 73. Pendry, J. B., et al., Science (2006) 312, 1780. 74. Chen, H., et al., Phys. Rev. Lett. (2007) 99, 63903. 75. Cummer, S. A., et al., Phys. Rev. E (2006) 99, 36621. 76. Schurig, D., et al., Science (2006) 314, 977. 77. Liu, R., et al., Science (2009) 323, 366. 78. Yan, M., et al., Opt. Express (2007)15, 17772. 79. Jiang, W. X., et al., Phys. Rev. E. (2008) 77, 66607. 80. Zhang, P., et al., Appl. Phys. Lett. (2008) 93, 243502. 81. Cummer, S. A., and Schurig, D., Phys. Rev. Lett. (2008) 100, 24301. 82. Zhang, S., et al., Phys. Rev. Lett. (2008) 100, 123002. 83. Pillai, S., et al., J. App. Phys. (2007) 101, 93105. 84. Li, X., et al., Nanotechnology (2008) 19, 355501. 85. Li, X., et al., Appl. Phys. Lett. (2009) 94, 063111. 86. Kong, J. A., Electromagnetic Wave Theory, John Wiley and Sons, New York, (1986). 87. Zhou, J., et al., Opt. Express (2007) 15, 17881. 88. Sakoda, K., Optical Properties of Photonic Crystals, Springer, Berlin, (2001). 89. Krauss, T. F., J. Phys. D: Appl. Phys. (2007) 40, 2666. 90. Baba, T., Nat. Photon. (2008) 2, 465. 91. Mori, D., and Baba, T., Appl. Phys. Lett. (2004) 85, 1101. 92. Petrov, A. Y., and Eich, M., Appl. Phys. Lett. (2004) 85, 4866. 93. Soljacˇic´, M., et al., J. Opt. Soc. Am. B (2002) 19, 2052. 94. Kiyota, K., et al., Appl. Phys. Lett. (2006) 88, 201904. 95. Beggs, D. M., et al., Opt. Lett. (2008) 33, 147. 96. He, J. L., et al., Opt. Express (2008) 16, 11077. 97. Vlasov, Y. A., et al., Nature (2005) 438, 65. 98. Vlasov, Y. A., and McNab, S. J., Opt. Lett. (2006) 31, 50. 99. Hugonin, J. P., et al., Opt. Lett. (2007) 32, 2638. Biomedical Optics ˇ Integrated Optoelectronics ˇ Lasers and Applications ˇ Micro & Nanofabrication Register Today 23­28 January 2010 San Francisco, California, USA Connecting minds for global solutions Gain visibility at the essential photonics and laser conference. spie.org/pw Untitled-2 1 10/13/09 9:50:18 AM ThermalAnalysis Excellence Mettler-Toledo AG, Analytical CH-8603 Schwerzenbach Tel. +41-44-806 77 11 www.mt.com/ta www.mt.com/ta-webinars Innovative Technology Versatile Modularity Swiss Quality METTLER TOLEDO sets the standards in thermal analysis as with its worldclass balances. Thermal_Analysis_Excellence_120x190.indd 1 02.11.2009 08:57:05 ISSN:1369 7021 Elsevier Ltd 2009DECEMBER 2009 | VOLUME 12 | NUMBER 1226 REVIEW Anisotropic metamaterial devices Anisotropic metamaterial devices In 2006, Pendry et al.1 proposed a mathematical description of optical transformation, which was soon regarded as an efficient method to manipulate electromagnetic (EM) waves using artificial media. The required electric permittivity and magnetic permeability of such media can be derived from the optical transformation2, 3. Alternatively, an optical conformal mapping method was used to design a medium that generated perfect invisibility in the ray-tracing limit4, 5. The invisibility cloaks were analyzed in details using the optical transformation6, and verified numerically by full-wave simulations7 and experimentally by a two-dimensional (2D) near-field mapping configuration at the microwave frequency8. Inspired by the progress in both theoretical and experimental studies of the invisibility cloaks, more and more researchers have put their effort into this subject area9­18. In addition, other devices such as EM rotators19­24 have been proposed to illustrate the versatility of optical transformation. Formulation of optical transformation Starting from the general procedure of transformation optical design, we here restrict our discussion to transformations that are time invariant3, 6, i.e. the media is only dependent of spatial coordinates. Suppose that the coordinate transformation between the original space (x, y, z) and the new transformed space (x', y', z') is ' '( , , ), ' '( , , ), ' '( , , ). x x x y z y y x y z z z x y z = = = (1) In the last few years, a rapid development has been achieved in a subject area, so called optical transformation, which is based on the property of metric invariance in Maxwell's equations. Optical transformation, also known as transformation optics, allows metamaterials to be tailormade according to practical needs. In this paper, we have reviewed the recent progress on the parametric design of transformation devices, such as invisibility cloaks, electromagnetic (EM) concentrator, EM-wave converter, etc. The technique of optical transformation can also be applied when the sources are included in the transformed space. Wei Xiang Jiang, Jessie Yao Chin and Tie Jun Cui* State Key Laboratory of Millimeter Waves, Institute of Target Characteristics and Identification, Department of Radio Engineering, Southeast University, Nanjing 210096, People's Republic of China *E-mail: tjcui@seu.edu.cn Anisotropic metamaterial devices REVIEW DECEMBER 2009 | VOLUME 12 | NUMBER 12 27 With the above equations, we can obtain the Jacobian transformation matrix, which is defined as ' ' ' ( ', ', ') ' ' ' . ( , , ) ' ' ' x x x x y z x y z y y y x y z x y z z z z x y z = = (2) By the metric invariance of Maxwell's equations2, the constitutive parameter tensors of the medium in the transformed space can be expressed as ' , det( ) T ' , det( ) T = = (3) in which det( ) is the determinant of the Jacobian matrix. Hence, the material parameters of the transformation medium can be obtained using the proposed method. Since the permittivity and permeability of the required media are often less than 1, generally, the transformation devices are composed of inhomogeneous and anisotropic metamaterials. Invisibility cloaks Based on the theory of optical transformation, a volume of free space can be transformed into a shell-type region, which can therefore hide the object inside the shell from incident EM waves. Further investigations have been conducted, based on pioneering work1, 6-8. In order to provide more insights into the physics, several groups have developed analytical methods based on Maxwell's equations to reveal the nature of invisible cloaking13­18. In the earlier investigations, all theoretical analyses, numerical simulations and parameter designs were devoted to circularly cylindrical and/or spherical cloaks, which were relatively easy to design and analyze. Though the circularly cylindrical or spherical cloaks can wrap up any objects to be invisible, they are not efficient or convenient for long and thin objects. As a consequence, cylindrical cloaks with elliptical shapes were presented to design invisibility with generality25-28. Consider an elliptical­cylindrical object with an arbitrary axis ratio embedded in free space, which is covered by an elliptical cloak: the cross section of the cylindrical cloak is an elliptical shell, the inner and outer short semi-axes of which are a and b, respectively. The inner and outer ellipses have the same axis ratio k, which describes a horizontal elliptical cloak when k > 1, a vertical elliptical cloak when k < 1, and a circular cloak when k = 1 (see25). Along the cylindrical axis (z axis), the transformation is an identity, hence we present the coordinate transformations for the elliptical cloaking in the xoy plane. Similar to the circularly cylindrical cloak, the transformation will compress the space from the outer elliptical region into the elliptical shell region. We can define the coordinate transformations as 2 2 2 2 2 2 ' ' ' b a ka x x b x k y b a ka y y b x k y z z - = + + - = + + = (4) Based on Eq. (4), we can obtain the values of relative permittivity and permeability tensors for the cloak defined by Eqs. (2) and (3). Fig. 1 shows the comparison between the electric field distributions and the power-flow lines in the transformed space and the physical space. In the cloak, the power-flow lines propagate smoothly around the inner elliptical region and the equal-phase surfaces are warped smoothly in the predicted way. Outside the cloak, the transverse-electric (TE)polarized plane waves are nearly unchanged as if there were no objects in the free space. Hence the invisible elliptical cloaking is well verified. Similar to the invisibility cloak, constitutive tensors of EM masking arbitrarily shaped convex conducting objects have been derived22. Such a masking can be regarded as a partial cloaking layer. Only when the ratio between the maximum and minimum radii of the object approaches 1, i.e., the object is a sphere, could the masking be equivalent to an invisible cloak22. Invisible cloaks of different shapes including a square cloak were reported30-36 , and a general method, namely, the non-uniform rational B-spline (NURBS)29, has been applied to design arbitrarily shaped transformation devices. Fig. 1 (a) Transformed space. The figure shows the propagation of a plane wave. (b) Physical space. The cloaking layer makes the EM waves propagate around the invisible region and return to their original propagation directions without distorting the waves outside the elliptical cloak. (b) (a) REVIEW Anisotropic metamaterial devices DECEMBER 2009 | VOLUME 12 | NUMBER 1228 NURBS is one of the most common mathematical tools to represent curves in geometric modeling. It is possible to split an arbitrary curve represented by NURBS into a sequence of Bézier curves. By introducing NURBS to represent the geometric modeling of any objects, analytical formulas of the permittivity and permeability tensors for the arbitrarily shaped transformation devices can be expressed31, 53. Moreover, the usage of NURBS will expand the generality of the transformation optics and could make a very general tool to interface with commercial softwares such as 3D STUDIOMAX and MAYA, and, hence the transformation optics can be made for the industrial use. Fig. 2 illustrates the simulation results of a heart-shaped cloak when the plane waves are incident from two different directions31. The geometric boundary of the cloak is represented by NURBS. In both cases, the power-flow lines within the cloak layer propagate smoothly around the heart-shaped object, making it invisible. It is even true when the incident waves travel toward the concave area of the cloak, as shown in Fig. 2b. One of the challenges to realize the full-parameter cloak is that, at its inner boundary, there often exist singularities in the material parameters, which make the full-parameter cloak difficult to achieve even by using metamaterials8. In view of the difficulty to realize the full-parameter cloak and the imperfection of reduced-parameter cloak, a recently published theory has described a carpet cloak, which can cause anything swept under a conducting plane to seem to disappear37. The great advantage of the carpet cloak is that it does not require singular values for the material parameters. The experimental validation of the carpet cloak design reported by Li and Pendry37 has been recently achieved with a broadband property40. A similar cloaking over a dielectric half-space using a singular cloak was proposed38. More recently, the optical transformation of a curved, non-Euclidean space has been presented, which does not require the extreme properties of materials and can lead to invisibility in a broad band of the spectrum39. To avoid any singularity in the constitutive parameters, it was also proposed that an elliptical cloaking region can be crushed to a line Fig. 3 (a) The distributions of the magnetic fields inside circular cloaks with an inner radius of 0.025 m, an outer radius of 0.05 m, and half of the focus p = 0.001 m. (b) The distributions of r , and z components in the cloak region. Fig. 2 The electric field distributions and power-flow lines in the computational domain for a heart-shaped cloak and a perfectly-electrical-conducting (PEC) object with different incident directions. (a) The plane waves propagate from the left to the right. (b) The plane waves propagate from the top to the bottom. (b) (a) (b) (a) Anisotropic metamaterial devices REVIEW DECEMBER 2009 | VOLUME 12 | NUMBER 12 29 segment using the coordinate transformation in the classical ellipticalcylindrical coordinate system41, instead of being shrunk to a point. When the focus of the ellipse becomes very small, the elliptical cloak approaches a circular cloak. The advantage of such an invisible cloak is that none of the parameters is singular and the changing range of all parameters is relatively small. The full-wave simulation result for an approximately circular transverse-magnetic (TM) cloak41 is illustrated in Fig. 3a. One observes that the phase fronts are bent smoothly around the perfectly-electrical-conducting (PEC) object inside the cloak, and the fields are smoothly excluded from the interior region with the tiny scattering. All material parameters for the above circular cloaks have relatively small ranges. Fig. 3b illustrates the parameter distributions inside the approximate TM cloaks. Obviously, for each case, the electric permittivities r and are constant, and the magnetic permeability z ranges from 0 to a small constant, all of which can be realized using metamaterials. From Fig. 3a, we clearly observe that the approximate cloak can achieve almost perfect cloaking performance because the cloaked object is crushed nearly to a point, which results in tiny scattered fields. An approximate quantum cloaking was presented42, and some other designs of transformation functions and nonmagnetic cloaks were reported43-50. In above discussions, the transformation medium is a metamaterial shell with its interior and exterior boundary of the similar shapes. In reality, however, the shielded object may have an arbitrary shape and the interior boundary of the metamaterial shell is preferred to be the same as the shape of the shielded object. Meanwhile the shape of the exterior boundary has to fit the external environment. Hence the exterior shape of the metamaterial shell is not always the same as the interior shape. As a consequence, it is necessary to discuss the design of cloaks with different inner and outer boundaries by the method of optical transformation. An invisible cloak with non-conformal interior and exterior boundaries using the technique of optical transformation51 was proposed. To illustrate its principle, we consider a shape with a square outer boundary and a circular inner boundary. The design of other cloaks with complicated and non-conformal interior and exterior boundaries can be achieved in a similar way52. Fig. 4 illustrates the numerical results of the distribution of the electric fields and power flows for the cloaks with a square outer boundary and a circular inner boundary. In Fig. 4a, the phase fronts of incident waves are parallel to the sides of the cloak. When the waves pass through the cloak, the cloaking effect is very clear as expected, although the cloak boundary possesses sharp corners. From Fig. 4a, the plane wave is almost unaltered, as if no scatterer were present. Inside the cloaking material, the power-flow lines and phase fronts are bent smoothly around the target. The fields are smoothly excluded from the interior region with the minimal scattering in any directions. Fig. 4b shows the electric fields and power-flow lines when the cloak is rotated by an angle of 45°. In such a case, the cloaking effect is also obvious, although the phase fronts of incident waves are not parallel to any sides of the cloak boundary. EM concentrators The concept of EM concentrator was first proposed by Rahm et al.30; it can concentrate electromagnetic waves into a small enclosed region. The concept of EM concentrators can be used to design efficient receiving antennas and efficient solar cells, etc. Arbitrarily-shaped EM concentrators were later presented using the coordinate transformation by using NURBS in representation of the geometrical boundary54. Closed-form formulas for the transformation optics of the arbitrarilyshaped concentrators were obtained, and a square concentrator could be used to amplify plane waves54. Fig. 5 demonstrates the numerical result of a heart-shaped concentrator54, when the TE wave propagates from the left to the Fig. 4 The distributions of electric fields and power-flow lines for the invisible cloaks with different inner and outer boundaries. (a) The square outline of the cloak is parallel to the x direction. (b) The square outline of the cloak is rotated by /4 with respect to the x direction. (b) (a) REVIEW Anisotropic metamaterial devices DECEMBER 2009 | VOLUME 12 | NUMBER 1230 right. The outer boundary of the concentrator is described by the Bézier curve. The ratio among the principal radii of the three "hearts" is 1:6:10. Clearly, the field intensities are strongly enhanced in the inner region of the concentrator. There are no reflected waves outside the concentrator due to the inherent impedance matching in the method of optical transformation. Fig. 5b illustrates the power-flow intensity distribution of the plane wave. It is obvious that the field intensities are strongly enhanced in the inner region within the concentrator material. Similar to the cloak with non-conformal boundaries, one can also design EM concentrator with irregular boundaries51. Fig. 6 demonstrates the numerical results of the electric field and power-flow lines for concentrators with non-conformal inner and outer boundaries. It is obviously shown that the fields are concentrated from the larger circular region into the smaller one in both cases, which leads to enhanced field intensities inside the EM concentrator. EM-wave converters An approach to convert cylindrical waves to plane waves in a short range using the optical transformation was proposed54-55. This can be used either as a four-beam antenna or a compact range for near-field measurement of plane waves. Fig. 7 illustrates the structure of the EM-wave converter and the distributions of electric fields inside and outside the converter. When the cylindrical waves propagate through the conversion metamaterial layer, four beams of plane waves emerge in the surrounding space. Hence, in a very short range, the cylindrical waves emitted from the line source are converted to plane waves in four directions. Clearly, the scattering effect at four corners of the square is quite small. In other words, the converter provides highly-directive radiation beams to four orthogonal directions, hence it can be used to design directive antennas or wave collimators62. Similarly, the coordinate transformation theory was employed to realize substrates that can modify the emission of an embedded source56. With proper transformations the energy radiated by a source Fig. 5 (a) The electric field distributions and power-flow lines for a heartshaped concentrator. The incident plane waves propagate from the left to the right. (b) Power flow distributions for the heart-shaped concentrator. Much stronger power flow enhancements can be observed. Fig. 6 The distributions of electric fields and power-flow lines for the concentrators with non-conformal inner and outer boundaries. (a) The square outline of the concentrator is parallel to the x direction. (b) The square outline of the concentrator is rotated by /4 with respect to the x direction. (b) (a) (b) (a) Anisotropic metamaterial devices REVIEW DECEMBER 2009 | VOLUME 12 | NUMBER 12 31 embedded in these space variant media will be concentrated in a narrow beam. The technique of optical transformations is a powerful approach for highly directive antenna designs57-59. EM-wave bending Rahm et al.60 expanded the class of transformation optical structures by introducing embedded coordinate transformations, which allow the EM waves to be shifted and split. The optical transformation can also be used to bend EM waves to the desired directions inside a waveguide or in free space without any reflections (or with tiny reflections) by designing proper inhomogeneous and anisotropic materials61-66. One can employ the finite embedded optical transformation to realize the wave bending. Define a mapping from the original space to the transformed space as ' cos , ' sin , ' , y x x h y y x h z z = = = Fig. 7 The distributions of electric fields and power-flow lines for the conversion from cylindrical waves to plane waves via the finite embedded optical transformation. Fig. 8 The distribution of magnetic fields ( components) inside the waveguide bends. (a) = /4 and h = 40 ; (b) = /2 and h = 40; (c) = 3/4 and h = 80; (d) = and h = 80 . 0 is the free-space wavelength. (b)(a) (d)(c) REVIEW Anisotropic metamaterial devices DECEMBER 2009 | VOLUME 12 | NUMBER 1232 REVIEW Anisotropic metamaterial devices where is the radian of the bending angle and h is an optional variable. Fig. 8 illustrates the magnetic-field distributions inside the waveguide bends with different bending angles and different values of h66. It is clear that incident waves travel through the waveguide bends with less reflection and keep their original field patterns in all cases. The arbitrary wave-bending structure have been designed and analyzed using the optical transformation66, which is composed of simple and realizable metamaterials. The reduced-parameter wave bender is uniaxial, and hence easy to realize using artificial structures. When such a "wave bender" is filled inside metallic waveguide bends, the incident waves will be guided through the bends with very small reflections. When such a "wave bender" is placed in the air, the incident waves will be bent to any designed directions. The discrete wave benders also have good performance in the wave bending. Other optical transformation devices The optical transformation can also be used to design a large number of other devices, such as high-performance antennas, EM-beam modulators, superscatterer, imaging devices, etc.67-76. As an example, we introduce a lens antenna realized by a discrete embedded optical transformation67, which could find important applications in communications and other EM engineering. Using the discrete embedded optical transformation, a layered high-gain lens antenna has been designed. All layers of the lens antenna are composed of homogeneous and uniaxially anisotropic metamaterials, which are simple and realizable. When the layered lens is embedded in a horn antenna, the lens antenna provides a high-directivity radiation beam67. When the layered lens is placed in free space, the EM beam modulation can be realized68. While applying the method of discrete optical transformation, one divides the physical and virtual spaces into several layers in the same way67. For each layer, one defines a separate mapping between the virtual space and the physical space. Hence the actual "physical space" is the staircase approximation of the trapezium obtained by stacking rectangles on top of each other. At this point, the larger the layer number is, the more accurate the transformation will be. As a comparison, the lens designed by continuous optical transformation is composed of inhomogeneous and strongly anisotropic metamaterials, which are much more difficult to manipulate in real applications. To reveal the performance of the proposed lens antennas67, fullwave simulation results are shown in Fig. 9. Fig. 9a illustrates the distribution of electric fields inside and outside the lens antenna designed by continuous optical transformation. Fig. 9b shows the electric-field distributions of the lens antenna designed by discrete optical transformation, in which the size of PEC horn and the number of layers are the same as those in Fig. 9a. Compared to Fig. 9a, fewer reflections are observed inside the lens antenna in Fig. 9b. Clearly, almost all EM powers are concentrated in a beam of plane waves in the front of the lens antennas. For a comparison with the conventional lens, a horn antenna filled with a collimating lens is designed, which is made of traditional dielectrics in accordance with the method explained in77. Fig. 9c demonstrates the electric field distribution inside and outside the Fig. 9 The distribution of normalized electric fields inside and outside the lens structures, which are placed in a PEC horn antenna, under the excitation of a linecurrent source. (a) The lens is designed by continuous optical transformation. (b) The lens is designed by discrete optical transformation. (c) The collimating lens is made of regular dielectric. (c)(b)(a) Anisotropic metamaterial devices REVIEW DECEMBER 2009 | VOLUME 12 | NUMBER 12 33 regular lens antenna, in which the size of the PEC horn is the same as that in earlier lens antennas. Clearly, the newly proposed lens antennas based on the optical transformation have much better performance than the conventional lens. The directivity of the transformation lens antennas is above 30 and the regular lens antenna is about 20. Summary In this paper, we introduced several categories of transformation optical devices that have been developed in the past years. The optical transformation enables the direct manipulation of EM waves, and therefore it can be regarded as a powerful design tool for novel microwave and optical devices. The optical transformation is expected to have further impact on real-life applications. Acknowledgments This work was supported in part by a key project of the National Science Foundation of China, the Natural Science Foundation of Jiangsu Province under Grant No. BK2008031, the National Basic Research Program (973) of China under Grant No. 2004CB719802, the National Science Foundation of China under Grant Nos. 60871016, 60671015, and 60621002, and in part by the 111 Project under Grant No. 111-2-05. WXJ acknowledges the support from Graduate Innovation Program of Jiangsu Province under grant No. CX08B_ 074Z, and the Scientific Research Foundation of Graduate School of Southeast University under grant No. YBJJ0816. References 1. Pendry, J. B., et al., Science (2006) 312, 1780. 