A solution to the complement of the generalized Luneburg lens
problem

J 2021

A solution to the complement of the generalized Luneburg lens problem

FONSECA, Nelson J. G., Tomáš TYC a Oscar QUEVEDO-TERUEL

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

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10308 Astronomy

Stát vydavatele

Německo

Utajení

není předmětem státního či obchodního tajemství

Odkazy

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

Změněno: 15. 3. 2022 15:42, Mgr. Marie Šípková, DiS.

Anotace

V originále

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.

Citovat

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.

@article{1824997,
   author = {Fonseca, Nelson J. G. and Tyc, Tomáš and QuevedoandTeruel, Oscar},
   article_number = {1},
   doi = {http://dx.doi.org/10.1038/s42005-021-00774-2},
   keywords = {Lenses; Metamaterials; Transformation optics; Luneburg lens problem},
   language = {eng},
   issn = {2399-3650},
   journal = {Communications Physics},
   title = {A solution to the complement of the generalized Luneburg lens problem},
   url = {https://www.nature.com/articles/s42005-021-00774-2},
   volume = {4},
   year = {2021}
}

TY  - JOUR
ID  - 1824997
AU  - Fonseca, Nelson J. G. - Tyc, Tomáš - Quevedo-Teruel, Oscar
PY  - 2021
TI  - A solution to the complement of the generalized Luneburg lens problem
JF  - Communications Physics
VL  - 4
IS  - 1
SP  - "270"
EP  - "270"
PB  - Nature Portfolio
SN  - 23993650
KW  - Lenses
KW  - Metamaterials
KW  - Transformation optics
KW  - Luneburg lens problem
UR  - https://www.nature.com/articles/s42005-021-00774-2
N2  - 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.
ER  -

FONSECA, Nelson J. G., Tomáš TYC a Oscar QUEVEDO-TERUEL. A solution to the complement of the generalized Luneburg lens problem. \textit{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.

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