Radiotekhnika
Publishing house Radiotekhnika

"Publishing house Radiotekhnika":
scientific and technical literature.
Books and journals of publishing houses: IPRZHR, RS-PRESS, SCIENCE-PRESS


Тел.: +7 (495) 625-9241

 

An invisible gradient spherical lens with negative refractive index

Keywords:

S.P. Skobelev – Dr. Sc. (Phys.-Math.), Leading Research Scientist, PJSC «Radiofizika» (Moscow); Associate Professor, Moscow Institute of Physics and Technology (State University)
E-mail: s.p.skobelev@mail.ru


A radially inhomogeneous (gradient) spherical lens made of material with negative refractive index, invisible from the viewpoint of geometrical optics, is proposed. An appropriate cubic equation for determining the refractive index profile is derived and solved. It is found that the refractive index varies within finite limits from −4 at the center to −1 on the boundary. A formula allowing calculation of the ray trajectories in the lens is derived and examples of the trajectories are given. The proposed lens is compared to the known invisible lens with positive refractive index going to infinity in the center.

References:
  1. Veselago V.G. E’lektrodinamika veshhestv s odnovremenno otriczatel’ny’mi znacheniyami ε i μ // Uspexi fizicheskix nauk. 1967. T. 92. № 3. S. 517−526.
  2. Minano J.C., et al. Design of spherical symmetric gradient index lenses // Proc. SPIE 8485. Nonimaging Optics: Efficient Design for Illumination and Solar Concentration IX, 848508 (11 October 2012). doi:10.1117/12.931505.
  3. Kwon D.H., Werner D.H. Transformation electromagnetics: An overview of the theory and applications // IEEE Antennas & Propagation Magazine. 2010. V. 52. № 1. P. 24−46.
  4. Hendi A., Henn J., Leonhardt U. Ambiguities in the Scattering Tomography for Central Potentials // Phys. Rev. Lett. 2006. V. 97. P. 073902.
  5. Minano J.C. Perfect imaging in a homogeneous three dimensional region // Optics Express. 2006. V. 14. № 21. P. 9627−9635.
  6. Sarbor M., Tyc T. Spherical media and geodesic lenses in geometrical optics // Journal of Optics. 2012. V. 14. P. 075705.
  7. Morgan S.P. General solution of the Luneberg lens problem // Journal of Applied Physics. 1958. V. 29. № 9. P. 1358−1368.
  8. Zelkin E.G., Petrova R.A. Linzovy’e antenny’. M.: Sov. radio. 1974.
  9. Flores J.R., Sochacki J., Sochacka M., Starohski R. Quasi-analytical ray tracing through the generalized Luneburg lens // Applied Optics. 1992. V. 31. № 25. P. 5167−5170.
June 24, 2020
May 29, 2020

© Издательство «РАДИОТЕХНИКА», 2004-2017            Тел.: (495) 625-9241                   Designed by [SWAP]Studio