2. Ward, A. J., and Pendry, J. B., J. Mod. Opt. (1996) 43, 773. 3. Leonhardt, U. and Philbin, T. G., New J. Phys. (2006) 8, 247. 4. Leonhardt, U., New J. Phys. (2006) 8, 118. 5. Leonhardt, U., Science (2006) 312, 1777. 6. Schurig, D., et al., Opt. Express (2006) 14, 9704. 7. Cummer, S. A., et al., Phys. Rev. E (2006) 74, 036621. 8. Schurig, D., et al, Science (2006) 314, 977. 9. Zolla, F., et al., Opt. Lett. (2007) 32, 1069. 10. Huang, Y., et al., Opt. Express (2007) 15, 11133. 11. Cai, W., et al., Nat. Photon. (2007) 1, 224. 12. Cai, W., et al., Appl. Phys. Lett. (2007) 91, 111105. 13. Yan, M., et al., Opt. Express (2007) 15, 17772. 14. Chen, H, et al., Phys. Rev. Lett. (2007) 99, 063903. 15. Yan, M., et al., Phys. Rev. Lett. (2007) 99, 233901. 16. Zhang, B., et al., Phys. Rev. B (2007) 76, 121101. 17. Chen, H., et al., Phys. Rev. B (2007) 76, 241104. 18. Ruan, Z. C., et al., Phys. Rev. Lett. (2007) 99, 113903. 19. Ozgun, O., and Kuzuoglu, M., Micro. Opt. Tech. Lett. (2007) 49, 2386. 20. Greenleaf, A., et al., Phys. Rev. Lett. (2007) 99, 183901. 21. Ozgun, O., and Kuzuoglu, M., IEEE Micro. Wirel. Comp. Lett. (2007) 17, 754. 22. Teixeira, F. L., IEEE Antennas Wireless Prop. Lett. (2007) 6, 163. 23. Chen, H., and Chan, C. T., Appl. Phys. Lett. (2007) 90, 241105. 24. Kong, F., et al., Appl. Phys. Lett. (2007) 91, 253509. 25. Jiang, W. X., et al., J. Phys. D: Appl. Phys. (2008) 41, 085504. 26. Kwon, D.-H., and Werner, D. H., Appl. Phys. Lett. (2008) 92, 113502. 27. Ma, H., et al., Phys. Rev. A (2008) 77, 013825. 28. Kwon, D.-H., and Werner, D. H., Appl. Phys. Lett. (2008) 92, 013505. 29. Piegl, L., and Tiller, W., The NURBS Book, 2nd ed. Springer-Verlag, New York (1996). 30. Rahm, M., et al., Photo. Nano. Fund. Appl. (2008) 6, 87. 31. Jiang, W. X., et al., Phys. Rev. E (2008) 77, 066607. 32. Ma, H., et al., Opt. Express (2008) 16, 15449. 33. Yan, W., et al., New J. Phys. (2008) 10, 043040. 34. You, Y., et al., Opt. Express (2008) 16, 6134. 35. Ma, H., et al., Phys. Rev. E (2008) 78, 036608. 36. Nicolet, A., et al., Opt. Lett. (2008) 33, 1584. 37. Li, J., and Pendry, J. B., Phys. Rev. Lett. (2008) 101, 203901. 38. Zhang, P., et al., Opt. Express (2008) 16, 3161. 39. Leonhardt, U., and Tyc, T., Science (2009) 323, 110. 40. Liu, R., et al., Science (2009) 323, 366. 41. Jiang, W. X., et al., Appl. Phys. Lett. (2008) 93, 194102. 42. Green, A., et al., Phys. Rev. Lett. (2008) 101, 220404. 43. Cai, W., et al., Opt. Express (2008) 16, 5444. 44. Yan, M., et al., Appl. Phys. Lett. (2008) 93, 021909. 45. Xu, X., J. Phys D: Appl. Phys. (2008) 41, 215504. 46. Luo, Y., et al., J. Phys D: Appl. Phys. (2008) 41, 235101. 47. Luo, Y., et al., Phys. Rev. B (2008) 78, 125108. 48. Gallina, I., et al., Micro. Opt. Tech. Lett. (2008) 50, 3186. 49. Luo, Y., et al., Appl. Phys. Lett. (2008) 93, 033504. 50. Chen, H., et al., Opt. Express (2008) 16, 14603. 51. Yu, G. X., et al., Eur. Phys. J. Appl. Phys. (2008) 44, 181. 52. Li, C., et al., Opt. Express (2008) 16, 19366. 53. Jiang, W. X., et al., Appl. Phys. Lett. (2008) 92, 264101. 54. Lin, L., et al., Opt. Express (2008) 16, 6815. 55. Jiang, W. X., et al., Appl. Phys. Lett. (2008) 92, 261903. 56. Zhang, J., et al., Progr. Electro. Res. (2008) 81, 437. 57. Zhang, J., et al., Opt. Express (2008) 16, 10962. 58. Kundtz, N., et al., Opt. Express (2008) 16, 21215. 59. Leonhardt, U. and Tyc, T., New J. Phys. (2008) 10, 115026. 60. Rahm, M., et al., Phys. Rev. Lett. (2008) 100, 063903. 61. Rahm, M., et al., Opt. Express (2008) 16, 11555. 62. Kwon, D.-H., and Werner, D. H., New J. Phys. (2008) 10, 115023. 63. Roberts, D. A., et al., Appl. Phys. Lett. (2008) 93, 251111. 64. Donderici, B., and Teixeira, F. L., IEEE Micro. Wirel. Comp. Lett. (2008) 18, 233. 65. Huangfu, J., et al., J. Appl. Phys. (2008) 104, 014502. 66. Jiang, W. X., et al., Phys. Rev. E (2008) 78, 066607. 67. Jiang, W. X., et al., Appl. Phys. Lett. (2008) 93, 221906. 68. Xu, X., et al., New J. Phys. (2008) 10, 115027. 69. Wang, W., et al., Opt. Express (2008) 16, 21142. 70. Kwon, D.-H., and Werner, D. H., Opt. Express (2008) 16, 18731. 71. Yang, T., et al., Opt. Express (2008) 16, 18545. 72. Zhang, X., et al., Opt. Express (2008) 16, 11764. 73. Yan, M., et al., Phys. Rev. B (2008) 78, 125113. 74. Kildishev, A. V., and Shalaev, V. M., Opt. Lett. (2008) 33, 43. 75. Chen, H., and Chan, C. T., Phys. Rev. B (2008) 78, 054204. 76. Tsang, M., and Psaltis, D., Phys. Rev. B (2008) 77, 035122. 77. Kraus, J. D., and Marhefka, R. J., Ant. For All Appl., 3rd ed., McGraw-Hill, New York (2002). ISSN:1369 7021 Elsevier Ltd 2009DECEMBER 2009 | VOLUME 12 | NUMBER 1234 REVIEW Phononic crystals and acoustic metamaterials Phononic crystals and acoustic metamaterials Classical waves, including elastic waves (acoustic waves) and electromagnetic waves (optical waves and microwaves), are described by conventional wave-propagation functions. Elastic waves were the first waveforms to be understood in condensed matter and have a wide range of applications from industry to defense, from healthcare to entertainment. In 19871,2, the photonic crystal was proposed to describe the propagation of optical waves in refraction index-modulated periodic structures analogous to the propagation of electrons in real crystals. This situation recalls the classical work by Brillouin3. Brillouin considered elastic waves in periodic strings, electromagnetic waves in electrical circuits, and electrons in crystals as a system, resulting in some important common concepts, such as the Brillouin zone, band gap, etc., which are generally shared by the various forms of waves: electrons as scalar waves, optical waves as vector waves, and elastic waves as tensor waves. Following on from photonic crystals, the concept of phononic crystals (PCs) was conceived with elastic waves propagating in periodic structures modulated with periodic elastic moduli and mass densities4. Over the past two decades, the study of elastic waves in artificially structured materials has proved to be of great interest due to their novel and unique properties and effects, and their potential for acoustic applications in everyday life4­30. A periodic structure with an elastic modulus and mass density modulated on a scale comparable to the wavelength of acoustic waves results in PCs that possess a number of important properties, such as band gaps4­6, band edge states7, and the ability to slow the velocity of sound (slow wave effect)8, 9, analogous to electron propagation in real crystals. Furthermore, by creating artificially designed structures on a deep subwavelength scale, artificial acoustic `atoms' can be purposely engineered into PCs to dramatically Phononic crystals have been proposed about two decades ago and some important characteristics such as acoustic band structure and negative refraction have stimulated fundamental and practical studies in acoustic materials and devices since then. To carefully engineer a phononic crystal in an acoustic "atom" scale, acoustic metamaterials with their inherent deep subwavelength nature have triggered more exciting investigations on negative bulk modulus and/or negative mass density. Acoustic surface evanescent waves have also been recognized to play key roles to reach acoustic subwavelength imaging and enhanced transmission. Ming-Hui Lu, Liang Feng* and Yan-Feng Chen National Laboratory of Solid-State Microstructures and Department of Materials Science and Engineering, Nanjing University, 210093, China *Present address: Department of Electrical and Computer Engineering, University of California, SanDiego, CA, 92093, USA Email: yfchen@nju.edu.cn Phononic crystals and acoustic metamaterials REVIEW DECEMBER 2009 | VOLUME 12 | NUMBER 12 35 change the excitation and propagation of acoustic waves, and thus give rise to subdiffraction-limited resolution and its related myriad novel effects, such as negative refraction10­19, negative elastic modulus20­22, and negative mass density23­27. Another way to approach subdiffraction-limited resolution is to create acoustic surface waves that are confined two-dimensionally in a single acoustic `atom' layer with such engineered PCs. The in-plane subwavelength properties are inherently associated with the evanescent nature of acoustic surface waves along the third dimension. These state-of-the-art, artificially structured bulk and surface PCs are called acoustic metamaterials (AMs). Acoustic metamaterials are a newly emerging field, which have inherently abnormal and interesting physical effects that are important to basic research, and offer potential for applications that might revolutionize acoustic materials. A universally accepted definition of AMs does not yet exist. Some researchers define a metamaterial as an artificially structured medium that shows some novel and counterintuitive effects for wavelengths much greater than their periodicities. Others extend the concept of metamaterials to include PCs. We subscribe to the latter view, and hence have tried in this review to describe AMs and PCs in terms of structural evolution, and to provide some detailed understanding of the methods involved. The phononic crystal and its novel properties Phononic crystals are artificial periodic composite materials consisting of periodically distributed individuals (single acoustic functional scatter) in a matrix with high impedance contrast of mass densities and/or elastic moduli, which can give rise to new acoustic dispersions and band structures due to the periodic Bragg scattering as well as localized Mie scatterings from the individuals. PCs can be classified into two categories: acoustic phononic crystals (APCs) with a fluid matrix, and elastic phononic crystals (EPCs) with an elastic solid matrix. In this article, we will mainly focus on APCs since most research has been conducted in this field. The formation of band structures in PCs has been much investigated in physics, and comparisons made with other waves: while the electrons in a semiconductor can only occupy certain energy bands, a PC allows acoustic waves in specific frequency ranges to travel through via the pass band; other frequencies are inhibited by the band gap. This offers a very precise means to control and manipulate phonons, sound, and other waves. Research into PCs initially focused on calculating the band structure and its mechanism of formation. Creating a PC with a full band gap, requires designing different topological structures with different geometric individuals or with different periodic lattices. The band structures of PCs can also be engineered and tailored by varying the filling ratio and using new materials with different elastic constants31, 32. In general, individuals with a low mass density in a matrix with a high mass density readily form a full band gap, and a high contrast in acoustic speeds also results in a full band gap. In the case of three-dimensional PCs, face-centered cubic structures more easily form a full band gap than body-centered cubic and PCs structures31, 32. In order to design PCs to satisfy specific requirements, several calculation methods have been developed, including plane wave expansion (PWE)3, 33, the transfer matrix method (TMM)34, multiple scattering theory (MST)35­37, finite-difference time-domain (FDTD)38, 39, and the finite element method (FEM)40. All these methods have particular advantages and disadvantages. Recently, genetic algorithms have been found to provide a better approach for searching optimal structural parameters to design PCs41, 42. Careful design with accurate calculation of band structures has enabled many novel effects to be achieved in PCs. When PCs have some point defects and line defects within the band gap, elastic waves localize in the point defect cavity, or propagate in the line defects, similar to light in photonic crystals43. In addition, the dynamic effects of PCs have also attracted much attention. Chan et al.44, 45 explored the tunneling effect in the band gap of a three-dimensional APC, and observed a supersonic velocity and anomalous phase shift associated with the resonant phenomena of slow waves. Recently, Zhang and Liu46 have found that the maximum transmission and beating effect of acoustic waves occurs near the Dirac point in a two-dimensional APC. The transmission of acoustic waves through an APC is inversely proportional to its thickness, different from the tunneling effect, which is attenuated exponentially in the band gap of an APC. Moreover, the focus of research on PCs has been also transferred from the band gap to the band edge states, where a number of new effects exist, such as bending of acoustic waves, strong dispersion of group velocity, and the superprism phenomenon8, 9. More importantly, negative refraction, which was first proposed in optical metamaterials47, has been achieved in acoustics both experimentally and theoretically by carefully designing acoustic dispersion in the Brillouin zones of APCs11, 14. Acoustic negative refraction, and the resulting acoustic superlens effect, has become one of the most active topics of APC research, attracting the interest of many scientists10­19. Negative refraction of acoustic waves in APCs occurs via two mechanisms: (i) strong Bragg scattering near the Brillouin zone boundaries in the first band without showing a negative refractive index14; (ii) band folding in the second band, causing backward negative refraction with a backward wave vector, which is similar to an AM with equivalent double-negative parameters16. Due to anisotropy, the propagation of acoustic waves in APCs is more complex than that in isotropic AMs as shown in Fig. 116. Using the negative refraction effect, we used an APC to focus an acoustic wave in order to achieve acoustic point source imaging14­18. As there is only one longitudinal polarization for acoustic waves in the fluid, the birefraction phenomenon can never occur for purely longitudinal acoustic waves. However, we have REVIEW Phononic crystals and acoustic metamaterials DECEMBER 2009 | VOLUME 12 | NUMBER 1236 successfully achieved negative birefraction and double-focusing of acoustic waves in an APC due to the overlap of two high Bloch bands as shown in Fig. 217. In addition, tunable negative refraction and tunable acoustic imaging are also of great interest. By rotating the square rod inclusions of an APC, we were able to modulate the band structure and dispersion of acoustic waves in the APC, and then tune the refraction of acoustic waves from positive to negative18. In order to study the propagation of acoustic waves in an APC, we must understand the nature of the eigen modes of the wave in the APC. As Bloch48 pointed out, a wave propagating in a periodic structure is different from a plane wave only by a periodic modulation. In other words, the wave in a PC is a Floquet­Bloch wave, which is the superposition of many plane waves from all individuals. Hence, the velocity of the Bloch wave is different from that of each plane wave, and instead there are three velocities: group velocity, energy velocity, and phase velocity. Sakoda30 has proved that the energy velocity of a Bloch wave is equivalent to the group velocity. Therefore we can express the velocity of the energy flow as the gradients of the equifrequency surface (EFS) as follows, where the direction of the normal line indicates the direction of propagation of the wave: ( ) ( ) kgknG Gkn e vkuGk c v rrr rr rrrrr ==+= , 2 , 2 0 , (1) The occurrence of negative refraction thus suggests that the frequency increases as the EFSs assume a concave form. Hence the propagation of acoustic waves in an APC can be understood by examining the acoustic band structure and the EFS. Development of PC research has shown that these materials have a wide range of potential applications. PCs can be used for sound insulation, shockproofing, slow wave effects, acoustic wave filtering49, as acoustic wave guides50, for collimation of acoustic waves and directed beaming51, 52, and in particular for high-resolution acoustic imaging53, 54. Recently a PC has also been used to achieve acoustic cloaking via transformation acoustics55. Acoustic metamaterials Although we introduced PCs by drawing an analogy with electrons in real crystals in which the atoms at crystal lattice sites are determined `naturally', we can not only preserve the lattice symmetry of PCs but also engineer acoustic `atoms' in the unit cells of PCs. It is therefore possible to extend the concept of PCs to the `atomic' scale and design and fabricate new types of artificial acoustic materials called AMs in which an individual resonance from single `atoms' and its interaction with the Bragg resonance from the lattice symmetry can lead to novel and exotic properties. The optical counterpart of an AM is an optical metamaterial, which can be regarded as an effective medium with simultaneously negative permittivity and permeability, and thus an effectively negative refractive index. Optical metamaterials have many striking effects compared to normal refractive index material, such as left-handed backward effects, negative refractions, superlens, inverse Doppler effects, inverse Cherenkov effects, etc56. Correspondingly it is highly desirable to achieve simultaneously negative mass density and elastic modulus as well as the resulting negative index with AMs. Although an equivalent negative index can be obtained with conventional PCs13­17, the high anisotropy and lattice constant limited resolution of such materials may hinder their actual application. Thus, it is of great interest to engineer material properties on the atomic scale. Obviously, the artificial `atom' dimension will greatly expand the properties and effects of a PC with simple `atoms', and some abnormal phenomena beyond the well-known space periodicity related effects have been Fig. 1 Illustration of refractions in both the first and second bands of PCs, as well as their counterparts in photonic crystals. Phononic crystals and acoustic metamaterials REVIEW DECEMBER 2009 | VOLUME 12 | NUMBER 12 37 keenly anticipated. Analogous to optical metamaterials, AMs also show many intriguing phenomena for sound waves such as low-frequency band gap, negative refraction, superlensing, localized confined waves, etc. For most PCs, conventional acoustic `atoms' have neither a negative mass density nor a negative elastic modulus. For AMs, however, the special unit cell with locally resonant elements can be assigned as an artificial `atom' with exotic effective acoustic parameters under the long-wavelength approximation. Various artificial `atoms' have their own resonant frequencies and features. State-of-the-art artificial acoustic `atoms' were classified as `intrinsic'20, 21 and `inertial'22­25 by Fok et al.57 as the resonant frequencies of `atoms' are dependent on the materials' intrinsic acoustic properties (phase velocity), or correlated with the scale and geometry of the `atoms', respectively. However, based on such a definition of `atoms', these two different cases cannot be distinguished independently since `atoms' can be designed to be sensitive both to geometries and intrinsic material properties. There are several ways to design acoustic `atoms' in AMs. Deep subwavelength local resonators with their own mechanical oscillator can serve as these artificial `atoms' and exhibit new effective elastic parameters (i.e. modulus and mass density; be singly or simultaneously negative) and other exotic acoustic properties based on the longwavelength approximation (see Fig. 3)20­26. Negative elastic parameters can be obtained at a certain resonant frequency range if a proper local resonator is built into the structures. With the long-wavelength Fig.2 (a) The spatial distributions of the intensity and the phase of the acoustic pressure field at 7 incidence and 73 kHz, which clearly shows the negative birefraction occurring. (b) The FDTD simulation of the field distribution of a point source 15 mm in front of the sonic crystal and its focusing images through the sonic sample with 16 layers at 73 kHz. (c) The experiment spatial intensity and phase distribution of its focusing images are measured at 73 kHz. (b) (a) (c) REVIEW Phononic crystals and acoustic metamaterials DECEMBER 2009 | VOLUME 12 | NUMBER 1238 approximation, the effective elastic parameters can be retrieved by further analysis of wave-scattering coefficients. These `atoms' can locally and globally show either dipolar resonance or monopolar resonance. The resonance of some cylindrical and spherical resonance `atoms' can be derived analytically with the coherent-potential approximation (CPA)58, 59. Three-component PCs with locally cylindrical and spherical resonant structures have also been experimentally proved to exhibit a negative mass density due to dipolar resonance27. For AMs consisting of air bubbles in water, different orders of Mie scatterings can lead to monopolar resonance and dipolar resonance at different frequencies, corresponding to negative effective bulk modulus and negative effective mass density, respectively23. Recently, an effective negative bulk modulus at monopolar resonant frequency has been achieved by an AM consisting of an array of subwavelength Helmholtz resonators (HRs)22, 23, 26, 60, 61. According to the transmission line theory62, some AMs with subwavelength HRs can be designed to realize backward effects such as left-handed transmission. Here, we reveal a low-frequency band gap due to monopolar resonance with negative