A solution to the complement of the generalized Luneburg lens problem

FONSECA, Nelson J. G., Tomáš TYC a Oscar QUEVEDO-TERUEL. A solution to the complement of the generalized Luneburg lens problem. Communications Physics. Nature Portfolio, 2021, roč. 4, č. 1, s. "270", 10 s. ISSN 2399-3650. Dostupné z: https://dx.doi.org/10.1038/s42005-021-00774-2.

Základní údaje

• Originální název: A solution to the complement of the generalized Luneburg lens problem
• Autoři: FONSECA, Nelson J. G. (garant), Tomáš TYC (203 Česká republika, domácí) a Oscar QUEVEDO-TERUEL.
• Vydání: Communications Physics, Nature Portfolio, 2021, 2399-3650.

Další údaje

• Originální jazyk: angličtina
• Typ výsledku: Článek v odborném periodiku
• Obor: 10308 Astronomy
• Stát vydavatele: Německo
• Utajení: není předmětem státního či obchodního tajemství
• WWW: URL
• Impakt faktor: Impact factor: 6.497
• Kód RIV: RIV/00216224:14310/21:00123894
• Organizační jednotka: Přírodovědecká fakulta
• Doi: http://dx.doi.org/10.1038/s42005-021-00774-2
• UT WoS: 000731252300001
• Klíčová slova anglicky: Lenses; Metamaterials; Transformation optics; Luneburg lens problem
• Štítky: rivok
• Příznaky: Mezinárodní význam, Recenzováno

Anotace

Lenses are of interest for the design of directive antennas and multi-optics instruments in the microwave, terahertz and optical domains. Here, we introduce an optical problem defined as the complement of the well-known generalized Luneburg lens problem. The spherically symmetric inhomogeneous lenses obtained as solutions of this problem transform a given sphere in the homogeneous region outside of the lens into a virtual conjugate sphere, forming a virtual image from a real source. An analytical solution is proposed for the equivalent geodesic lens using the analogy between classical mechanics and geometrical optics. The refractive index profile of the corresponding inhomogeneous lens is then obtained using transformation optics. The focusing properties of this family of lenses are validated using ray-tracing models, further corroborated with full-wave simulations. The numerical results agree well with the predictions over the analyzed frequency bandwidth (10-30 GHz). This virtual focusing property may further benefit from recent developments in the fields of metamaterials and transformation optics. Spherically-symmetric lenses can create sharp virtual images, but a general expression for their refractive index profiles had not yet been developed. Here, this expression is provided via analogy between classical mechanics and geometrical optics, yielding solutions complementary to existing lenses obtained from the generalized Luneburg lens problem.