An invisible gradient spherical lens with negative refractive index

S.P. Skobelev

An invisible gradient spherical lens with negative refractive index

S.P. Skobelev¹

research article UDC 621.371.16 Pages: 30-34

¹ Dr. Sc. (Phys.-Math.), Leading Research Scientist, PJSC «Radiofizika» (Moscow); Associate Professor, Moscow Institute of Physics and Technology (State University)

Keywords: geometrical optics gradient lens invisible lens negative refractive index

Abstract

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.

How to cite

Скобелев С.П. Невидимая градиентная сферическая линза с отрицательным показателем преломления // Радиотехника. 2017. № 10. С. 30–34.

References

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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.
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Minano J.C. Perfect imaging in a homogeneous three dimensional region // Optics Express. 2006. V. 14. № 21. P. 9627−9635.
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Morgan S.P. General solution of the Luneberg lens problem // Journal of Applied Physics. 1958. V. 29. № 9. P. 1358−1368.
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[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.

Abstract

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