stiffness in an AM consisting of HRs (Fig. 4). By using a two-step homogenization approach, the effective mass density and effective bulk modulus can be analytically derived for AMs of HRs in fluid and the format of these analytical solutions can thus be compared to those for three-component locally resonant elements63. In addition, using the long-wavelength approximation, the effective mass density and elastic modulus can also be retrieved from the transmission and reflection coefficients64, 65. The effective negative refractive index of AMs is given by: e e B B n 0 0 = . (2) Here n is the refractive index, B0 and 0 are the reference bulk modulus and the reference mass density, respectively, and Be and e are the effective bulk modulus and effective mass density, respectively. Although a negative index requires both negative modulus and mass density, the negative refraction of an acoustic energy flow can occur without double negativities. Similar to electromagnetically induced transparency66, negative group velocity can be achieved with loss associated with coupling between two resonant modes67. Two resonators with the same polar resonance can thus realize negative refractions of acoustic waves as long as the coupling of these resonances is strong enough. This offers a more feasible approach to construct AMs with monopolar resonant `atoms' since it is in practice very difficult to create dipolar resonant elements. Generally because of the deep subwavelength nature of its local resonant elements, an AM can be regarded as an isotropic and homogeneous material showing a local resonant response globally. As the artificial `atoms' always contain mechanical oscillators with the proper resonant frequency, the AM is not a static acoustic material but a dynamically effective medium even though the size of the `atoms' is comparably small. Although conventional PCs can also show equivalent negative elastic parameters68, 69, as the validity of the effectivemedium approximation can be rigorously analyzed via the single-mode approximation69, AMs clearly provide greater opportunities to realize more fascinating acoustic phenomena by engineering materials through fundamental building blocks. Both acoustic and optical artificial metamaterials are unprecedented in nature and exhibit novel, abnormal and even counterintuitive features; the subwavelength characteristics of these metamaterials may well reduce the size and enhance the integration of devices, overcoming the deficiencies of PCs and photonic crystals. Fig. 3 (a) Cross section of a coated lead sphere that forms the basic man-made `atom' with local resonance; (b) Unit cells arranged in an 8 × 8 × 8 sonic crystal, which is the block of acoustic metamaterial that was experimentally tested; (c) A simple cubic structure of coated spheres from 200 to 2000 Hz. Three modes (two transverse and one longitudinal) are distinguishable in the [110] direction, to the left of the point. The two transverse modes are degenerate along the [100] direction, to the right of the point. Note the expanded scale near the point. (b)(a) (c) Phononic crystals and acoustic metamaterials REVIEW DECEMBER 2009 | VOLUME 12 | NUMBER 12 39 Acoustic surface evanescent waves on the surface of artificially structured metamaterials In addition to the interesting acoustical physics and possible applications in bulk PCs and AMs discussed above, the existence of surface states of acoustic waves in artificial acoustic surface metamaterials (ASMs) and their unique properties are of great interest. Since the energy of acoustic waves is strongly confined to the surface, the amplitude of the acoustic surface wave decays exponentially along the third dimension. Hence, the associated larger in-plane wave vector can produce a shorter effective wavelength and a slower propagation speed, thus leading to promising chip-scale acoustic device applications. In general there are two approaches to describing surface acoustic waves. An acoustic surface evanescent wave (ASEW)70 can be excited in the interface between two semi-infinite homogeneous fluids with different signs of elastic parameters, as shown in Fig. 5a-b. The condition for the existence of such an ASEW is very similar to the equation governing the presence of surface plasmon polaritons (SPPs) at the interface between metal and dielectric media: 0=+ II II z I I z kk , (3) and its propagation wave vector can be expressed as follows: ( ) ( ) 2/1 22 - - = II I I II III III y BB k (4) This equation is very similar to the dispersion equations of SPPs. SPPs, which are excited by the interaction between light and electron plasma on metal surfaces, have attracted much scientific interest, though the elementary excitation of such ASEWs remains a mystery. However, due to the similar nature of field distributions and highenergy confinement on the surface, it is highly desired to duplicate some of the exciting and exotic phenomena of SPPs, such as enhanced transmission71, superlensing72, 73, enhanced absorption of light in molecules, and enhanced surface Raman scattering74. Like SPPs, possible schemes for exciting ASEWs may include attenuated total reflection and grating coupling via phase-matching conditions. As discussed above, however, it is difficult to design and fabricate AMs with double negative parameters. Therefore it is necessary to explore other methods to excite an ASEW. For example, we can reduce the thickness of a conventional PC to a single `atomic' layer and thus achieve two-dimensional confinement using this single-layer PC. As anticipated, ASEWs be indeed excited on such single-layer Fig. 4 The profile (a) and the platform (b) of the PC consisted of HRs formed by stereolithography. (c) the band structure of the PC consisted of HRs, clearly showing a low-resonant frequency gap with negative stiffness. (d) The amplitude transmission coefficient along the (X) [100] direction plotted as a function of frequency. The observed transmission characteristics correspond well with the calculated band structures. Here the period is 5 mm, so the normalized frequency f0 is 69 kHz. (b)(a) (c) (d) REVIEW Phononic crystals and acoustic metamaterials DECEMBER 2009 | VOLUME 12 | NUMBER 1240 REVIEW Phononic crystals and acoustic metamaterials structures. The rectangular-groove grating75, 76 ASEWs are different from conventional acoustic hybrid surface waves, such as Rayleigh waves and Lamb waves excited on the fluid­solid interface, as ASEWs are still purely longitudinal waves. In this case (Fig. 5c), the in-plane propagation wave vector and evanescent vertical wave vector are expressed, respectively, as follows: ( 2/1 2 2 2 /)2(logtan1 -+= ahk d a kkx , ) (5) ( )( )/)2(logtan ahk d a kz -= ,jk (6) where a is the width of the groove, d is the period and h is the thickness of the groove. As Eq. (5) indicates, since the propagation wave vector of an ASEW is larger than the wave vector in free space, it is necessary to use grating coupling to meet the phase-matching condition of the wave vector. From Eqs. (5) and (6), we find h to be the most important parameter; in other words, for longitudinal waves, the thickness h determines the localized Fabry­Perot resonance. We can thus draw the conclusion that the coupling between the incoming wave and the eigen mode of the local oscillation in the direction of vibration (i.e. the Fabry­Perot resonance) causes the excitation of ASEWs. The localized Fabry­Perot resonance makes the effective parameters exhibit single negative mass densities at certain frequencies. ASEWs are not only excited on the surface between the grating and air, but can also be excited along the surface of a PC. Within the band gap, PCs may be regarded as effective media with a single negative parameter. The detailed surface resonant state has been calculated and elucidated by Liu et al.77 using a supercell method. According to Liu et al.'s theory, ASEWs can be excited on the surface of a finite PC within the band gap via a point wave source near the PC or a plane wave at a larger incidence angle. ASEWs have already shown promise in several applications, including extraordinary acoustic transmission (EAT)78­81, extraordinary sound shielding (EAS)82, acoustic collimation and direct beaming51, 83, extraordinary tunneling through a metal plate84, wave confinement and slow wave effects85, and superlensing70. Here we will focus on EAT since the physics behind EAT is the same as these other novel effects. EAT via ASEWs is very similar to extraordinary optical transmission (EOT), a hot topic since 199871. EAT was investigated in a subwavelength system without any surface collective oscillation like plasma, which is helpful for understanding the possible mechanisms of EOT. We theoretically and experimentally elucidated the EAT phenomena through a onedimensional grating with very narrow apertures79, and revealed that the coupling between the diffracting wave and the wave-guide FP (FabryPerot) resonance mode plays a key role in EAT derived by the rigorous coupling wave approximation (RCWA) method (Fig. 6a). We believe that this work is consistent with Christensen's theory80, which attributes EAT to the coupling between the leaky acoustic surface waves in the two sides of the gratings through narrow slits. As discussed above, the ASEW above the surface of the grating is due entirely to the coupling between the incoming wave diffracted by the narrow slits of the grating, and the eigen mode of the local resonance (i.e. the Fabry­Perot resonance). The localized Fabry­Perot resonance makes the effective parameters exhibit a single negative mass density at certain frequencies. The dispersion relations of the ASEW mode (which is not a guided mode) are also shown in Fig. 6b. Although the discrepancies between EAT and EOT are obvious (the zero-order propagating mode exists in narrow apertures for the acoustic system, but in optical subwavelength systems, the truncated evanescent mode exists in the metal slits), they also share Fig. 5 (a) Schematic of the surface state at an interface separating two semi-infinite media. Medium I is considered to have positive material parameters whereas medium II is taken as an acoustic metamaterial with exotic material parameters. The pressure profile of surface bound states; it is maximum at the interface and decays exponentially normal to the interface. (b) Dispersion curve of the surface state at the interface between two semi-infinite media with mass densities of opposite signs. (c) A rectangular-groove grating, a surface wave that propagates along the periodic direction is represented over the structure. (c)(a) (b) Phononic crystals and acoustic metamaterials REVIEW DECEMBER 2009 | VOLUME 12 | NUMBER 12 41 some similarities: for transverse electromagnetic waves, the transverse surface charge oscillation coupling leads to SPPs, while for longitudinal acoustic waves, the longitudinal Fabry­Perot oscillation coupling results in ASEWs. We believe these studies provide the fundamental basis for the extraordinary transmission in subwavelength systems. On the other hand, ASEWs also play key roles in some interesting phenomena in bulk AMs such as negative refraction and subdiffractionlimited focusing. According to Pendry's theory72, in order to obtain a higher resolution, beyond Rayleigh's prediction, we must collect as large a spectrum of evanescent waves as possible and use all of this in the imaging process. Great efforts have been made to explore such approaches. For instance, in a superlens made of an AM with doublenegative parameters, ASEWs are excited on the air­AM interface, and thus contribute to the far-field imaging. Another method is to adopt a metamaterial with a highly anisotropic EFS for the magnification of subwavelength features in the far field for acoustic waves86, like an electromagnetic hyperlens87. Very recently, He et al.88 have reported a method for obtaining subwavelength imaging of acoustic waves using a two-dimensional PC based on a canalization mechanism88. By designing a PC with flat EFSs, the evanescent modes of the acoustic source can be canalized by the Bloch modes in the PC and hence transmitted through the PC to reach the image88. It is therefore very important to explore significant improvements to achieve subwavelength imaging of acoustic waves, not only for the study of the basic theory, but also for ultrasonic applications, especially for medical photography. We believe the crucial step to reaching this target is knowledge of how to control and make use of ASEWs. Prospects While numerous exciting effects have been demonstrated, such as bulk acoustic waves, other forms of elastic waves, e.g. Lamb waves89 and Rayleigh waves90, could in principle be controlled by the corresponding PCs and AMs when two-dimensional structures are prepared in the thin solid plate or on the surface of solid. These kinds of PC and AM would be better suited for chip integration to create devices that can exploit acoustic surface waves for signal processing and as sensors. However, since these surface waves are quasi-two-dimensional waves and have complicated eigen modes, the methods for calculating their band structures need further development. In the meantime, the fabrication of these PC and AM structures to experimentally explore the interesting effects described above is also a big challenge due to the relatively large thickness of several micrometers or more. Another important aspect is to realize hypersonic PCs and AMs. Some examples have successfully been shown in colloidal crystal at THz frequencies91­93. These frequency bands are important because they lie between the bulk vibration and heat vibration of atoms in real crystals, and correspond to the collective vibration of nanomaterials. These phenomena are thus crucial to understanding nanomaterials and related elementary excitation. For the last two decades acoustic structured materials have developed side by side with optical ones. Although acoustic and optical waves are quite different, photonic crystals were followed by the proposal of PCs, optical metamaterials stimulated studies of AMs, and SPPs triggered studies of ASEWs. As the frequency of acoustic structured materials becomes higher and higher, and their size smaller and smaller, the two counterparts will meet, perhaps resulting in very different and extraordinary effects that would never occur without each of type of material participating. Phononphoton interaction and coupling will play key roles in these artificial structures and provide a new platform for each to be manipulated by the other. Fig. 6 (a) Numerical (black curve) and experimental (red curve) zero-order transmission spectra for a rectangular grating with the size of 4 mm and a period of 4.5 mm. The figure clearly shows the extraordinary transmission for acoustic sub-wavelength system. (b) Left: the amplitude transmission as a function of wave number and transverse wave vector kx. Right: dispersion relation of the leaky acoustic surface evanescent waves. (b)(a) REVIEW Phononic crystals and acoustic metamaterials DECEMBER 2009 | VOLUME 12 | NUMBER 1242 Acknowledgments Thanks to Prof. T. J. Cui. His kindness and efforts to organise the conference are gratefully acknowledged. The work was jointly supported by the National Basic Research Program of China (2007CB 613202) and the National Nature Science Foundation of China (50632030). We also acknowledge the support from the Changjiang Scholars and Innovative Research Team in University (PCSIRT) and the Nature Science Foundation of Jiangsu Province (BK2007712) References 1. Yablonovitch, E., Phys. Rev. Lett. (1987) 58, 2059. 2. John, S., Phys. Rev. Lett. (1987) 58, 2486. 3. Brillouin, L., Wave Propagation in Periodic Structures Dover, New York, (1953). 4. Kushwaha, M. S., et al., Phys. Rev. Lett. (1993) 71, 2022 5. Martinez-Sala, R., et al., Nature (1995) 378, 241. 6. Sigalas, M., and Economou, E. N., J. Sound Vib. (1992)158, 377. 7. Qiu, C. Y., Appl. Phys. Lett. (2006) 89, 063106. 8. Page, J. H., et al., Science (1996) 271, 634. 9. Schriemer, H. P., et al., Phys. Rev. Lett. (1997) 79, 3166. 10. Zhang, X. D., and Liu, Z. Y., Appl. Phys. Lett. (2004) 85, 341. 11. Yang, S. X., et al., Phys. Rev. Lett. (2004) 93, 024301. 12. Imamura, K., and Tamura, S., Phys. Rev. B (2004) 70, 174308. 13. Qiu, C., et al., Phys. Rev. B (2005) 71, 054302. 14. Feng, L., et al., Phys. Rev. B (2005) 72, 033108. 15. Ke, M., et al., Phys. Rev. B (2005) 72, 064306. 16. Feng, L., et al., Phys. Rev. Lett. (2006) 96, 014301. 17. Lu, M. H., et al., Nature Mater. (2007) 6, 744. 18. Feng, L., et al., Phys. Rev. B (2006) 73, 193101. 19. Hu, X. H., et al., Phys. Rev. E (2004) 69, 030201. 20. Liu, Z., et al., Science (2000) 289, 1734. 21. Li, J., and Chan, C. T., Phys. Rev. E (2004) 70, 055602. 22. Fang, N., et al., Nat. Mater. (2006) 5, 452. 23. Cheng, Y., et al., Appl. Phys. Lett. (2008) 92, 051913. 24. Mei, J., et al., Phys. Rev. Lett. (2006) 96, 024301. 25. Ding, Y. Q., et al., Phys. Rev. Lett. (2007) 99, 093904. 26. Hu, X. H., and Chan, C. T., Phys. Rev. E (2005) 71, 055601. 27. Liu, Z. Y., et al., Phys. Rev. B (2005) 71, 014103 28. Soukoulis, C. M., Photonic Band Gap Materials, Kluwer Academic, Dordrecht (1996). 29. Joannopoulos, J. D., et al., Photonic Crystals, Princeton University Press, Princeton, (1995). 30. Sakoda, K., Optical Properties of Photonic Crystals, Springer-Verlag Berlin Heidelberg, 2nd ed. (2005) 31. Economou, E. N., and Sigalas, M., Phys. Rev. B (1993) 48, 13434. 32. Kushwaha, M. S., and Halevi, P., J. Acoust. Soc. Am. (1997) 101, 619. 33. Vasseur, J. O., et al., Phys. Rev. Lett. (2001) 86, 3012. 34. Li, Z. Y., and Ho, K. M., Phys. Rev. B (2003) 68, 155101. 35. Li, L. M., et al., Phys. Rev. B (1998) 58, 9587. 36. Kafesaki, M., and Economou, E. N., Phys. Rev. B (1999) 60, 11993. 37. Liu, Z. Y., et al., Phys. Rev. B (2000) 62, 2446. 38. Tanaka, Y., et al., Phys. Rev. B. (2000) 62, 7378. 39. Vasseur, J. O., et al., Phys. Rev. Lett. (2001) 86, 3012. 40. Goffaux, C., and Sanchez-Dehesa, J., Phys. Rev. B (2003) 67,144301. 41. Shen, L. F., et al., Phys. Rev. B (2003) 68, 035109. 42. Sigmund, O., and Hougaard, K., Phys. Rev. Lett. (2008) 100, 153904. 43. Torres, M., et al., Phys. Rev. Lett. (1999) 82, 3054. 44. Sanchis-Alepuz, H., et al., Phys. Rev. Lett. (2007 ) 98, 134101. 45. Yang, S. X., et al., Phys. Rev. Lett. (2002) 88, 104301. 46. Zhang, X. D., and Liu, Z. Y., Phys. Rev. Lett. (2008) 101, 264303. 47. Luo, C., et al., Phys. Rev. B (2002) 65, 201104. 48. Kittel, C., Introduction to Solid State Physics, John Wiley & Sons, New York (1996), p. 175. 49. Kushwaha, M. S., Appl. Phys. Lett. (1997) 70, 3218. 50. Khelif, A., Phys. Rev. B (2003) 68, 024302. 51. Chen, L. S., et al., Appl. Phys. Lett. (2004) 85, 1072. 52. Ke, M. Z., et al., Appl. Phys. Lett. (2007) 90, 083509. 53. Li, J., et al., Phys. Rev. B (2006) 73, 054302. 54. Sukhovich, A., et al., Phys. Rev. B (2008) 77, 014301. 55. Torrent, D., and Sanchez-Dehesa, J., New. J. Phys. (2008) 10, 063015. 56. Veselago, V. G., Sov. Phys. Uspekhi (1968) 10, 509. 57. Fok, L., et al., MRS Bull. (2008) 33, 931. 58. Sheng, P., Introduction to Wave Scattering, Localization and Mesoscopic Phenomena, Academic, New York, 1995 59. Ye, Z., and Hsu, H., Appl. Phys. Lett. (2001) 79, 1724. 60. Wang, Z. G., et al., J. Appl. Phys. (2008) 103, 064907. 61. Cheng, Y., et al., Phys. Rev. B (2008) 77, 045134. 62. Lai, A., et al., Microwave. Mag. IEEE (2004) 5, 34. 63. Hu, X. H., et al., Phys. Rev. B (2008) 77, 172301. 64. Fokin, V., et al., Phys. Rev. B (2007) 76, 144302. 65. Hou, Z., et al., Phys. Rev. E (2005) 71, 037604. 66. Papasimakis, N., et al., Phys. Rev. Lett. (2008) 101, 253903. 67. Chen, Y. F., et al., Phys. Rev. Lett. (2005) 95, 067402. 68. Decoopman, T., et al., Phys. Rev. Lett. (2006) 97, 073905. 69. Smigaj, W., and Gralak, B., Phys. Rev. B (2008) 77, 235445. 70. Ambati, M., et al., Phys. Rev. B (2007) 75, 195447. 71. Ebbesen, T. W., et al., Nature (1998) 391, 667. 72. Pendry, J. B., Phys. Rev. Lett. (2000) 85, 3966. 73. Fang, N., et al., Science (2004) 308, 534. 74. Raether, H., Surface Plasmons on Smooth and Rough Surfaces and on Gratings, Springer-Verlag, Berlin Heidelberg, New York, London (1986). 75. Kelders, L., et al., J. Acoust. Soc. Am. (1998) 103, 2730. 76. Kelders, L., et al., J. Acoust. Soc. Am. (1998) 104, 882. 77. Zhao, D., et al., Phys. Rev. B (2007) 76, 144301. 78. Zhang, X. D., Phys. Rev. B (2005) 71, 241102. 79. Lu, M.-H., et al., Phys. Rev. Lett. (2007) 99, 174301. 80. Christensen, J., et al., Phys. Rev. Lett. (2008) 101, 014301. 81. Hou, B., et al., Phys. Rev. B (2007) 76, 054303. 82. Estrada, H., et al., Phys. Rev. Lett. (2008) 101, 084302 83. Christensen, J., et al., Nature Phys. (2007) 3, 851 84. Ke, M., et al. Phys. Rev. Lett. (2007) 99, 044301. 85. Christensen, J., et al. Appl. Phys. Lett. (2008) 93, 083502. 86. Ao, X. Y., and Chan, C. T., Phys. Rev. E (2008) 77, 025601. 87. Liu, Z. W., et al., Science (2007) 315, 1686. 88. He, Z. J., et al., Appl. Phys. Lett. (2008) 93, 233503. 89. Bonello, B., et al., Appl. Phys. Lett. (2007) 90, 021909. 90. Tanaka, Y., and Tamura, S. I., Phys. Rev. B (1998) 58, 7958. 91. Gorishnyy, T., et al., Phys. Rev. Lett. (2005) 94, 115501. 92. Cheng, W., et al., Nature Mater. (2006) 5, 830. 93. Akimov, V., et al., Phys. Rev. Lett. (2008) 101, 033902. J A N I S Janis Research Company 2 Jewel Drive Wilmington, MA 01887 USA TEL +1 978 657-8750 FAX +1 978 658-0349 sales@janis.com Visit our website at www.janis.com Janis has a wide range of products geared towards the materials scientist, covering nearly any temperature range or application. Typical techniques include: VSM, MOKE, FTIR, ESR, EPR, NMR, Hall effect, DLTS, Mossbauer, STM, AFM and more Typical applications include: .Microscopy .UV-Vis-IR optical measurements .Nanoscale electronics .Spintronics .High frequency measurements .Non-destructive device and wafer testing .Photovoltaics .High Tc superconductors .Terahertz detectors and devices Cryogenic Products for Materials Characterization .. 575 McCorkle Boulevard Westerville OH 43082 Phone: (614) 891-2244 Fax: (614) 818-1600 info@lakeshore.com www.lakeshore.com 10 ) to 200 G) resistances 2 K to 800 K temperatures Fields to 9 T Easy sample access Accommodate up to one 6-inch or four 1 cm2 samples QMSA resolves individual carriers in multi-carrier devices AC current for low resistance, high resolution measurement H A L L E F F E C T MEASUREMENT SYSTEMS 81.760 .000 CLCC CLCC 26.8 27.350 .76 11.76 85.00 86.880 944.8880 9550000 CLCC 22.350 26.850 0 24.63 7.950 0.900 0.900000 00..22660 0.7400 15.3601.000 080 1.000 0.400 1.44000 0.400 0.30000 7 8 11111 5 999 0 0 0330000 50 88888..00000000 88.00 000 17.35017.95 00000000 000 000.333000 00000...33333300000000000000 350 7350 173 99.55 00.08 2222000.0 1122 2000.00000 Phone ˇ (608) 204.8756 E-mail ˇ info@npoint.com Web ˇ npoint.com Visit us at MRS Booth # 607 Untitled-1 1 10/9/2009 10:37:00 AM See your work on the cover ofSee your work on the cover of Materials Today!Materials Today! Materials TodayMaterials Today invites you to submit your bestinvites you to submit your best materials-research related image to be consideredmaterials-research related image to be considered for publication on the cover for one of the 2010for publication on the cover for one of the 2010 monthly issues.monthly issues. The winning images last year made a real impact onThe winning images last year made a real impact on our covers. Unlike last year there will be one overallour covers. Unlike last year there will be one overall winner which will appear on a cover during the yearwinner which will appear on a cover during the year and 2 runners up which will appear in another formatand 2 runners up which will appear in another format withinwithin Materials TodayMaterials Today magazine during the year.magazine during the year. Closing date for submissionClosing date for submission of images is 14th December 2009of images is 14th December 2009 Please visit our website for further information:Please visit our website for further information: www.materialstoday.comwww.materialstoday.com cover_comp_house.indd 1 10/11/2009 14:36:34 ISSN:1369 7021 Elsevier Ltd 2009DECEMBER 2009 | VOLUME 12 | NUMBER 1244 REVIEW Electromagnetic wave in 2D photonic crystals Electromagnetic wave in 2D photonic crystals During the past two decades, a significant effort has been devoted to the study of photonic crystals (PCs) both theoretically and experimentally1-3. The PCs are regular arrays of materials with different refractive indices, which are classified mainly into one-, two-, and three-dimensional structures according to the dimensionality of the stack. Since the PCs can have spectral gaps in which electromagnetic wave propagation is forbidden in all directions, they offer the possibility of controlling the flow of photons in a way analogous to electrons in a semiconductor4-8. Thus, it can have profound implications for quantum optics, high-efficiency lasers, optoelectronic devices, and other areas of applications1-11. In the first decade, studies have focused on the materials with large gaps. Various photonic band-gap structures have been successfully fabricated for frequencies in both microwave and near-infrared regions1-3, 12-18. Based on them, some wave guides, optical fibers, cavities, optical switches, lowthreshold lasers and high-efficient light-emitting diodes have been designed1-3, 19-22. It is also proposed that such PCs may hold the key to the continued progress towards all-optical integrated circuits23. In contrast to the study of gaps in the PCs, wave transport in band regions can also exhibit some different properties in comparison with those in general homogeneous media24. For example, negative refraction can occur at the interface between a PC and a positive (conventional) medium25, 26. In the past decade, there has been a great deal of interest in studying the negative refraction and left-hand materials (LHMs)27-40. In fact, the phenomena of negative refraction of waves at interfaces have been analyzed theoretically by Mandel'shtam in the early 1940s41, but they have only been recently demonstrated experimentally28. As was shown by Veselago42, the LHMs possess a number of unusual electromagnetic effects including negative refraction, inverse Snell's law, reversed Doppler shift, and reversed Cerenkov radiation. These anomalous phenomena have also been observed in the PCs25, 26, 43-52. In this article, we have reviewed recent progresses on the negative refraction and the abnormal transmission of electromagnetic wave in two-dimensional photonic crystals. The physical mechanisms related to these phenomena have been analyzed, and the focusing properties of the point source through the photonic-crystal-based flat lens have been discussed. Recent investigations on the abnormal transmission and Zitterbewegung effect of wave transport near the Dirac point in twodimensional photonic crystals have also been introduced. Xiangdong Zhang Department of Physics, Beijing Normal University, Beijing 100875, China E-mail: zhangxd@bnu.edu.cn Electromagnetic wave in 2D photonic crystals REVIEW DECEMBER 2009 | VOLUME 12 | NUMBER 12 45 Negative refraction and focusing by 2D photonic crystals Negative refraction in the PCs was first observed by Kosaka et al.25 in 1998. Subsequently, there have been a number of reported experimental demonstrations and theoretical studies in this field26, 43-66. The physical principles that allow negative refraction in the PCs arise from the dispersion characteristics of wave propagation in a periodic medium, which can be well described by analyzing the equifrequency surface (EFS) of the band structure26, 43-50. Fig. 1 shows a typical branch of a dispersion surface in reciprocal space. The curvature of the dispersion surface turns from downward to upward, and incident light comes from the top of the figure. The direction of propagation light in the PCs is normal to the dispersion surface. Due to different shape of the curvature, the flux directions of the propagation wave at various points are different, which can be obtained by the group velocity, g=() , where is the optical frequency at the wave vector . This means that there are various transport properties of the wave in the PCs, for example, divergent propagation as in a concave lens (point A), collimated propagation (point B) and negative refraction (point C). Therefore, the negative refraction is only one kind of way for the wave transport in the PCs. It is determined by the shape of the EFS or the structure of the PCs. Thus, we can tune it by choosing the various structures of the PCs53. Because the phenomena and the physical origin for the negative refraction in 2D and 3D PCs are similar44-72, in the following we will focus our discussion on the negative refraction in the 2D PCs. Fig. 2b describes several constant frequency contours for the second band of the 2D PC with a triangular lattice for the S wave. The corresponding band structure is plotted in Fig. 2a. It is clear from the figure that the frequencies increase inwards, meaning that S k < 0 and the group velocities g are opposite to the phase velocity. Here, S and k represent the Poynting vector and wave vector, respectively. This indicates that the transmitting features of the wave in such a PC structure have a left-handed behavior. At the same time, we also notice Fig. 1 A schematic illustration of wave transmitting through the PC. Arrows above the dispersion surface indicate incident wavevectors in reciprocal space. Arrows below the dispersion surface indicate the energy flow in real space. Fig. 2 (a) The calculated photonic band structure of a triangular lattice of coated cylinder in air for the S wave. The radii of the dielectric cylinder and inner metallic cylinder are R=0.45a and r=0.25a, respectively. The dielectric constant of the cylinder is taken as 11.4. (b) Several constant frequency contours for the corresponding structure. (b) (a) REVIEW Electromagnetic wave in 2D photonic crystals DECEMBER 2009 | VOLUME 12 | NUMBER 1246 that some EFS contours such as = 0.42 - 0.47(2a/c) are very close to a perfect circle, indicating that the crystal can be regarded as an effective homogeneous left-handed medium at these frequencies26, 56. By using such a PC, we can design a flat lens to focus a point source on one side of the lens into a real point image on the other side54-62. Fig. 3 represents the typical field intensity pattern for such a lens. X and Y are vertical and transverse directions of the wave propagating, respectively. The field intensity in the figure is over a 30a x 30a region around the center of the sample (here a is the lattice constant of the structure). The geometry of the PC slab is also displayed for clarity. The high quality image in the opposite side of the slab and the focusing in the middle of the slab are clearly observed. If we move the position of the source, the image distance changes simultaneously. The relation between the length of the object and the image distance explicitly follows the well-known wave-beam negative refraction law. This means that the image is non-near-field. Such a theoretical result has been demonstrated experimentally62. The above example shows that the maximum of the dispersion curve is located at the point of the Brillouin zone and the negative refraction comes from the backward wave effect. In fact, the negative refraction can also be realized without employing the backward wave effect by using the PCs45, 46, 63-69. Fig. 4a-b display the band structure Fig. 3 (a) The intensity distribution of point source and its image across a 11a 2D PC slab at = 0.42 (2a/c) for the S wave. The structure and parameters are identical with those in Fig. 2. (b) Schematic picture depicting the lensing of a source by a PC slab to an image are shown on top of the figure. Fig. 4 (a) The calculated photonic band structure of a square lattice of coated cylinder in air for the S wave. The radii of the dielectric cylinder and inner metallic cylinder are R=0.45a and r=0.15a, respectively. The dielectric constant of the cylinder is taken as 14. (b) Several constant frequency contours for the corresponding structure. (b) (a) (b) (a) Electromagnetic wave in 2D photonic crystals REVIEW DECEMBER 2009 | VOLUME 12 | NUMBER 12 47 and several constant frequency contours for the first band of the 2D PC with a square lattice for the S wave. We find that the lowest bands have S k > 0 everywhere within the first Brillouin zone, meaning that the group velocities are never opposite to the phase velocity. However, some low frequency contours such as 0.232(2a/c) are significantly distorted from a circle, being convex around points M. The conservation of the k component along the surface of refraction will also result in the negative refraction effect. The advantages of the negative refraction in the lowest valence band are single-mode and high transmission. In the high frequency case, the left-handed and the right-handed behaviors are easily produced simultaneously due to the excitations of the multiple-mode44. The single-mode and allangular negative refraction are very important to some applications in designing optical devices. The two seemingly rather different situations (Fig. 2 and Fig. 4) do share one common feature; the photonic effective mass near a local maximum of the dispersion curve is negative-definite. From such a point of view, they rely on the same mechanism that the relative wave vector of a local frequency maximum is pointed opposite to the group velocity. There is also the same usefulness for them. For example, they all can be applied to design the flat lens and realize the focusing of the wave. Fig. 5 describes the intensity distributions of the flat lens realized by the PCs with a square lattice. In such a case, the position of the image does not change while moving the source, and the image is located in the near-field region. This is due to the anisotropy of the dispersion or the self-collimation effect65. However, the self-collimation effect can in principle be suppressed by changing the scatters, and the positions of the focusing (in the near-field region or the non-near-field region) can be tuned53, 60. The focusing in the near-field region or the non-near-field region have the same origins. All come from the negative refraction. It is well known that the electromagnetic wave can be decomposed into E polarization (S wave) and H polarization (P wave) modes for the 2D PC structures. However, the above discussions focus on a certain polarized wave, S wave or P wave. It is interesting that a complete negative refraction region for all polarized waves can also be realized by engineering the 2D PC structure60, 64. Therefore, the same structure and parameters yield the relative refractive index of n=-1 at the same frequency for both polarized waves. Thus the focusing of unpolarized electromagnetic waves can be realized by the same PC slab60. There are two aspects relating to the focusing. One is position (in the near-field region or the non-near-field region), and the other is resolution (full width at half maximum of the focus spot). The position of the image depends on the effective refractive index of the sample and the homogeneity of the materials, and it does not depend on whether or not the evanescent waves are amplified. The focus and image can still be observed if only the propagating waves are considered. In such a case, the image resolution cannot beat the diffraction-limit. In contrast, the superlensing effect comes from the evanescent waves (or resonance transmission). Several studies46, 67, 69 have shown that the surface termination within a specific cut of the structure can excite surface waves and allow the reconstruction of evanescent waves for a better focus. In fact, apart from the surface termination, the other methods such as changing the dielectric constants of interface layers, adding symmetric cap layers and introducing optical gain in the surface layers can also improve the image resolution61. In contrast, the effect of disorder always reduces the image resolution (including image peaks and full width at half maximum of the focusing). The role of the disorder is similar to that of material absorption61. In addition, we would like to point out that the negative refraction not only exists in the periodic PCs, but also in some high-symmetric photonic quasicrystals (PQC). This has been demonstrated both theoretically and experimentally73-75. Similar to the periodic PCs, we can also use the PQC to design the flat lens and realize the focusing of the wave. Although the flat lens consisting of the PQC is not better than the periodic PCs in all aspects, it has some advantages in producing the non-near-field images due to their higher rotational symmetry. For example, it is very difficult to construct a flat lens by using pure dielectric cylinder of periodic structure to realize the nonnear-field focus for the S wave, but it is easy to complete by high symmetry PQC slab. Thus, the investigation of the negative refraction and the focusing of the PQC can open a new window in the realistic application of such a phenomenon. The above introduction about the application of the negative refraction is only for the flat lens and focusing. In fact, the negative Fig. 5 The intensity distribution of a point source and its image across a 11a 2D PC slab at = 0.231 (2a/c). The structure and parameters are identical with those in Fig. 4. REVIEW Electromagnetic wave in 2D photonic crystals DECEMBER 2009 | VOLUME 12 | NUMBER 1248 refraction can also play important roles in other areas such as open cavity76, slow light77, 78 and so on. Abnormal transmission of electromagnetic wave through 2D PC slab In general, there are two kinds of regime for the electromagnetic wave transport in the PCs1-3. One is at the gap regions; the transmission is suppressed exponentially with the increase of the sample thickness. The other is at the band regions; the transmission does not depend on the thickness of the sample and exhibits the standard ballistic behavior. The transport of the wave in the band regions is similar to the case of an effective medium. Thus, the PCs behave as the materials having an effective refractive index controllable by the band structure. The effective refractive index can vary from negative Fig. 6 Calculated photonic band structure of P wave for a triangular lattice of dielectric cylinder with R/a=0.3 and = 11.4 in an air background. Fig.7 (a) Schematic picture depicting simulation processes. (b) The product of T and L as a function of sample thickness at different frequencies. The frequencies are in unit of a/2c . Red line and green line are plotted only for view. The other parameters are identical to those in Fig.1. (b)(a) Electromagnetic wave in 2D photonic crystals REVIEW DECEMBER 2009 | VOLUME 12 | NUMBER 12 49 to zero and then to positive with frequency. Fig. 6 describes the band structure of P wave for the system with a 2D triangular lattice of cylinders immersed in air background. The key feature of this band structure is that the band gap may become vanishingly small at corners of the Brillouin zone at = 0.466a/2c, where two bands touch as a pair of cones in a linear fashion. Such a conical singularity is referred to as the Dirac point79, 80. Above the Dirac point, the effective refractive index of the PC is positive. In contrast, it becomes negative below the point. The negative refraction and focusing of the wave transport in such a case have been discussed in the above part. At the Dirac point, the effective refractive index is zero. Recent investigations show that the transmission properties of the wave near the Dirac point are different from the above two kinds81-84. It can be regarded as a new transport regime, which is similar to the properties of electron transport at the Dirac point of the graphene85, 86. According to analyses79, 80, wave transport near the Dirac point in the PCs can be described by the Dirac equation. For such a PC slab with thickness L in air background, we can obtain the transmission T 1/L by applying the resolution of Dirac equation and boundary condition of flux conservation81. The transmission of the wave through 2D PC slab is inversely proportional to its thickness. Such a theoretical result has been demonstrated by the exact numerical simulations82-84. The triangular dots in Fig. 7 represent the numerical result for the product of T along the K direction and L as a function of the sample thickness at = 0.468a/2c (near the Dirac point). For comparison, we also give the results at = 0.44a/2c (away from the Dirac point ) and = 0.32a/2c (another band) in Fig. 7 as circle dot and square dot, respectively. They exhibit different feature although all these frequencies are in band region. At = 0.468a/2c, T x L keeps constant (red line) with the increase of L although it oscillates around red line. Here the red line is drawn only for view. The oscillating characteristic depends on the interface and the thickness of the sample, but the red line remains unaffected. This indicates that the transmission is inversely proportional to the thickness of the sample, which is similar to diffusion behavior of the wave transport through a disordered medium even in the absence of any disorder in the PCs. This is completely different from the case at = 0.32a/2c. The transmission is near constant and T x L increases linearly with the increase of L, which exhibits the standard ballistic behavior characteristic. The change feature of the transmission at = 0.44a/2c is in between the above two cases. It oscillates around green line (drawn only for view) and the average values increase with the increase of L, but the slope of green line is smaller than that of square-dot line ( = 0.32a/2c). This means that the transmission possesses both the ballistic and diffusion behaviors in this case. The numerical results are in agreement with the theoretical analysis based on the Dirac equation81-84. Zitterbewegung effect of wave near the Dirac point After the new transport regime of the wave in the PCs has been demonstrated, the dynamic behavior of wave transport near the Dirac Fig. 8 (a) After the injection of a Gaussian pulse with center frequency c = 0.466a/2c, we show the time dependence of the transmission coefficient for the samples with different thicknesses. Solid line, dashed line and dotted line correspond to the results with L=14a, 24a and 32a, respectively. (b) The inverse values of oscillation period (1/A) as a function of pulse width . Circle and triangles correspond to the cases with L =14a and L = 32a, respectively. The other parameters are identical to those in Fig. 6. (b)(a) REVIEW Electromagnetic wave in 2D photonic crystals DECEMBER 2009 | VOLUME 12 | NUMBER 1250 REVIEW Electromagnetic wave in 2D photonic crystals point has been discussed87, 88. Fig. 8a shows the numerical results for the transmission coefficients as a function of time for the samples with different thickness, when a Gaussian pulse is injected into the PCs. The center frequency of the pulse is taken as that at the Dirac point. The results show unusual oscillation features. (1) The period of the oscillation (A) depends weakly on the thickness of the sample. (2) The ratios of the intensity between the second peak and the first peak increase considerably. For the thin sample, the second peak basically disappears. No oscillation can be observed. This is due to the finite size effect of the sample. When the thickness of the sample is very small, the wave transport exhibits a ballistic behavior. With the increase of the sample thickness, the diffusion behavior appears gradually. When the thickness of the sample is bigger than several wavelengths, the diffusion behavior plays a leading role. In such a case, remarkable oscillations can be observed. (3) The period of oscillation is linearly dependent on the pulse width and is not determined by the central frequency (Fig. 8b). These features are completely different from the oscillation of the wave in a dielectric slab or cavity originating from the interface reflection or Fabry-Perot effect, in which the oscillation period is determined by the thickness of the sample and the central frequency of the pulse. In addition, the features are also not related to the localization effect, because wave transport exhibits diffusion behavior. Such an inherent oscillation is directly related to the Zitterbewegung (ZB) effect. ZB represents an oscillatory motion of free electrons described by the Dirac equation in the absence of external fields, which is caused by the interference between the positive and negative energy states89. It was believed that the experimental observation of the effect is impossible since one would confine the electron to a scale of the Compton wavelength. Although many theoretical investigations have shown that such a phenomenon can also be found for non-relativistic electrons in solid systems, it has not been observed directly from the numerical simulation or experimental measurement. According to the theory of the ZB, the time-dependent displacement (x­(t)) of a wave packet with time in the systems can be obtained analytically. After the average displacement is obtained, the velocity of the wave packet can be calculated by ­(t) =x­(t) / dt. The velocity of the wave packet ­(t) is proportional to the energy flux ( j(t)) of the wave ( j(t) ­(t)). At the same time, j(t) is a time-derivative of the pulse intensity (I(t)) ( j(t) = dI(t) / dt). The intensity (I(t)) or transmission coefficient can be obtained from the numerical simulation or the experimental measurement. Thus, we can obtain j(t) from the numerical simulation and quantitatively compare it with the theoretical result for ­(t). These have been done87 and the agreement between the numerical simulation and the theoretical results of the ZB has been found. The numerical simulation shows that an optical analogue effect to ZB of the relativistic electron can be found. In fact, such a phenomenon not only exists for electromagnetic wave in the PCs, but also appears for acoustic wave in sonic crystals (SCs)88. In order to test such a phenomenon experimentally, a series of SC slabs with different thicknesses has been fabricated88. The dynamic behavior of the acoustic wave transport near the Dirac point in the above SC samples has been investigated experimentally. The measured results for filter frequency widths = 0.01 MHz, 0.02 MHz and 0.03 MHz are plotted in Fig. 9a-c. The dark, red and green curves correspond to the results with L = 14a, 19a and 24a, respectively. It is obvious that all of them are oscillating and the period of the oscillation depends weakly on the thickness of the sample, while it is linearly dependent on the filter frequency widths. Comparing them with the theoretical results of the ZB, the agreements between them have been demonstrated88. This means that an acoustic analogue effect to the ZB of relativistic electrons has been observed from experimental measurements. We anticipate the work to be a starting point for more experimental investigations on the phenomena of relativistic quantum mechanics by using classical waves. Summary After providing a brief historic of the study of photonic band gap materials, we have reviewed recent progresses on the negative refraction and the focusing of electromagnetic wave through 2D PCs. The physical principles causing such a phenomenon have also been analyzed. Different kinds of focusing by 2D PC slabs have been Fig.9 Experimental data of the transmission after the injection of a Gaussian pulse with center frequency = 0.55MHz (Dirac point) into the sample, which consists of a hexagonal array of steel cylinders immersed in water with a lattice constant a =1.5mm and a filling ratio 0.403. Dark, red and green correspond to the cases with L =14a, 19a and 24a, respectively. (a),(b) and (c) correspond to the cases with the filter frequency widths = 0.01MHz, 0.02MHz and 0.03MHz, respectively. (b) (a) (c) Electromagnetic wave in 2D photonic crystals REVIEW DECEMBER 2009 | VOLUME 12 | NUMBER 12 51 summarized. The abnormal transmission of the electromagnetic waves near the Dirac point in the 2D PCs has been discussed. Recent investigation on observing Zitterbewegung effect of wave transport near the Dirac point has also been introduced. Acknowledgments This work was supported by the National Natural Science Foundation of China at No. 10825416 and the National Key Basic Research Special Foundation of China at No. 2007CB613205 and No. 2004CB719804. REFERENCES 1. Joannopoulos, J. D., et. al., Photonic Crystal-Molding the Flow of Light, Princeton University Press, Princeton, NJ, (1995) 2. Soukoulis C. M., Photonic Band Gap Materials, Kluwer Academic, Dordrecht, (1996) 3. Sakoda, K., Optical properties of photonic crystals, Springer, (2001) 4. Yablonovitch, E., Phys. Rev.Lett. (1987) 58, 2059 5. John, S., Phys. Rev. Lett. (1987) 58, 2486 6. Ho, K. M., et. al., Phys. Rev.Lett. (1990) 65, 3152 7. Leung, K. M., and Liu, Y. F., Phys. Rev. Lett. (1990) 65, 2646 8. Zhang, Z., and Satpathy, S., Phys. Rev. Lett. (1990) 65, 2650 9. John, S., and Wang, J., Phys. Rev. Lett. (1991) 64, 2418 10. Petrov, E. P., et. al., Phys. Rev. Lett. (1998) 81, 77 11. Megens, M., et. al., Phys. Rev. Lett. (1999) 83, 5401 12. Yablonovitch, E., et. al., Phys. Rev. Lett. (1991) 67, 2295. 13. Anderson, C. M., and Giapis, K. P., Phys. Rev. Lett. (1996) 77, 2949 14. Li, Z. Y., et. al., Phys. Rev. Lett. (1998) 81, 2574 15. Zhang, X. D., et al., Phys. Rev. B (2000) 61, 1892 16. Chan, Y. S., et al., Phys. Rev. Lett. (1998) 80, 956 17. Zoorob, M. E., et al., Nature (2000) 404, 740 18. Zhang, X. D., et al., Phys. Rev. B (2001) 63, 081105 19. Mekis, A., et al., Phys. Rev. Lett. (1996) 18, 3787 20. Kwan, K.-C., et al., Appl. Phys. Lett. (2003) 82, 4414 21. Knight, J. C., et al., Science (1998) 282,1476 22. Scalora, M., et al., Phys. Rev. Lett. (1994) 73, 1368 23. Joannopoulos, J. D., et al., Nature (1997) 386, 143 24. Kosaka, H., et al., Appl. Phys. Lett. (1999) 74, 1212 25. Kosaka, H., et al., Phys. Rev. B (1998) 58, 10096 26. Notomi, M., Phys. Rev. B (2000) 62, 10696 27. Pendry, J. B., Phys. Rev. Lett. (2000) 85, 3966 28. Shelby, R. A., et al., Science (2001) 292, 77 29. Smith, D. R., et al., Phys. Rev. Lett. (2000) 84, 4184 30. Smith, D. R., and Kroll, N., Phys. Rev. Lett. (2000) 84, 2933 31. Markos, P., and Soukoulis, C. M., Phys. Rev. E (2002) 65, 036622 32. Marques, R., et al., Phys. Rev. Lett. (2002) 89, 183901 33. Foteinopoulou, S., et al., Phys. Rev. Lett. (2003) 90, 107402 34. Smith, D. R., and Schurig, D., Phys. Rev. Lett. (2003) 90, 077405 35. Houck, A. A., et al., Phys. Rev. Lett. (2003) 90, 137401 36. Parazzoli, C. G., et al., Phys. Rev. Lett. (2003) 90, 107401 37. Grbic, A., and Eleftheriades, G. V., Phys. Rev. Lett. (2004) 392, 117403 38. Chen, L., et al., Phys. Rev. Lett. (2004) 92, 107404 39. Zhang, Y., et al., Phys. Rev. Lett. (2003) 91, 157404 40. Agranovich, V. M., and Gartstein, Y. N., Phys. Usp. (2006) 49, 1029 41. Mandel'shtam, L. I., Zh. Eksp. Teor. Fiz. (1945) 15, 475 42. Veselago, V. G., Sov. Phys. Usp. (1968) 10, 509 43. Gralak, B., et al., J. Opt. Soc. Am. A (2000) 17, 1012 44. Foteinopoulou, S., and Soukoulis, C. M., Phys. Rev. B (2003) 67, 235107 45. Luo, C., et al., Phys. Rev. B (2002) 65, 201104 46. Luo, C., et al., Phys. Rev. B (2003) 68, 045115 47. Luo, C., et al., Appl. Phys. Lett. (2002) 83, 2352 48. Cubukcu, E., et al., Nature (2003) 423, 604 49. Parimi, P. V., et al., Nature (2003) 426, 404 50. Cubukcu, E., et al., Phys. Rev. Lett. (2003) 91, 207401 51. Reed, E. J., et al., Phys. Rev. Lett. (2003) 91, 133901 52. Luo, C., et al., Science (2003) 299, 368 53. Zhang, X. D., Appl. Phys. Lett. (2005) 86, 121103 54. Berrier, A., et al., Phys. Rev. Lett. (2004) 93, 073902 55. Wang, X., et al., Optics Express (2004) 12, 2919 56. Zhang, X. D., Phys. Rev. B (2004) 70, 195110 57. Wang, X., et al., Phys. Rev. B (2005) 71, 085101 58. Hu, X., and Chan, C. T., Appl. Phys. Lett. ( 2004) 85, 1520 59. Zhang, X. D., Phys. Rev. E (2005) 71, 037601 60. Zhang, X. D., Phys. Rev. B (2005) 71, 235103 61. Zhang, X. D., Phys. Rev. B (2005) 71, 165116 62. Feng, Z., et al., Phys. Rev. B (2006) 73, 075118 63. Decoopman, T., et al., Phys. Rev. Lett. (2006) 97, 073905 64. Zhang, X. D., Phys. Rev. B (2004) 70, 205102 65. Li, Z. Y., and Lin, L. L., Phys. Rev. B (2003) 68, 245110 66. He, S. L., et al., Phys. Rev. B (2004) 70, 115113 67. Xiao, S., et al., Appl. Phys. Lett. (2004) 85, 4269 68. Belov, P., et al., Phys. Rev. B (2005) 71, 193105 69. Moussa, R., et al., Phys. Rev. B (2006) 74, 115111 70. Ao, X. Y., and He, S. L., Opt. Lett. (2004) 29, 2542 71. Lu, Z., et al., Phys. Rev. Lett. (2005) 95, 153901 72. Ren, K., et al., Phys. Rev. B (2007) 75, 115108 73. Feng, Z., et al., Phys. Rev. Lett. (2005) 94, 247402 74. Zhang, X. D., Phys. Rev. B (2007) 75, 024209 75. Zhang, X. D., et al., Opt. Express (2007)15, 1292 76. Ruan, Z., and He, S., Opt. Lett. (2005) 30, 2308 77. Krauss, T. K., Nature photon. (2008) 2, 448 78. Baba, T., Nature photon. (2008) 2, 465 79. Haldane, F. D. M., and Raghu, S., Phys. Rev. Lett. (2008) 100, 013904 80. Raghu, S., and Haldane, F. D. M., Phys. Rev. A (2008) 78, 033834 81. Sepkhanov, R. A., et.al., Phys. Rev. A (2007) 75, 063813 82. Zhang, X. D., Phys. Lett. A (2008) 372, 3512 83. Sepkhanov, R. A., and Beenakker, C. W. J., Opt. Commun. (2008) 281, 5267 84. Diem, M., et al., arXiv: (2008) 0807.3351 85. Novoselov, K. S., et.al., Science (2004) 306, 666 86. Ando, T., J. Phys. Soc. Jpn. (2005) 74, 77. 87. Zhang, X. D., Phys. Rev. Lett. (2008) 100, 113903 88. Zhang, X. D., and Liu, Z. Y., Phys. Rev. Lett. (2008) 101, 264303 89. Schrodinger, E., Sitzungsber. Preuss. Akad. Wiss. Phys. Math. Kl. (1930) 24, 418 ISSN:1369 7021 Elsevier Ltd 2009DECEMBER 2009 | VOLUME 12 | NUMBER 1252 REVIEW Resonance properties of metallic ring systems Resonance properties of metallic ring systems Introduction In 1968, Veselago1 proposed that a medium with simultaneously negative permittivity and permeability possesses a negative refractive index, and exhibits many unusual electromagnetic (EM) properties. This proposal did not attract immediate attention since it is well accepted that a natural material shows no magnetism at high frequencies2. A breakthrough appeared in 1999 when Pendry3 showed that a split ring resonator (SRR) could provide magnetic responses at any desired frequency. People then successfully fabricated metamaterials by combining magnetic resonators and electric wires, and demonstrated many unusual EM phenomena based on metamaterials, such as the negative refraction4-10, the super focusing11-14 and the subwavelength cavity15-17. Scientists continued to explore other extraordinary EM phenomena related to metamaterials, including the unusual photonic bandgap effects18-20, the invisibility cloaking21-23, the unusual nonlinear effects24-29, etc. When the concept of metamaterial was pushed to optical frequencies, other magnetic resonant structures were proposed, such as the rod-pair structure30, 31, the fishnet structures9, 32, 33, and a circular array of nano-spheres33-35. As the first realization of artificial magnetism, the SRR structures naturally attracted the most extensive attention. People have studied the circular SRRs3, 4, 6, 36-53, the rectangular SRRs5, 54-68, SRRs with different cross-sections, metal line widths, metal thicknesses, and substrates6, 36, 55, 60, 61, SRRs with different numbers of splits36, 37, 56, and different numbers of rings48, 64, and so on. Some applications were also proposed for the SRR. For instance, researchers proposed to use SRRs as antennas69 and as couplers for channel dropping70, inserted SRRs into a cut-off waveguide to enhance transmissions71, 72, We review our recent efforts in understanding the resonance properties of metallic ring systems using a rigorous mode-expansion theory. In the quasi-static limit, we established a matrix-form circuit equation to calculate the frequencies and current distributions for all resonance modes in a ring system. We then applied the theory to study different split ring resonators (SRR). We show that the circuit equations can be analytically solved in the thin-wire limit. Our theoretical results were all successfully verified by finite-different-time-domain simulations on realistic systems and available experiments. Lei Zhou1*, Xueqin Huang1, Yi Zhang1, Siu-Tat Chui2 1Surface Physics Laboratory (State Key Laboratory) and Physics Department, Fudan University, Shanghai 200433, P. R. China 2Bartol Research Institute, University of Delaware, Newark, Delaware 19716, USA * Email: phzhou@fudan.edu.cn Resonance properties of metallic ring systems REVIEW DECEMBER 2009 | VOLUME 12 | NUMBER 12 53 and used SRRs as lenses for imaging73, 74. Some groups attempted to scale down the size of SRR to realize artificial magnetism at higher frequencies4-6, 57, 58, 63, 75. However, the scaling does not always work, and the increase of resonance frequency will saturate under certain conditions56, 60. Some other groups tried to tune the resonance frequency of a SRR, by inserting additional capacitance in the ring gaps36, 39, using photocapacitance of the semi-insulating GaAs in the gap38, and combining the SRRs with nematic liquid crystals62. Recently, the designs and fabrications of isotropic metamaterials based on SRRs began to draw intensive attentions76-82. Many theoretical efforts were devoted to understanding the exotic EM wave properties of the SRR structures. In a pioneering paper, Pendry et al.3 analyzed the resonance properties of a SRR by assuming a metallic ring as a single lumped element with empirical circuit characteristics. Later, Shamonin et al.42 considered more inductive/capacitive effects by assuming the SRR to consist of an infinite number of lumped circuit elements. Many other analytical methods were developed to study the properties of the SRRs41, 43-46, 48, 49, 64, 65 from various aspects. However, in all these approaches, the inductive/capacitive effects in the rings were not completely considered. In addition, all these approaches need a set of empirical circuit parameters that cannot be calculated rigorously. Those empirical parameters were usually determined under some approximations3, 42. The SRR systems were also studied by numerical calculations54, 55, 61, 62, 66-68. Although such full-wave studies contain all relevant field information, it is sometimes difficult to extract useful properties of a SRR, such as the bi-anisotropy polarizabilities, from the obtained information. In reviewing these efforts, we find that an analytical approach on more rigorous ground is highly desirable to study the metallic ring systems. In this paper, we review our recent efforts to establish such a theory, with inductive/capacitive effects fully included and all circuit parameters calculated rigorously, to study the EM properties of various metallic ring systems50-53. We first briefly review the theoretical developments in next section, and then present the applications of our theory to several typical SRR systems. We finally summarize our results in the last section. Theoretical developments of the modeexpansion theory Basic theory for a single-ring We consider a single ring of radius R in the xy-plane, as shown in Fig. 1a50. In what follows, a common time-varying factor exp(i) is omitted for every quantity. In the quasi-static limit, the inductive field ( )LE r r r and the capacitive field ( )CE r r r can be expressed as 0( ) ( ') '/(4 | '|)LE r i j r dr r r = - r rr r r r , 0 1 1 ( ) ' ( ') '/ | '| 4 CE r j r dr r r i = - r rr r r r r where j (r ') describes the current flowing in the wire. Suppose that the wire has a circular cross-section with a radius a and a << R, the current distribution can be written as ( ') ( )sin (cos ) ( ' ) /j r e I r R R = r r r with sin cosx ye e e = - + r r r . We expand every physical quantity as a Fourier series, ( ) im mI I e + = , , ,( ) m im L C L CE e E e + = r r . (1) Then we carry out the integrations in ( ), ( )L CE r E r r rr r to obtain m L m mE i L I= - , /( )m C m mE I i C= - (2) where the circuit parameters are defined by 0 1 1( )/ 4m m mL A A - += + , ( )1 2 0/ 2 ( )m mC m A R R a= - (3) Here the key function is 2 | | ( )! (0) ( )! l m m l l m l m A P l m = - = + (4) in which m lP is the associated Legendre function and = (R-a)/R<1. In the thin-wire limit (a << R), we found an asymptotic form. This logarithmic Am Dm-ln(2a/R)/(m) divergence is a typical Fig. 1 Geometries of (a) single SRR, (b) co-planar SRR, and (c) BC-SRR. (b)(a) (c) REVIEW Resonance properties of metallic ring systems DECEMBER 2009 | VOLUME 12 | NUMBER 1254 characteristic of a thin-wire system83. Ohm's law tells us that ( ) ( ) ( ) ( ) ( )L C extj r r E r E r E r = + + r r rr r r r r r where ( )extE r r r is the external field and ( )r r is the resistivity function of the ring. In terms of the Fourier components, we get the following matrix equation, ' '' m mm m extm H I E= , (5) where ( )2 2 ' '( ') 1 /mm m m mmH m m i L = - + - % ; ( ')m m -% is the Fourier component of () = ()/S (S is the wire cross-section area) and m = 1/LmCm. Diagonalizing the H matrix, we obtain the eigenvalues {j} and eigenvectors of all EM modes, from which we can calculate the resonance frequencies, induced EM dipole moments, and the polarizabilities and the bi-anisotropic polarizabilities. For example, all resonance frequencies j of the SRR are obtained through solving the equation det[Hmm'()] = mm() = 0 (6) Extensions to other situations The above mode-expansion theory can be easily extended to more complex situations. For the two ring systems, we find that the matrixcircuit equation could be written as { },{ ' } ' ' ' = ext mj m j m j mj m j H I E (7) where the matrix elements are ' { }.{ ' '} ' '' 1 ( ') jj mj m j j jj m mmjj m H m m i L C = - + - . (8) Here j, j' = 1, 2 label the two rings, jj mL and jj mC are the self inductive/capacitive parameters and 'jj mL and 'jj mC are the mutual inductance/capacitance parameters. The above theory can be applied to study the coplanar double-ring SRR in which two rings are placed on the same plane but with different radii (Fig. 1b), and the broadside coupled SRR (BC-SRR) with two identical rings placed on different planes (Fig. 1c). In addition, the gap position of each ring can be arbitrary in our system, which is simply described by the resistivity function (). It is straightforward to extend our theory to study multiring systems. For the detailed forms of those circuit parameters, please refer to the original publications51, 52. Strictly speaking, the theory presented so far is only applicable to rings formed by thin wires with circular cross-sections. In practical situations, the metallic rings often have rectangular crosssections3-6, 36-49, 54-68, where the delta-like current distribution is no longer reasonable. Suppose the wire's cross-section is defined as tx2a, where 2a and t are the width and thickness of the wire, we focus on the flat-wire case satisfying R >> 2a >> t. For a good metal, the skin effect dictates that the current should mainly distribute on the metal surface. Noting that a << with being the wavelength of the probing EM wave of interest, we further assume that the current distributes uniformly along the wire width. Therefore, the current distribution in the flat wire can be written as, [ ]( ) ( / 2) ( / 2) , ( ) 0 , j t z t z t e j r + + = r r r [ , ] otherwise R a R a - + (9) where t << t is the skin depth of the metal. We average both , ( )L CE r r r and ( ')j r r r over the cross-section area of the wire, and then set up the relationship between the two averaged quantities. For example, the averaged inductive field is [ ] [ ] ( , , ) ( / 2) ( / 2) ( ) ( / 2) ( / 2) L L E z e t z t z t dzd E t z t z t dzd + + - = + + - r r . (10) and the total current is given by I() = j().4at. By linking these two averaged quantities, we can calculate the relevant circuit parameters52. Therefore, the circuit equations (5), (7) are still correct for flat-wire SRR cases, but with a set of modified circuit parameters52. Applications and discussions Our theory can be applied to study the resonance properties of various metallic ring systems. In the following three subsections, we summarize our results on a single-ring SRR, a coplanar double-ring SRR, and a BCSRR, correspondingly. Single-ring SRR Consider a single-ring SRR illustrated in Fig. 1a. In the microwave frequency regime, we can safely set the resistivity of the metal as 0, and that of the air-gap as r. We will let r in the end. The magnitude of the lowest eigenvalue of matrix H is shown as a function of frequency in Fig. 2 for a typical SRR. The series of resonances in Fig. 2 can be categorized into two classes. The even-numbered resonances 2m coincide well with the intrinsic resonances m, which in the thinwire limit (a/R0) becomes m mu where u=c/R is the frequency unit of the present problem. Noting that 2m = 2c/2m = m.2R, we find that these resonances are solely determined by the ring geometry, with currents forming standard standing waves in the ring. The oddnumbered ones, however, must be introduced by the air gap . In fact, these resonance frequencies can be calculated analytically in the following limits: (1) 0; (2) a/R0; (3) metal is perfect and the gap is ideal insulator (r). Under these conditions, we have rigorously solved the matrix problem (6) and found two sets of solutions53. One set of resonance frequencies is 2m = mu, m = 1, 2, ... (11) with eigenvectors exhibiting odd-symmetries (i.e., I-m = -Im). These modes correspond to the even-numbered resonance modes as shown in Fig. 2. Another set of resonance modes are determined by the following polynomial equation, Resonance properties of metallic ring systems REVIEW DECEMBER 2009 | VOLUME 12 | NUMBER 12 55 2 0 2 1 2 1 0 1/m m m L L C = + = - (12) and their eigenvectors exhibit even symmetry (i.e., I-m = -Im). Since as a/R0, we have Lmln(R/a) and 1/Cmm2ln(R/a), using the identity 2 2 2 1 cot( ) 1 2 /( ) m k k k k m = = + - , we found that Eq. (12) can be written as (/u)cot(/u) = 0, leading to the following solutions 2m+1 = (m + 1/2)u, m = 0, 1, 2,... (13) These solutions are just the odd-numbered resonance modes depicted in Fig. 2. The information of the eigenvectors enables us to evaluate the EM responses of the system. Consider different probing plane waves with (a) ^ ^|| , ||E y k z rr , (b) ^^|| , ||E y k x rr , (c) ^ ^|| , ||E x k z rr , (d) ^^|| , ||E x k y rr , we show in Fig. 3 the induced dipole moments as functions of frequency. The odd-numbered resonance modes possess both magnetic (mz) and electric (py) responses, while the even-numbered ones only electric (px) responses. The appearance of py is always accompanied by the appearance of mz, manifesting the bi-anisotropy property of the SRR43, 47, 49. Symmetry restricts a probing field to excite only a particular set of resonance modes of the SRR, and therefore, not all the resonance peaks appear simultaneously in each spectrum. We have performed finite-difference time-domain (FDTD) simulations84 to verify these theoretical results. We first calculated the transmission spectra through arrays of such realistic SRR's, and then identify all resonance modes from the dips in the spectra. The transmission spectra under the four plane wave inputs are shown respectively in Fig. 4a-d. When we compare Fig. 4 with Fig. 3, we find that they agree with each other quite well. We clearly identify the dips at 0.42u shown in Fig. 4a, b, d as the lowest eigen resonance mode (1), the dips at 1.19u shown in Fig. 4c, d as the second resonance mode (2), and the dips at 1.46u as the third one (3). The quantitative differences between analytical and FDTD results must be caused by the couplings between different SRRs, since we have to adopt periodic arrays of SRRs to study the transmission spectra in the FDTD simulations. Coplanar double-ring SRR Now consider the coplanar double-ring SRR as shown in Fig. 1b. Suppose the two rings have radius R1 = R, R2 = R - d, and each wire has Fig. 3 Amplitudes of the induced moments, |px|, |py|, |mz|, of the SRR as functions of /u for different probing fields as shown in the figure. Reproduced from50 with permission from the American Physical Society. Fig. 2 min[|m|] as functions of /u for a single-ring SRR with = /40 and = 0.99, calculated with different values of Mmax (the cutoff value of m) and r (in units of 0u). Reproduced from50 with permission from the American Physical Society. (b) (a) (c) (d) REVIEW Resonance properties of metallic ring systems DECEMBER 2009 | VOLUME 12 | NUMBER 1256 a radius a1 = a2 = a << R. For an example with structural details shown in the caption of Fig. 5, we solved the matrix equation (7) and showed in Fig. 5 the calculated min[|l|] as a function of /u. Compared with the spectra of a single-ring SRR shown in the same figure, we find that each single-ring mode has split into a pair of modes in the double-ring case through mutual inductance/capacitance effects. Such inter-ring interactions may combine components of different rings with a certain relative phase to form a double-ring eigenmode51. Therefore, the magnetic (electric) polarizations are highly diminished in the 1 H (1 L) mode, and as the results, the bi-anisotropy is also highly suppressed as two rings approach. Fig. 6 shows the dipole moments of the structure induced by different external plane waves. Similar to the single-ring case (Fig. 3), we find that the odd-numbered modes (1 L, 1 H, 3 L, 3 H,...) carry both electric (Py) and magnetic (Mz) polarizations, while the even-numbered ones (2 L, 2 H, 4 L, 4 H,...) carry only electric (Px) polarizations. In particular, one may easily find that mz is much stronger than py for the mode 1 L, but things become reversed for the mode 1 H. These are precisely the evidence of the polarization decreasing effects discussed above. We performed FDTD simulations84 to calculate the transmission spectra through arrays of realistic SRR structures, and again the transmission dips in the spectra show excellently one-by-one correspondence to the moment peaks in Fig. 651. The present theory allows us to quantitatively examine the bi-anisotropy of the SRR. We derived all elements of the electric/magnetic polarizabilities of the structure51, following the definitions in43, 47, 49. We showed in Fig. 7a-b the calculated values of electric polarizability (e y e y) and bi-anisotropic polarizability (e y m z )43, 47, 49, respectively, for double-ring SRR's with different values of d. Clearly, both e y e y and e y m z are significantly suppressed as d decreases. As a result, such a mode becomes purely magnetic in the limit of d 0. The magnetic resonance frequency 1 L is drastically lowered compared to the single-ring mode (denoted by 1). Under the condition d >> a, we applied a perturbation theory with a 3-mode approximation to derive the following analytical formula to quantitatively account for such a frequency shift51, 1 L 1 [1-2ln(2d/R) / (3 ln(2a/R))]. (14) Fig. 5 min[|l|] (in arbitrary units) as the functions of /u calculated for a double-ring SRR (symbols) with R = 4 mm, d = 0.4 mm, a = 0.1 mm, = /90, and a single-ring SRR (lines) with R = 3.8 mm, a = 0.1 mm, = /90. Reproduced from51 with permission from the American Institute of Physics. Fig. 4 FDTD calculated transmission spectra of the SRR arrays as functions of /u for plane wave inputs specified in the figure. Here the SRR has R = 4 mm, a = 0.1 mm, and = /40. Reproduced from50 with permission from the American Physical Society. (b) (a) (c) (d) Resonance properties of metallic ring systems REVIEW DECEMBER 2009 | VOLUME 12 | NUMBER 12 57 The physics behind (14) is that /1 is dictated by a competition between the mutual interaction (ln(2d/R)) and the self interaction (ln(2a/R)). FDTD simulations51 on realistic SRR structures excellently verified the analytical formula (14). This formula can also account for experiments very well. For the series of SRR's studied experimentally36, adopting their definitions (i.e., set R = r-w/2, a = w/2, d = t+w where w is the metal line width and t is the gap distance between two rings36) and taking the experimental data 1 = 2x4.58GHz36, we get an expression, = 4.58[1-2ln(2(t+w)/(r-w/2))/[3ln(w/(r-w/2))]] (15) to estimate the resonance frequencies of SRR's measured36. Fig. 8 shows that the experimental data36 are reasonably described by (15). BC - SRR We now consider the BC-SRR as shown in Fig. 1c. The spectrum of resonance frequency in the BC-SRR case is quite similar to that of a coplanar SRR (see Fig. 5), and each single-ring mode has again split into a pair of modes with different symmetries52. However, we found that the dipole moments exhibited by the resonance modes in a BC-SRR52 are quite different from those in the coplanar SRR51. In particular, in addition to the perpendicular magnetic polarization mz, two more in-plane polarizations mx, my can also be induced for the BC-SRR under specific conditions. We summarized the characteristics of the EM polarizations for the lowest four modes in Table 1. Two important conclusions can be drawn. First, all the resonance modes in a BCSRR are completely free of bi-anisotropy (i.e., either purely magnetic or purely electric). This important character has also been noted previously43, 47, 49. Second, some resonance modes (say, 1 L ) could possess two magnetic moments simultaneously. The second property of the BC-SRR enables us to design a super resonance unit for metamaterials. Metamaterials that possess magnetic responses along all three dimensions drew much attention recently76-82. As many resonant structures are inherently anisotropic, a standard method to design 3D magnetic materials is to rotate the unite cell element and combine it with the original one to form an isotropic unit cell76-82. Recently, several non-SRR-based schemes were also Fig. 6 Dipole moments (in arbitrary units) of the double-ring SRR (same as Fig. 5) induced by external plane waves with E and k directions specified in the legends. Reproduced from51 with permission from the American Institute of Physics. Fig. 7 Amplitudes of (a) electric polarizability e y e y and (b) bi-anisotropic polarizability e y m z as the functions of /u, for double-ring SRR's with R = 4 mm, a = 0.1 mm, and different values of d specified in the legend. Reproduced from51 with permission from the American Institute of Physics. (b) (a) (b) (a) (d) (c) REVIEW Resonance properties of metallic ring systems DECEMBER 2009 | VOLUME 12 | NUMBER 1258 REVIEW Resonance properties of metallic ring systems proposed to fabricate 3D isotropic metamaterials85-88. Here, we provide an alternative approach. We demonstrate that a layered structure, composed by planar arrays of BC-SRR's, can exhibit magnetic responses along all three dimensions at the same frequency. Since the structure is basically a multilayer system, it is very easy to fabricate, particularly in higher frequency regime where the complex 3D structures are relatively difficult to fabricate. As shown in Fig. 9a, the unit cell of the designed metamaterial contains two BC-SRR's, with one rotated by 90 degrees with respect to the other. To understand the resonance properties of the designed system, we employed FDTD simulations84 to calculate the transmissions of EM plane waves with magnetic fields polarized along different directions and with different propagation directions52. The transmission spectra in different cases are compared in Fig. 9b. It is clearly shown that for B field along all three directions, a common resonance is excited at the frequency 0.386u, implying that the system exhibits strong responses to external magnetic fields along all three directions at this particular frequency. Conclusions In this concise review, we have briefly summarized our recent efforts in establishing a rigorous mode-expansion theory and employing it to study the EM resonance properties of various SRR structures. The theory was established under the quasi-static limit and can be applied to study the resonance eigenmodes in arbitrary metallic ring systems, in which the inductive/capacitive effects were included completely and the relevant circuit parameters were calculated rigorously. The theory has been employed to study various SRR systems, including a single-ring SRR, a coplanar double-ring SRR and a broadside coupled SRR, and the obtained results are generally in good agreements with the FDTD simulations on realistic structures. We have also developed several analytical formulas, which agree well with FDTD and available experimental results, and might be useful for future metamaterial designs. In a very recent work, Page et al.89 established a theoretical approach which can also be applied to calculate all resonance frequencies of ring-like resonators. That approach can give additional physical insight into how geometry parameters affect the resonance frequencies by using the concepts of characteristic impedances and effective phase velocities89. However, that theory relies on finding a well-defined transmission-line description for Fig. 9 (a) A schematic picture of the designed 3D magnetic material, with the inset showing the unit cell of structure. Here, R = 4 mm, 2a = 0.2 mm, t = 0.05 mm, d = 3 mm, b = 11 mm and the gap width = /40. (b) FDTDcalculated transmission spectra through the designed 3D magnetic material with different probing EM waves as specified in the figure. Reproduced from52 with permission from the American Physical Society. Fig. 8 SRR resonance frequency (measured in GHz) as a function of t (setting w = 0.9 mm, solid line) and w (setting t = 0.2 mm, dotted line), calculated by our analytical formula. Symbols are experimental data taken from Figs. 7 and 8 of36. Reproduced from51 with permission from the American Institute of Physics. Table 1 Characteristics of electric/magnetic polarizations of low-lying modes for a BC-SRR and a single-ring SRR. Reproduced from52 by permission of the American Physical Society. System Mode px py mz mx mz Single 1 No Yes Yes No No Double 1 L No Disappear Enhanced New No 1 H No Enhanced Disappear No No Single 2 Yes No No No No Double 2 L Enhanced No No No No 2 H Disappear No No No New (b) (a) Resonance properties of metallic ring systems REVIEW DECEMBER 2009 | VOLUME 12 | NUMBER 12 59 the structure and still needs some model parameters determined from other methods89. We believe that our theory and that one89 are complementary in many aspects and are applicable to different situations. While there have been lots of efforts to study the SRRs theoretically, we believe an analytical theory established on more rigorous grounds is still highly desirable, particularly since it can yield more physical insights and analytical formulas helpful for researchers working in this area. We look forward to more applications of our theory and extensions to other related problems. Acknowledgements This work was supported by the China-973 Program (2004CB719800), the NSFC (60725417, J0730310) and PCSIRT. STC is supported in part by the US DOE. References 1. Veselago, V. G., Sov. Phys. Usp. (1968) 10, 509. 2. Landau, L., and Lifschitz, E. M., Electrodynamics of Continuous Media, Elsevier, New York (1984). 3. Pendry, J. B., et al., IEEE Trans. Microwave Theory Tech. (1999) 47, 2075. 4. Smith, D. R., et al., Phys. Rev. Lett. (2000) 84, 4184. 5. Shelby, R. A., et al., Science (2001) 292, 77. 6. Moser, H. O., et al., Phys. Rev. Lett. (2005) 94, 063901. 7. Dolling, G., et al., Opt. Lett. (2007) 32, 53. 8. Dolling, G., et al., Opt. Lett. (2006) 31, 1800. 9. Zhang, S., et al., Phys. Rev. Lett. (2005) 95, 137404. 10. Shalaev, V. M., et al., Opt. Lett. (2005) 30, 3356. 11. Pendry, J. B., Phys. Rev. Lett. (2000) 85, 3966. 12. Fang, N., et al., Science (2005) 308, 534. 13. Ono, A., et al., Phys. Rev. Lett. (2005) 95, 267407. 14. Belov, P. A., et al., Phys. Rev. B (2006) 73, 033108. 15. Engheta, N., IEEE Antennas Wireless Propag. Lett. (2002) 1, 10. 16. Zhou, L., et al., Appl. Phys. Lett. (2005) 86, 101101. 17. Li, H., et al., Appl. Phys. Lett. (2006) 89, 104101. 18. Li, J., et al., Phys. Rev. Lett. (2003) 90, 083901. 19. Shadrivov, I. V., et al., Phys. Rev. Lett. (2005) 95, 193903. 20. Sun, S., et al., Phys. Rev. E (2007) 75, 066602. 21. Leonhardt, U., Science (2006) 312, 1777. 22. Pendry, J. B., et al., Science (2006) 312, 1780. 23. Schurig, D., et al., Science (2006) 314, 977. 24. Klein, M. W., et al., Science (2006) 313, 502. 25. Feth, N., et al., Opt. Lett. (2008) 33, 1975. 26. Wang, B., et al., Opt. Express (2008) 16, 16058. 27. O'Brien, S., et al., Phys. Rev. B (2004) 69, 241101. 28. Zharov, A. A., et al., Phys. Rev. Lett. (2003) 91, 037401. 29. Liu, Y., et al., Phys. Rev. Lett. (2007) 99, 153901. 30. Dolling, G., et al., Opt. Lett. (2005) 30, 3198. 31. Podolskiy, V. A., et al., Opt. Express (2003) 11, 735. 32. Dolling, G., et al., Science (2006) 312, 892. 33. Mary, A., et al., Phys. Rev. Lett. (2008) 101, 103902. 34. Al, A., and Engheta, N., Phys. Rev. B (2008) 78, 085112. 35. Al, A., et al., Opt. Express (2006) 14, 1557. 36. Aydin, K., et al., New J. Phys. (2005) 7, 168. 37. Radkovskaya, A., et al., Microwave Opt. Technol. Lett. (2005) 46, 473. 38. Boulais, K. A., et al., Appl. Phys. Lett. (2008) 93, 043518. 39. Aydina, K., and Ozbay, E., J. Appl. Phys. (2007) 101, 024911. 40. Aydin, K., et al., Opt. Express (2004) 12, 5896. 41. Sauviac, B., et al., Electromagnetics (2004) 24, 317. 42. Shamonin, M., et al., J. Appl. Phys. (2004) 95, 3778 . 43. Marqués, R., et al., IEEE Trans. Antennas Propag. (2003) 51, 2572. 44. Aznar, F., et al., Appl. Phys. Lett. (2008) 92, 043512. 45. Zhurbenko, V., et al., Microwave Opt. Technol. Lett. (2008) 50, 511. 46. Shamonin, M., et al., Microwave Opt. Technol. Lett. (2005) 44, 133. 47. García-García, J., et al., J. Appl. Phys. (2005) 98, 033103. 48. Baena, J. D., et al., Phys. Rev. B (2004) 69, 014402. 49. Marques, R., et al., Phys. Rev. B (2002) 65, 144440. 50. Zhou, L., and Chui, S. T., Phys. Rev. B (2006) 74, 035419. 51. Zhou, L., and Chui, S. T., Appl. Phys. Lett. (2007) 90, 041903. 52. Huang, X. Q., et al., Phys. Rev. B (2008) 77, 235105. 53. Chui, S. T., et al., J. Appl. Phys. (2008) 104, 034305. 54. Katsarakis, N., et al., Appl. Phys. Lett. (2004) 84, 2943. 55. Markos, P., and Soukoulis, C. M., Phys. Rev. E (2002) 65, 036622. 56. Zhou, J., et al., Phys. Rev. Lett. (2005) 95, 223902. 57. Yen, T. J., et al., Science (2004) 303, 1494. 58. Linden, S., et al., Science (2004) 306, 1351. 59. Zhou, J., et al., Opt. Express (2007) 15, 17881. 60. Klein, M. W., et al., Opt. Lett. (2006) 31, 1259. 61. Economou, E. N., et al., Phys. Rev. B (2008) 77, 092401. 62. Zhao, Q., et al., Appl. Phys. Lett. (2007) 90, 011112. 63. Enkrich, C., et al., Phys. Rev. Lett. (2005) 95, 203901. 64. Bilotti, F., et al., IEEE Trans. Antennas Propag. (2007) 55, 2258. 65. Azad, A. K., et al., Appl. Phys. Lett. (2008) 92, 011119. 66. Smith, D. R., et al., Appl. Phys. Lett. (2000) 77, 2246. 67. Smith, D. R., et al., Phys. Rev. B (2002) 65, 195104. 68. Popa, B., and Cummer, S. A., Phys. Rev. B (2005) 72, 165102. 69. Alicia, K. B., and Ozbay, E., J. Appl. Phys. (2007) 101, 083104. 70. Little, B. E., et al., J. Lightwave Technol. (1997) 15, 998. 71. Marques, R., et al., Phys. Rev. Lett. (2002) 89,183901. 72. Xu, H., et al., Appl. Phys. Lett. (2008) 92, 041122. 73. Wiltshire, M. C. K., et al., Science (2001) 291, 849. 74. Wiltshire, M. C. K., et al., Opt. Express (2003) 11,709. 75. Zhang, S., et al., Phys. Rev. Lett. (2005) 94, 037402. 76. Verney, E., et al., Phys. Lett. A (2004) 331, 244. 77. Baena, J. D., et al., Appl. Phys. Lett. (2006) 88, 134108. 78. Baena, J. D., et al., Appl. Phys. Lett. (2007) 91, 191105. 79. Baena, J. D., et al., Phys. Rev. B (2007) 76, 245115. 80. Gay-Balmaz, P., and Martin, O. J. F., Appl. Phys. Lett. (2002) 81, 939. 81. Zhao, Q., et al., Phys. Rev. Lett. (2008) 101, 027402. 82. Koschny, Th., et al., Phys. Rev. B (2005) 71, 121103. 83. Jackson, J. D., Classical Electromagnetic, Wiley, New York (1999), 3rd edition. 84. CONCERTO 4.0, Vector Fields Limited, England, 2005. 85. Zedler, M., et al., IEEE Trans. Micro. Theory Tech. (2007) 55, 2930. 86. Grbic, A., and Eleftheriades, G. V., J. Appl. Phys. (2005) 98, 043106. 87. Alitalo, P., et al., J. Appl. Phys. (2006) 99, 064912. 88. Vendik, I., et al., Micro. Opt. Tech. Lett. (2006) 48, 2553. 89. Page, J. E., et al., Int. J. Electron Commun. (AEU) (2008), doi: 10.1016/j.aeue.2008.02.006 ISSN:1369 7021 Elsevier Ltd 2009DECEMBER 2009 | VOLUME 12 | NUMBER 1260 REVIEW Mie resonance-based dielectric metamaterials Mie resonance-based dielectric metamaterials Metamaterials are artificial electromagnetic media structured on a scale much shorter than their operating wavelength. Under this condition they can be considered as homogeneous media whose electromagnetic properties rely mainly on the basic cell rather than periodic effects as it is the case for photonic crystal or more generally electromagnetic band gap material. Their basic cells are generally constituted of resonant inclusions which yield a phaseshift in the material response above the resonant frequency. As a consequence, their effective permittivity and permeability can be negative either in separate or overlapping frequency bands, a unique and distinct property that is not observed in naturally occurring materials1 . For the latter condition they can be considered as double negative or negative index media hence opening the effective parameter space, so that new functionalities in the light scattering can be envisaged. Also recently, the achievement of near-zero or less than unity values of the effective permittivity and permeability was also recognized as one of the major goals of this research area. Great progress in electromagnetic metamaterials has been achieved for these unique physical properties and novel potential applications, such as negative refraction2, 3, perfect lens4, 5 and cloaking6-8 have been shown. They have been experimentally demonstrated in a frequency range from the radio frequencies9 to millimeter waves10, infrared wavelengths11-13, and visible optics14. Up to date, most of metamaterials are constructed with the use of sub-wavelength resonant metallic elements. For instance, the first left-handed Increasing attention on metamaterials has been paid due to their exciting physical behaviors and potential applications. While most of such artificial material structures developed so far are based on metallic resonant structures, Mie resonances of dielectric particles open a simpler and more versatile route for construction of isotropic metamaterials with higher operating frequencies. Here, we review the recent progresses of Mie resonance-based metamaterials by providing a description of the underlying mechanisms to realize negative permeability, negative permittivity and double negative media. We address some potential novel applications. Qian Zhao1,2, Ji Zhou1,*, Fuli Zhang3, Didier Lippens3 1 State Key Lab of New Ceramics and Fine Processing, Department of Materials Science and Engineering, Tsinghua University, Beijing, PRC 2 State Key Lab of Tribology, Department of Precision Instruments and Mechanology, Tsinghua University, Beijing, PRC 3 Institut d'Electronique de Micro-électronique et de Nanotechnologie, UMR CNRS 8520, University of Lille 1, Villeneuve d'Ascq Cedex, France *E-mail: zhouji@mail.tsinghua.edu.cn Mie resonance-based dielectric metamaterials REVIEW DECEMBER 2009 | VOLUME 12 | NUMBER 12 61 metamaterials (LHMs) with simultaneously negative permittivity and permeability have been fabricated by means of metallic split ring resonators (SRRs) and wires15, 16, for tailoring the magnetic and electric responses, respectively. Other metallic elements, such as -shaped structures17, 18, U-shaped structures19, staplelike structures20, paired rods21, dendritic22 and fishnet structures23, are also successfully used to fabricate LHMs. Usually, the metallic constitutive elements have conductive loss and anisotropic electromagnetic responses. Several authors have suggested methods24-26 to construct isotropic metamaterials by combining metallic SRRs and wires. However it is difficult to fabricate the bulk arrays of complex geometry with submicron or nanoscale sizes in order to generate a negative permeability effect at infrared and optical frequencies27. Recently, another route based on the interaction between electromagnetic waves and dielectric particles28, 29 was proposed to achieve the electric or magnetic resonances. The Mie resonances of dielectric inclusions provide a novel mechanism for the creation of magnetic or electric resonance based on displacement currents, and offer a simpler and more versatile route for the fabrication of isotropic metamaterials operating at higher frequencies. The progress on metallic elements-based metamaterials has been reviewed in many articles30-32 and books33, 34. In this review, we focus on the scattering mechanisms based on Mie resonance in dielectric particles and describe the recent progress in these metamaterials including ferroelectric and polaritonic particles and their tunable behaviors. Mie resonance of particles From the viewpoint of scattering theory, all scattering objects can be represented by effective electric and/or magnetic polarizability densities. Light scattering by small (relative to the incident light wavelength) spherical particles is a fundamental topic in classical electrodynamics35, and is based upon the exact Mie solution of the diffraction problem36. The scattered field of a single isolated dielectric sphere with radius r0 and relative refractive index n can be decomposed into a multipole series with the 2m-pole term of the scattered electric field proportional to )()()()( )()()()( '' '' nxxxnxn nxxxnxn a mmmm mmmm m - = (1) whereas the 2m-pole term of the scattered magnetic field is proportional to )()()()( )()()()( '' '' nxxnxnx nxxnxnx b mmmm mmmm m - = (2) where x=k0r0, k0 is the free-space wavenumber, and m(x) and m(x) are the Riccati-Bessel functions. The primes indicate derivation with respect to the arguments. The scattering coefficient am and bm are related to the electric and magnetic responses of the sphere, respectively. From the Mie theory we can calculate the electric and magnetic dipole coefficients, a1 and b1, respectively. From effective medium theory, we know that these are the multipole terms which contribute most significantly to the effective permittivity and Fig. 1 Electric and magnetic field distribution in a dielectric cube with the magnetic field polarized along the z axis and electric field polarized along the y axis. (a) Electric field in the plane z=0 near the first Mie resonance. (b) Magnetic field in the plane y=0 near the first Mie resonance. (c) Electric field in the plane z=0 near the second Mie resonance. (d) Magnetic field in the plane y=0 near the second Mie resonance. (Reprinted with permission from37. 2008 American Physical Society.) (b)(a) (c) (d) REVIEW Mie resonance-based dielectric metamaterials DECEMBER 2009 | VOLUME 12 | NUMBER 1262 permeability of the particle composite. Since the magnetic response of a nonmagnetic particle is usually weak, it is important to strengthen the electromagnetic resonant behavior. For the lowest resonant frequencies of a1 and b1, the sphere exhibits electric and magnetic dipoles. This conclusion can be assessed from the electromagnetic intensity distributions in a high dielectric ceramic cube for a plane incident wave propagating along the x axis37 (Fig. 1). It can be seen that the electric or magnetic fields are mainly localized in the cubes. The azimuthal component of the displacement current inside each cube is greatly enhanced at the first Mie resonance (Fig. 1a) resulting in a large magnetic field along the z axis (Fig. 1b) which corresponds to the TE011 Mie resonance mode. At the second Mie resonance, the y component of the displacement current inside the cubes increases dramatically (Fig. 1c) and hence with a large magnetic field along the azimuth (Fig. 1d), which corresponds to the TM011 Mie resonance mode. These electric and magnetic dipole resonances act as artificial `atoms' which form the basis of new optical materials. In a material made up of a collection of such resonant particles, their combined scattering response can act like a material with almost arbitrary values of effective permittivity and permeability. This idea can be verified by using the model proposed in 1947 by Lewin38 who considered the electromagnetic scattering properties of a composite material which was constituted of an array of lossless magnetodielectric spheres (2 and 2) embedded in another background matrix (1 and 1). The effective permittivity eff and permeability eff expressions based on Mie theory are as follows38. - - + += f e e f eff v bF bF v )( 2)( 3 11 (3) - - + += f m m f eff v bF bF v )( 2)( 3 11 (4) where cossin)1( )cos(sin2 )( 2 +- =F (5) 21 =eb , 21 =mb (6) The volume fraction of the spherical particles, 30 )( 3 4 p r vf = , 2200 rk= , r0 and p are the particle radius and the lattice constant, respectively. Eq 5 shows that F() is a resonant function and becomes negative above resonance in some range of , resulting in the negative permittivity or permeability for negative values of F() with a magnitude on the order of unity as given by Eqs. (3) and (4). In Lewin's model, the constitutive parameters were formulated only considering the spheres resonating either in the first or second resonant modes of the Mie series. This is because the higher order Mie resonances often occur at frequencies beyond the long wavelength limit, and thus the Clausius-Mossotti equation does not apply. Then, Jylha et al.39 improved those formulations by taking into account the electric polarizabilities of spheres operating in the magnetic resonant modes. Independent of Lewin's model, O'Brien and Pendry28 showed that a negative effective permeability can be obtained in a two-dimensional array of ferroelectric rods with the magnetic field polarized along the axes of the rods. Although the underlying physics is the same, the authors used another method40 (transfer matrix method) to find the effective media values with similar conclusion. The aforementioned theoretical results show that a high permittivity microstructured medium can exhibit isotropic negative values of the effective permeability and permittivity. Mie resonance as a new route for metamaterials With the rapid development of LHMs, Lewin's model was reconsidered and introduced into the realm of metamaterials to realize single and double negative media. Based on Lewin's model, Holloway et al.29 numerically demonstrated the feasibility of achieving simultaneously negative eff and eff in the magnetodielectric sphere arrays for wavelengths where the electric and magnetic resonances are excited in the spheres. Eqs. (3) and (4) show that eff and eff depend on the permeability and permittivity of the dielectric inclusions and host medium, as well as the volume fraction of spheres of radius r0. Fig. 2 shows eff and eff calculated for f = 0.5, 1 = 1 = 1, 2 = 40, and Fig. 2 Calculated effective permittivity eff and permeability eff of the magnetodielectric sphere arrays composite. (Reprinted with permission from29. 2003 IEEE.) Mie resonance-based dielectric metamaterials REVIEW DECEMBER 2009 | VOLUME 12 | NUMBER 12 63 2 = 200 as a function of k0r0. There are two regions where both eff and eff become negative with the bandwidths becoming narrower by decreasing the volume fraction f. From a practical point of view, many kinds of materials and shapes of particles have been proposed in the literature to fabricate negative or less than unity permeability and permittivity dielectric metamaterials operating in different frequency regions. The designing ideas are summarized in the following. Magnetic response The realization of abnormal permeability is a tricky issue for various metamaterials, because the magnetic response of materials is usually weak, especially at infrared or visible frequencies. Lewin's model shows that two methods based on Mie resonance can be used to achieve a negative effective permeability effect. The first one is to use magnetodielectric inclusions with large values of permeability and permittivity. The second method is to use nonmagnetic dielectric particles with extremely large permittivity values. In the former case, two terms be and bm in Eqs. (3) and (4) contribute to the negative permeability, while only be plays an important role for the latter. The possibility to use magnetodielectric particles has been numerically demonstrated29. However a magnetodielectric particle with simultaneously large values of permittivity and permeability seems physically unattainable even in the microwave. Eq. (4) indicates that nonmagnetic spheres with very high permittivity values can also be employed to induce negative permeability and permittivity effects at the different Mie resonance frequencies. Polaritonic materials, such as ionic solids and polar semiconductors, or ferroelectric materials can provide the large permittivity. For ferroelectric materials, their extreme high permittivity values can be preserved at least up to millimeter wavelengths41. At infrared frequencies however a roll-off of the dielectric constant is observed so that they cannot be used in this frequency range. In contrast, the lattice resonance in polaritonic crystals can be exploited to tailor the permittivity resonance at infrared and optical frequencies. As a consequence, the polaritonic resonance of crystals could be potentially used in the infrared spectral region. The relative permittivity is42 -- - += iT TL r 22 22 1)()( , (7) where () is the high-frequency limit of the permittivity, T and L are the transverse and longitudinal optical phonon frequencies, and is the damping coefficient. Therefore, large values of r() can be achieved near the transverse phonon frequency. A three-dimensional dielectric composite consisting of an array of dielectric cubes [Ba0.5Sr0.5TiO3 (BST)] with a relative permittivity of 1600 in a Teflon substrate was fabricated (Fig. 3a) to demonstrate the feasibility of this full dielectric metamaterial route. On this basis, isotropic negative values of the effective permeability were experimentally demonstrated in the microwave region37. The dielectric cube side length l was 1.0 mm for a lattice constant of 2.5 mm. And the first TE and TM resonance modes, i.e., magnetic and electric resonances were determined by transmission measurements at 6.12 and 8.28 GHz respectively. Using smaller cubes (l =0.75 mm) with a magnetic resonance near 8.5 GHz, in conjunction with an electric response from metallic wires, researchers fabricated double negative media. The results of transmission measurements are displayed in Fig. 3b and the retrieved electromagnetic parameters (Fig. 3c) further verified the negative permeability near the first Mie resonance. A rectangular dielectric block43 and piezoelectric disks44 were also experimentally verified to design very low-loss magnetic metamaterials. Fig. 3 A three-dimensional dielectric composite with isotropic negative permeability. (a) Photograph of BST cubes arrayed in Teflon substrate. (b) Transmission for the dielectric cube array only (dashed line), wire array only (dotted line), and the combination of BST cubes and wires (solid line). Inset of Fig. 3(b) shows the measured and calculated transmission phase. (c) Retrieved refractive index and permeability (inset). (Reprinted with permission from37. 2008 American Physical Society.) (b) (a) (c) REVIEW Mie resonance-based dielectric metamaterials DECEMBER 2009 | VOLUME 12 | NUMBER 1264 Also a two-dimensional square lattice of dielectric disk inserted between two metallic parallel-plate waveguide (Fig. 4a) was also used to demonstrate negative refraction, where the macroscopic behavior of dielectric disk provides negative effective permeability and the waveguide plays a role in a TE cut-off waveguide leading to negative effective permittivity45. A dielectric block [(Zr,Sn)TiO4 ceramics, dielectric constant 36.7] with a thin metallic rod screwed inside was proposed to fabricate gradient metamaterial lenses and numerically demonstrated to deflect and focus the incident plane waves46. Dielectric-resonator-based composite right/left-handed transmission lines used to the design of leaky wave antenna can alleviate the significantly large conducting loss and increase the radiation efficiency47. Terahertz metamaterials based on the Mie resonance of polycrystalline TiO2 cubes-arrays on the Al2O3 substrate (Fig. 4b) were also experimentally demonstrated by Shibuya et al.48, in which the negative permeability and permittivity occur around 0.28 and 0.38 THz, respectively. A three-dimensional collection of polaritonic spheres was proposed to obtain isotropic negative effective permeability near the first Mie resonance at infrared frequencies49. The calculated effective parameters (LiTaO3 crystal) reported in this reference are shown in Fig. 5 and the isotropy of electromagnetic properties was also verified by a comparison with a full multiple scattering approach. Semiconductor nanoparticles, such as CuCl with a Z3 exciton line at 386.93 nm, Cu2O with a 2P exciton50, and GaP51 were also suggested to realize negative permeability within and below the optical region. Metal nanoclusters possessing large permittivity at visible frequency can also be used to obtain magnetic Mie resonance52, 53. Similar to spherical or cubic dielectric elements, the cylindrical particles can also generate the Mie electromagnetic resonances. The most important issue is to determine the resonant modes. For Fig. 5 The calculated effective relative permeability (a) and permittivity (b) of a collection of LiTaO3 spheres. (Reprinted with permission from49. 2005 American Physical Society.) Fig. 4 Schematic of metamaterials based on Mie resonance. (a) A two-dimensional lattice structure for one dielectric-resonator in the cutoff microwave waveguide. (Reprinted with permission from45. 2007 IEEE.) (b) Terahertz metamaterial consisting of polycrystalline TiO2 cubes-arrays on the Al2O3 substrate. (Reprinted with permission from48. 2008 Metamaterials.) (b)(a) (a) (b) Mie resonance-based dielectric metamaterials REVIEW DECEMBER 2009 | VOLUME 12 | NUMBER 12 65 a TE polarization (E field perpendicular to the rod axis), the lowest Mie resonance mode (TE0) corresponds to the magnetic response, resulting in negative permeability values. A two-dimensional array of ferroelectric rods28, 54 and polaritonic rods55 were proposed to obtain negative effective permeability56, which can be considered as the TE0 mode. For TM polarization (E field parallel to the rod axis), the lowest two Mie resonances modes, TM0 and TM1, correspond to the electric and magnetic responses, and consequently lead to negative permittivity and permeability, respectively. The electromagnetic field distribution displayed for the TM1 mode (Fig. 6) can further clarify the magnetic resonance mechanism57. The electric field is distributed along the z directions with opposite signs along the propagation direction (Fig. 6b), accounting for a strong circular displacement current (Fig. 6d). Such displacement current results in a large magnetic field along the y axis (Fig. 6c), which corresponds to the TM1 mode. Electric response An electric response can be accomplished with simpler metallic structures, such as uncoupled rods or strips. The first method to obtain negative permittivity is the bulk metals at optical frequencies, where conduction electrons can be assumed to be reasonably free and plasma-like behavior is responsible for a negative dielectric permittivity at frequencies less than the plasma frequency58. Usually, the plasma frequencies of metals are at ultraviolet frequencies and dissipation is small. As the frequency is much lower than the plasma frequency, the imaginary part of the complex permittivity increases dramatically while very large negative values of the real part are obtained. Pendry et al.59 suggested a metallic wire array structure to realize a plasma-like state. With such a configuration, the negative permittivity frequency range can be tuned by the lattice constant and the wire diameter in the low frequency spectral region even at microwave frequencies. Additionally, negative dielectric permittivity can also be obtained in more ordinary dielectric media with bound charges, within a frequency band above a resonance frequency, where the resonant Lorentz permittivity occurs58. Another method is to use the electric resonant mode of the Mie resonance of dielectric particles. For the dielectric sphere or cube, it can be equivalent to a dipole at the second resonant mode as exemplified by the field mapping shown in Fig. 1. For a dielectric column particle, it can be equivalent to an electric dipole at the first resonance mode (TM0) and can result in negative permittivity. Negative refraction The mechanisms of electric and magnetic resonances in dielectric particles (spheres, cubes or rods) have been analyzed above. Negative refraction can be fulfilled by combing the two resonances together. However, the first electric resonance (TM mode) is at a higher frequency than the fundamental magnetic resonance (TE mode) for the identical sphere. Due to the different resonance frequencies of TE and TM modes in the different-sized particles, we can consider the conditions when the first lowest resonance of TM011 mode related to a bigger sphere coincides with the TE011 resonance in a smaller sphere. Recently, Vendik et al.60, 61 numerically studied an artificial double negative media whose basic unit cell is composed by two Fig. 6 Electric and magnetic field distributions in a dielectric rod at the second resonant mode (TM1 mode). (a) Unit cell configuration. (b) Electric field distribution. (c) Magnetic field distribution. (d) Equivalent current ring. (Reprinted with permission from57. 2007 American Physical Society.) (b) (d) (a) (c) REVIEW Mie resonance-based dielectric metamaterials DECEMBER 2009 | VOLUME 12 | NUMBER 1266 REVIEW Mie resonance-based dielectric metamaterials dielectric spheres of different sizes. The larger sphere was used for the negative permittivity while the small one allows achieving a negative permeability in the same microwave frequency band. At the same time, two sets of spheres, having the same size but different materials, were also developed to realize negative refraction62. More recently, a threedimensional isotropic negative-index composite at infrared or visible frequencies was reported51, 63-66. The proposed homogeneous isotropic structures consist of dielectric spheres (gallium phosphide) embedded randomly in a negative permittivity host medium (Cesium)51, or two interpenetrating lattices of spheres63-66. One lattice ensures a negative permeability using a polaritonic material (LiTaO3, SiC, CuCl) and the other lattice creates a negative permittivity effect by using a plasmonic material (n-type Ge, Au, MgB2). Negative refraction index effect exists not only in the situation of a regular lattice arrangement but also for randomly distributed nanoparticles when the losses are ignored. However, the numerical results also demonstrated that the negative refraction could not be achieved owing to the large imaginary part of the wave vector corresponding to evanescent rather than propagating waves when the losses of the constitutive materials were taken into account. Another method to fabricate isotropic LHMs based on Mie resonance is using only one kind of micron-scale non-magnetic coated spheres67-69. The underlying physical mechanisms correspond to a negative effective permeability effect due to polaritonic sphere core while a negative effective permittivity effect results from an electric-dipole resonance of sphere coating on its outer surface whose dispersion follows a Drude model. For an isolated sphere, an electric dipole resonance can be driven when its material permittivity is -2. Since this permittivity value is negative, the electric field is evanescent within the sphere so that such electric dipole resonance is a surface resonance in contrast to the volume effect of the magnetic resonance. Therefore, the coating can be designed to have a negative permittivity. Note that the magnetic resonance of the core is hardly affected, as long as the permittivity of the coating remains small in comparison to the large permittivity of the core. The spheres with a core of a polaritonic crystal LiTaO3 and the coated thin layer of a Drude model semiconductor (or a polaritonic material) were used to demonstrate isotropic negative refraction70. The calculated effective electromagnetic parameters are shown in Fig. 7. Such threedimensional LHMs consisting of metal-coated semiconductor spheres can be used to realize subwavelength imaging71 and electromagnetic transparency72, 73. Besides dielectric spheres array, the electric and magnetic Mie resonances in dielectric rods can also be used to achieve negative permittivity and permeability values. Under TM illumination, a resonant permittivity due to the TM0 mode excitation and a resonant permeability due to the TM1 mode excitation can be used to realize negative permittivity and permeability, respectively. Schuller et al.74 experimentally and numerically observed and identified the Mie resonance modes of SiC particles at mid-IR under various polarization conditions. Also they proposed to obtain a negative refractive index by combining the two resonances of TM0 and TM1 modes (Fig. 8). A theory on the electric and magnetic dipole activities of dielectric rods in s-polarized light was presented recently. The authors claimed that large wavelength-to-period ratios do not necessarily result in an isotropic metamaterial. They also suggested that silicon rod arrays could exhibit a true metamaterial left handed dispersion branch in the visible to mid-IR despite the moderate value of the refractive index (n~3.5)75. Such a conclusion is interesting by considering Mie resonance in moderate permittivity materials in optics. It has however to be checked by experiments in order to discriminate negative refraction effects resulting from the conventional band folding in the diffraction regime76 from pure left handed branch effects in the Fig. 7 The effective (a) permeability, (b) permittivity, and (c) index of a collection coated spheres. The cores are made of LiTaO3 with radius 4 m, and the coatings are a Drude material with radius 0.7 m. (Reprinted with permission from70. 2006 American Physical Society.) (b) (a) (c) Mie resonance-based dielectric metamaterials REVIEW DECEMBER 2009 | VOLUME 12 | NUMBER 12 67 long wavelength regime. A verification of negative refraction in a TM illuminated array of large permittivity ceramic rods was experimentally verified at microwave frequencies, corresponding to the combination of TM0 and TM1 modes57. All-dielectric cloaks Conformal transformation of electromagnetic domains has been proposed as an exciting approach to control the flow of propagating waves and realize invisibility cloak6. Effective permeability can be less than unity around the magnetic resonance and such metamaterials have been suggested to construct invisibility cloak7, 8. An all-dielectric cloak (Fig. 9) consisting of radially positioned micrometer-sized ferroelectric cylinders was suggested to perform cloaking at 0.58 THz, which exhibits a strong magnetic resonance based on Mie theory77. At last, Silicon Carbide (SiC) rod, a polaritonic material with phonon resonance bands centered around 12.5 m, was also suggested to built transparency cloak (Fig. 10) at mid-infrared with the TE resonance mode78. To sum up, an all-dielectric configuration provides an attractive route for designing cloaking devices at microwave, terahertz and infrared frequencies. Tunable Mie resonance-based metamaterials As seen in the previous sections, resonance effects in the electric and magnetic responses appear as a necessary condition for fabricating left-handed metamaterials. Such resonances are strongly dependent on the geometrical dimensions and on the dielectric properties of the constitutive elements. Usually negative values can only be achieved over a narrow frequency range near the resonances, especially for the magnetic resonance. From the application point of view, and for a deeper understanding of the intrinsic properties of negative media, it is desirable to implement structures with tunable and reconfigurable resonant properties79. Some tunable metamaterials based on the metallic structures have been proposed by modifying the locally dielectric or permeability environment. For example, a control of the electric and magnetic responses of SRRs and related configurations was experimentally demonstrated through photoexcitation of free carriers in a GaAs substrate80, electrically or magnetically controlled liquid crystals81, 82, along with electrorehological fluids83, 84, ferroelectric85, ferromagnetic materials86-89 and other methods90. All these examples correspond however to anisotropic tunable metamaterials whereas Fig. 8 (a) Calculated effective permeability for a normal incidence TE illuminated array of infinitely long SiC rods. (b) Calculated permittivity (permeability) due to excitation of the zeroth (first) order TM mode. (Reprinted with permission from74. 2007 American Physical Society.) Fig. 9 (a) Schematic of a terahertz all-dielectric cloak. Steady-state Ez pattern calculated at 0.58 THz for a copper rod without (b) and with cloak (c). (d) Magnified view of the field pattern of (c). (Reprinted with permission from77. 2008 Optical Society of America.) Fig. 10 Schematic of a cylindrical non-magnetic cloak for TE polarization at mid-infrared. (Reprinted with permission from78. 2008 Optical Society of America.) (a) (b) (b) (d) (a) (c) REVIEW Mie resonance-based dielectric metamaterials DECEMBER 2009 | VOLUME 12 | NUMBER 1268 isotropic properties can be more suitable for potential applications notably for all angle negative refraction. The first dynamic tuning of isotropic metamaterial relying on Mie resonance has been demonstrated recently by altering the dielectric property of the basic cell91. As expected from the Mie resonance theory, at the first resonance the dielectric sphere is equivalent to a magnetic dipole with a resonance frequency )/( 20 rc within the long-wavelength limit. Usually, the permittivity of the high ceramic inclusions varies as a function not only of the local field, but also of temperature92. Therefore, a variation of the effective permeability of the composite material can be realized by changing the sample temperature. For a proof of this principle, a simple cubic lattice of ceramic cubes of 0.45 mm side length (BST doped with 5wt% MgO) were arrayed in a Teflon substrate with a lattice constant of 1.25 mm. The microwave scattering parameters were measured under various temperature conditions (Fig. 11a, b). The magnetic resonance corresponding to the first Mie resonance in the dielectric cubes can be continuously and reversibly adjusted from 13.65 GHz to 19.28 GHz with a temperature changing from -15°C to 35°C. The frequency dependence of the effective permeability, displayed in Fig. 11c, shows that negative permeability values can be achieved in a frequency band of about 6 GHz by a temperature variation of 50°C. It is believed that this temperature controlled metamaterial could be used for the design of adaptive three-dimensional metamaterials and invisibility cloaks which exhibit basically a very narrow fractional bandwidth of the order of 1%93. Another method used to adjust the negative refraction of Mie resonance is to alter the dielectric property of the background medium. Khoo et al.94 proposed nanospheres dispersed liquid crystals to realize tunable negative­zero­positive index of refraction in the optical and terahertz regimes. Outlook As an alternative method for the design of electromagnetic metamaterials, the dielectric particles show several advantages, notably in terms of isotropic parameters, and the fabrication techniques targeting at higher frequencies of operation. Although several experimental demonstrations have allowed the verification of the first principles at microwave and terahertz frequencies, it appears that the research on this area is at a very primary stage with numerous theoretical and numerical studies. Further experimental works are expected at mid-term in order to demonstrate the possibility of fabricating isotropic negative index material notably in the infrared and visible frequency ranges. Towards this goal the challenging issues are the preservation of large dielectric constant and low loss in these frequency ranges, which appear as the necessary condition to operate in the long wavelength regime. The introduction of active materials may alleviate or even overcome the problem of intrinsic losses95. At last the inexpensive chemical methods, such as colloidal crystallization, may be suitable for the synthesis of nanoparticles96, 97. Although much work is needed before practical implementations are possible, dielectric metamaterials are a promising candidate for real-world application of the many exciting opportunities provided by electromagnetic metamaterials. Acknowledgments This work is supported by the National Science Foundation of China under Grant Nos. 50425204, 50621201, 50632030, 60608016 and 10774087, and by the State Key Lab of Tribology under Grant No. SKLT 08B12. D.L. would like also to thank the Delegation Générale pour l'Armement for its support in the framework of the contract 06.34.021. Fig. 11 The actively modulated isotropic negative permeability dielectric composite. (a) Dependence of the first magnetic resonance on the temperature. (b) Dependence of transmission phases on the temperature. (c) Calculated effective permeability under different temperature. (Reprinted with permission from91. 2008 American Institute of Physics.) (b) (a) (c) Mie resonance-based dielectric metamaterials REVIEW DECEMBER 2009 | VOLUME 12 | NUMBER 12 69 Reference 1. Pendry, J. B., Nature Mater. (2006) 5, 763. 2. Shelby, R. A., et al., Science (2001) 292, 77. 3. Houck, A. A., et al., Phys. Rev. Lett. (2003) 90, 137401. 4. Pendry, J. B., Phys. Rev. Lett. (2000) 85, 3966. 5. Fang, N., et al., Science (2005) 308, 534. 6. Pendry, J. B., et al., Science (2006) 312, 1780. 7. Schurig, D., et al., Science (2006) 314, 977. 8. Cai, W., et al., Nat. Photonics (2007) 1, 224. 9. Wiltshire, M. C. K., et al., Science (2001) 291, 849. 10. Zhang, F. L., et al., Appl. Phys. Lett. (2008) 93, 083104. 11. Dolling, G., et al., Science (2006) 312, 892. 12. Linden, S., et al., Science (2004) 306, 1351. 13. Liu, H., et al., Adv. Mater. (2008) 20, 2050. 14. Dolling, G., et al., Opt. Lett. (2007) 32, 53. 15. Pendry, J. B., et al., IEEE Trans. Microw. Theory Tech. (1999) 47, 2075. 16. Smith, D. R., et al., Phys. Rev. Lett. (2000) 84, 4184. 17. Huangfu, J., et al., Appl. Phys. Lett. (2004) 84, 1537. 18. Zhang, F. L., et al., IEEE Trans. Microw. Theory Tech. (2008) 56, 2566. 19. Enkrich, C., et al., Phys. Rev. Lett. (2005) 95, 203901. 20. Zhang, S., et al., Phys. Rev. Lett. (2005) 94, 037402. 21. Shalaev, V. M., et al., Opt. Lett. (2005) 30, 3356. 22. Zhou, X., and Zhao, X. P., Appl. Phys. Lett. (2007) 91, 181908. 23. Dolling, G., et al., Opt. Lett. (2006) 31, 1800. 24. Baena, J. D., et al., Appl. Phys. Lett. (2006) 88, 134108. 25. Gay-Balmaz, P., and Martin, O. J. F., Appl. Phys. Lett. (2002) 81, 939. 26. Koschny, T., et al., Phys. Rev. B (2005) 71, 21103. 27. Veselago, V. G., and Narimanov, E. E., Nat. Mater. (2006) 5, 759. 28. O'Brien, S., and. Pendry, J. B., J. Phys.: Condens. Matter (2002) 14, 4035. 29. Holloway, C. L., et al., IEEE Trans. Antennas Propag. (2003) 51, 2596. 30. Shalaev, V. M., Nat. Photon. (2007) 1, 41. 31. Padilla, W. J., et al., Materials Today (2006) 9, 28. 32. Soukoulis, C. M., et al., Adv. Mater. (2006) 18, 1941. 33. Engheta, N., and Ziolkowski, R. W., (eds.), Electromagnetic Metamaterials: Physics and Engineering Explorations, Wiley-IEEE Press, New Jersey, USA, (2006). 34. Marques, R., Martin, F., and Sorolla, M., Metamaterials with Negative Parameters: Theory, Design, and Microwave Applications, Wiley-Interscience Press, New Jersey, USA, (2007). 35. Jackson, J. D., Classical Electrodynamics, 2nd ed., Wiley, New York, USA, (1999). 36. Bohren, C. F., and Huffman, D. R., Absorption and Scattering of Light by Small Particles, Wiley-Interscience, New York, USA, (1983). 37. Zhao, Q., et al., Phys. Rev. Lett. (2008) 101, 027402. 38. Lewin, L., Proc. Inst. Electr. Eng. (1947) 94, 65. 39. Jylha, L., et al., J. Appl. Phys. (2006) 99, 043102. 40. Contopanagos, H. F., et al., J. Opt. Soc. Am. A (1999) 16, 1682. 41. Houzet, G., et al., Appl. Phys. Lett. (2008) 93, 053507. 42. Kittel, C., Introduction to Solid State Physics, 7th ed., John Wiley and Sons Inc., New York, USA, (1996). 43. Popa, B.I., and Cummer, S.A., Phys. Rev. Lett. (2008) 100, 207401. 44. Acher, O., et al., Appl. Phys. Lett. (2008) 93, 032501. 45. Ueda, T., et al., IEEE Trans. Microw. Theory Tech. (2007) 55, 1280. 46. Lin, X. Q., et al., Appl. Phys. Lett. (2008) 92, 131904. 47. Ueda, T., et al., IEEE Trans. Microw. Theory Tech. (2008) 56, 2259. 48. Shibuya, K., et al., Terahertz metamaterials composed of TiO2 cube arrays, Presented at 2nd International Congress on Advanced Electromagnetic Materials in Microwaves and Optics, Pamplona, Spain, September 21-26, 2008. 49. Wheeler, M. S., et al., Phys. Rev. B (2005) 72, 193103. 50. Yannopapas, V., and Vitanov, N. V., Phys. Rev. B (2006) 74, 193304. 51. Seo, B. J., et al., Appl. Phys. Lett. (2006) 88, 161122. 52. Wu, Q., and Park, W., Appl. Phys. Lett. (2008) 92, 153114. 53. Rockstuhl, C., et al., Phys. Rev. Lett. (2007) 99, 017401. 54. Felbacq, D., and Bouchitte, G., New J. Phys. (2005) 7, 159. 55. Huang, K. C., et al., Appl. Phys. Lett. (2004) 85, 543. 56. Felbacq, D., and Bouchitte, G., Phys. Rev. Lett. (2005) 94,183902. 57. Peng, L., et al., Phys. Rev. Lett. (2007) 98, 157403. 58. Ramakrishna, S. A., Rep. Prog. Phys. (2005) 68, 449. 59. Pendry, J. B., Phys. Rev. Lett. (1996) 76, 4773. 60. Vendik, O. G., and Gashinova, M. S., in Proceedings of the 34th European Microwave Conference, Amsterdam (IEEE Press, Piscataway, NJ, 2004), Vol. 3, pp. 1209-1212. 61. Vendik, I. B., et al., Tech. Phys. Lett. (2006) 32, 429. 62. Ahmadi, A., and Mosallaei, H., Phys. Rev. B (2008) 77, 045104. 63. Yannopapas, V., Phys. Rev. B (2007) 75, 035112. 64. Kussow, A. G., et al., Phys. Stat. Sol. B (2008) 245, 992. 65. Kussow, A. G., et al., Phys. Rev. B (2007) 76, 195123. 66. Yannopapas, V., Appl. Phys. A (2007) 87, 259. 67. Qiu, C. W., and Gao, L., J. Opt. Soc. Am. B (2008) 25, 1728. 68. Yannopapas, V., Phys. Stat. Sol. (RRL) (2007) 1, 208. 69. Alu, A., and Engheta, N., J. Appl. Phys. (2005) 97, 094310. 70. Wheeler, M. S., et al., Phys. Rev. B (2006) 73, 045105. 71. Yannopapas, V., J. Phys.: Condens. Matter (2008) 20, 255201. 72. Gao, L., et al., Phys. Rev. E (2008) 78, 046609. 73. Alu, A., and Engheta, N., Phys. Rev. E (2005) 72, 016623. 74. Schuller, J. A., et al., Phys. Rev. Lett. (2007) 99, 107401. 75. Vynck, K., et al., "All-dielectric rod-type metamaterials operating at optical frequencies," http://arxiv.org/abs/0805.0251 (2008). 76. Fabre, N., et al., Phys. Rev. Lett. (2008) 101, 073901. 77. Gaillot, D. P., et al., Opt. Express (2008) 16, 3986. 78. Cai, W., et al., Opt. Express (2008) 16, 5444. 79. Chen, H. T., et al., Nature (2006) 444, 597. 80. Padilla, W. J., et al., Phys. Rev. Lett. (2006) 96, 107401. 81. Zhao, Q., et al., Appl. Phys. Lett. (2007) 90, 011112. 82. Zhang, F. L., et al., Appl. Phys. Lett (2008) 92, 193104. 83. Hou, B., et al., Opt. Express (2005) 13, 9149. 84. Huang, Y., et al., Prog. Nat. Sci. (2008) 18, 907. 85. Hand, T. H., and Cummer, S. A., J. Appl. Phys. (2008) 103, 066105. 86. Kang, L., et al., Appl. Phys. Lett. (2008) 93, 171909. 87. Kang, L., et al., Opt. Express (2008) 16, 8825. 88. Kang, L., et al., Opt. Express (2008) 16, 17269. 89. Zhao, H. J., et al., Appl. Phys. Lett. (2007) 91, 131107. 90. Chen H., et al., Appl. Phys. Lett. (2006) 89, 053509. 91. Zhao, Q., et al., Appl. Phys. Lett. (2008) 92, 051106. 92. Vendik, O. G., and Zubko, S. P., J. Appl. Phys. (1997) 82, 4475. 93. Gaillot, D. P., et al., New J. Phys. (2008) 10, 115039. 94. Khoo, I. C., et al., Opt. Lett. (2006) 31, 2592. 95. Gordon, J. A., and Ziolkowski, R. W., Opt. Express (2007) 15, 2622. 96. Huang, X. G., et al., Langmuir (2007) 23, 8695. 97. Li, W., et al., Langmuir (2008) 24, 13772. TOOLS & TECHNIQUES DECEMBER 2009 | VOLUME 12 | NUMBER 1270 Carl Zeiss has launched a new system for optical sectioning The ELYRA product family features several new superresolution microscopy methods and significantly expands the application of light microscopy by clearly resolving details which previously could not be imaged by commercially available systems. ELYRA's high resolution and flexibility will allow scientists to expand their experimental design to enable study of cellular components smaller than the diffraction limit. The new LSM 780 expands the LSM 7 laser scanning microscopy family. This new system has about double the sensitivity of existing laser scanning microscopes and allows the study of samples with very weak or quickly bleaching fluorescence signals. The improved sensitivity can also be used to collect images at higher speeds. The third new product, VivaTome, is a new optical sectioning system created for developmental and cell biologists to examine the dynamics of living specimens. The VivaTome is easy to use and provides clear and quantifiable images of cell structures, tissue sections or living organisms. With the launch of the new systems, ELYRA, LSM 780 and VivaTome, Carl Zeiss offers important new tools to allow scientists to expand their research horizons. Contact: www.zeiss.de Combined AFM and raman solution for advanced materials research Bruker announces the official launch of the new N8 NEOS SENTERRA microanalysis system that combines the Raman Spectroscopy and Atomic Force Microscopy (AFM) on a single optical microscope platform. A comprehensive materials research investigation demands a multitechnique approach. Bruker Optics' SENTERRA Raman spectrometer and Bruker Nano's N8 NEOS Atomic Force Microscope was combined to allow morphological, structural and chemical analysis of the same sample area. Calibrated sample positioning allows simple and precise serial measurements, where the resultant Raman spectra is easily correlated with the AFM image. Contact: www.brukeroptics.com Powdery melting points With M5000 melting point of powdery substances can be analyzed. Measuring is fully automatic. A fan cooling allows fast measurments in every range of temperature. A printer may be connected optionally. * Digital temperature control with 0.1 °C resolution * Ventilator cooling * Automatic determination of melting point * Signal tone when melting point is reached * Keypad for easy cleaning * RS-232 interface for printer connection * English and german error message in clear text Contact: www.kruess.com Opportunity under the microscope A six figure investment in sophisticated new equipment is helping Teesside-based scientists focus in on new opportunities. Intertek MSG, which is based at the Wilton Centre, has acquired a state-of-the-art electron microscope to enhance the services offered to its customers working in the areas of nanotechnology and materials science. The purchase, which was made jointly with fellow Wilton Centre tenant NanoCentral, will enable Intertek MSG to offer researchers the ability to examine an extended range of materials in even greater detail. Director Dr Simon Allen said: "Our work involves the investigation and analysis of products as diverse as aerospace composites, pharmaceuticals and medical devices. The new addition to our equipment ensures our scientists have the best available resource to help solve our customers' problems and grow their businesses." He added: "For many years electron microscopes have enabled us to look in minute detail at structures too small for a light microscope but until now we could only study dry or dried samples." "The exciting thing about our new analytical instrument is that for the first time we can also examine the microstructures of wet materials. This greatly expands the range of industries that we can support and is excellent news both for our business and our customers." Formerly part of ICI, Intertek MSG has been based at the Wilton Centre since the 1970s. Dave Willis, Wilton Centre manager, said the company "flies the flag" for excellence in scientific research. "With continued investment like this to support them, the team can only go from strength to strength," he added. Contact: www.wiltoncentre.co.uk Residual gas analyzer Micromeritics introduces the MicroStar residual gas analyzer, a quadrupole mass spectrometer that complements Micromeritics' AutoChem 2920 and 2950 dynamic chemisorption analyzers. The MicroStar is ideally suited for pulse chemisorption studies and temperature-programmed reactions allowing the user to follow the evolution of residual gases from the AutoChem. This information may then be used to determine reaction kinetics, product selectivity, and reaction yields; all of which are vital components of a successful catalyst development program. Unlike traditional temperature-programmed desorption or reduction experiments where only one active gas is monitored, the MicroStar provides continuous monitoring of reaction products (up to 128 different masses). Contact: www.micromeritics.com Temperature measurement and control. The first of a new generation of innovative temperature measurement and control solutions by Lake Shore, the Model 336 temperature controller comes standard equipped with many advanced features promised to deliver the functionality and reliable service you've come to expect from the world leader in cryogenic thermometry. The Model 336 is the only temperature controller available with four sensor inputs, four control outputs and 150 W of low noise heater power. Two independent heater outputs providing 100 W and 50 W can be associated with any of the four sensor inputs and programmed for closed loop temperature control in proportional-integral-derivative (PID) mode. The improved autotuning feature of the Model 336 can be used to automatically collect PID parameters, so you spend less time tuning your controller and more time conducting experiments. Contact: www.lakeshore.com In-Situ Nanomechanical Testing Techniques: Opening Doors to a New World of Materials Characterization Date: Now available on demand (Webinar recorded: Wednesday 18th November 2009) Registration: Free Moderator: Jonathan Agbenyega, Commercial Editor, Materials Today Magazine Panelists: Dr. Oden Warren, CTO, Hysitron, Inc. Dr. William Gerberich, University of Minnesota Dr. S.A. Syed Asif, Director of R&D, Hysitron, Inc. Description: Next generation materials research is highly dependent on the development and application of innovative nanomechanical testing techniques. This webinar will cover the background and future of advanced in-situ nanomechanical characterization techniques that are becoming increasingly pertinent to research institutions and industries around the world. The newest developments in nanoindentation-based techniques have further expanded materials characterization capabilities of researchers by combining several other cutting-edge techniques and capabilities, including: TEM/SEM, heating/cooling, acoustic emission monitoring, dynamic mechanical analysis (DMA), quantitative mechanical property mapping, electrical contact resistance, and scanning probe microscope (SPM) imaging. Combining standard nanomechanical testing with any of the in-situ capabilities discussed in this webinar greatly enhances the amount of information one can obtain from depth-sensing indentation testing. In partnership with Registration Details: www.materialstoday.com/webinars From Molecules to Monolayers: Self-Assembly and Analysis, Molecule by Molecule Date: Now available on demand (Webinar recorded: Tuesday 17th November 2009) Registration: Free Moderator: Jonathan Agbenyega, Commercial Editor, Materials Today Magazine Panelists: Paul Weiss, Director, California NanoSystems Institute and Professor, Chemistry and Biochemistry at University of California, Los Angeles Milan Mrksich, Professor of Chemistry at the University of Chicago and Investigator at the Howard Hughes Medical Institute Description: Self-assembly has been likened to taking a jigsaw puzzle box, shaking it and when you open the box you find the jigsaw puzzle correctly made! As research in this field develops, we are continually finding more and more naturally occurring self-assembly systems in the complex world around us. The breadth of application of self-assembly vast and this educational webinar will focus on: Using Self-Assembled Monolayers and Mass Spectrometry for BioChip Applications Self and Directed Assembly for the Control of Single Molecule Environments The webinar is aimed at alternative energy researchers, surface chemists, mass spec audience, organic electronics, polymer science, selfassembly, molecular electronics and a number of biological audiences such as: proteomics, enzyme researchers and analytics. In partnership with Registration Details: www.materialstoday.com/webinars M A T E R I A L S S C I E N C E EVENTS DIARY DECEMBER 2009 | VOLUME 12 | NUMBER 1272 30 November 2009 ­ 4 December 2009 Materials Research Society Fall Meeting Boston ­ MA ­ USA The increasingly cross-disciplinary worldwide activity on materials research culminates every year in the MRS Fall Meetings. Symposium organizers from around the world have created a program that addresses leading-edge research and captures the extraordinary progress in materials science and technology, featuring an exciting mix of well-established and popular topics. http://www.mrs.org/s_mrs/ 4 ­ 7 December 2009 Nanotech Business Summit Cairo ­ Eygpt This conference brings together senior business leaders and world-renowned innovators to explore the ways that nanotechnology will become the next big growth innovation. The summit provides informative presentations, business match-making services and numerous networking opportunities to serve as an incubator of new ideas and new relationships. http://www.nanobus.sabrycorp.com/ conf/nanobus/09/ 6 ­ 11 December 2009 11th Pacific Polymer Conference: Progress in Polymers for the New Millennium Cairns ­ Australia PPC11/31APS will be a major international gathering of polymer scientists and engineers. All aspects of our profession will be covered in a comprehensive program, including modern polymerization methodologies, living free radical polymerization, complex polymer architectures, functional polymers, nano-composites, traditional composites, electro- and optico-active polymers, polymers in biology and medicine, naturally-derived polymers, polymers at interfaces and surfaces, polymer engineering, polymer rheology, polymer processing, mechanical properties and polymer characterization. http://www.ppc11.org/ 7 ­ 11 December 2009 Characterisation of Advanced Materials University of Surrey ­ UK The aim of this five-day course is to introduce the principles of the most popular materials analysis characterisation methods based on microscopy, chemical, physical and structural analysis and thermal techniques. Consideration is also given to the analysis of particulate materials and coatings. http://portal.surrey.ac.uk/portal/page?_ pageid=822,1938861&_dad=portal&_ schema=PORTAL 13 ­ 17 December 2009 Third International Conference on Mechanics of Biomaterials & Tissues Clearwater Beach ­ FL ­ USA The aim of the Third International Conference on Mechanics of Biomaterials is to provide a forum for the discussion of the modeling and measurement of deformation and fracture behavior in biological materials and in those materials which are used to replace them in the human body. A particular theme of the conference will be how lessons learnt in the study of engineering materials can be made relevant to the study of biomaterials. http://www.icmobt.elsevier.com/ 10 ­ 14 January 2010 PCSI-37 Santa Fe ­ New Mexico, USA The annual PCSI conference is devoted to achieving a fundamental understanding of the physical, chemical, biological, structural, optical, magnetic and electrical properties of surfaces and interfaces. These studies include characterization of growth processes, interfacial phenomena, transport and the structure and influence of defects. Generous amounts of discussion time will be included in the program in order to emphasize the workshop character and to stimulate the exchange of new ideas. http://www.pcsiconference.org/ 20 ­ 22 January 2010 Electronic Materials and Applications 2010 Orlando ­ FL ­ USA Jointly programmed by the Electronics Division and Basic Science Division of ACerS, this is the first in a series of annual meetings. The 2010 focus is on electronic ceramics for energy storage and conversion applications and the complementary fundamental science issues http://ceramics.org/electronic-materials- and-applications-2010/ 23 ­ 28 January 2010 SPIE Photonics West San Francisco ­ USA Experience SPIE Photonics West--the worlds leading photonics, laser, and biomedical optics event http://spie.org/x2584.xml 24 ­ 29 January 2010 34th International Conference and Exposition on Advanced Ceramics and Composites (ICACC) Daytona Beach ­ FL ­ USA This conference showcases cutting-edge research and product developments in advanced ceramics, armor ceramics, solid oxide fuel cells, ceramic coatings, bioceramics and more. Investigate the 11 symposia and 4 focused sessions planned for 2010. http://ceramics.org/34th-international- conference-exposition-on-advanced- ceramics-composites/ 01 ­ 05 February 2010 Introduction to Physical Metallurgy University of Surrey ­ Surrey ­ UK The course aims to provide a general introduction to the field of Physical Metallurgy. It covers phase diagrams, transformation diagrams and the associated thermodynamics, diffusion, liquid-solid transformations, ferrous and non-ferrous materials and cold work, recovery and recrystallisation. http://portal.surrey.ac.uk/portal/page?_ pageid=822,1938865&_dad=portal&_ schema=PORTAL 15 ­ 19 February 2010 Polymers: Science, Engineering and Applications University of Surrey ­ Surrey ­ UK This course combines a comprehensive study of the science and engineering of polymers with an up-to-date appreciation of the development and application of polymers in traditional and new areas. The course starts with a good insight into the physical and chemical structure and the various types of polymers. Polymer synthesis, chemical and physical processing techniques and manufacturing technologies are presented for the development of polymer structures and the manufacturing of polymer products for various applications. http://portal.surrey.ac.uk/portal/page?_ pageid=822,2436682&_dad=portal&_ schema=PORTAL FORTHCOMING EVENTS 30 November 2009 ­ 4 December 2009 Materials Research Society Fall Meeting Boston ­ MA ­ USA The increasingly cross-disciplinary worldwide activity on materials research culminates every year in the MRS Fall Meetings. Symposium organizers from around the world have created a program that addresses leading-edge research and captures the extraordinary progress in materials science and technology, featuring an exciting mix of wellestablished and popular topics. http://www.mrs.org/s_mrs/ diary Each month we publish brief details of current and forthcoming meetings. The forthcoming meetings are listed for a 3 months period of time starting 3 months after the current issue, leaving sufficient time for registration. This list is not exhaustive. If you are organizing a future conference or workshop and would like to have it listed in Materials Today please contact Jonathan Agbenyega ­ j.agbenye@elsevier.com. Events Materials Today has a contra deal with and that are relevant to the current issue of the magazine are listed in the box below. If, as an organizer, you would like to discuss a contra deal, please contact Francesca Webb ­ f.webb@elsevier.com For further information please visit www.materialstoday.com/events J.A. Woollam Co., Inc. 645 M Street, Suite 102 ˇ Lincoln, NE 68508 ˇ USA Ph. 402-477-7501 ˇ Fx. 402-477-8214 www.jawoollam.com Nanosurf easyScan 2 FlexAFM Your Versatile AFM System for Materials and Life Science Flexure-Based Scanner Technology The flexure structure at the basis of the XY-scanner is inherently flat and rugged. Being electromagnetically actuated, all scanning motions in this plane are highly linear. A decoupled piezo-based Z-scanner provides fast feedback response, thus allowing high scan speeds with high accuracy to be obtained. SureAlignTM Laser Optics Nanosurf's patented SureAlignTM technology makes laser adjustment upon changing to liquid environments a thing of the past. Whether measuring in air or in liquid, the FlexAFM laser is always right on target. Superior Top and Side View in Liquid Smart top and side view through the FlexAFM's optical system allow easy sample observation and approach. There is no difference in viewing quality between air and liquid. www.nanosurf.com Nanosurf AG Grammetstrasse 14 CH-4410 Liestal / Switzerland