Exact analytical solution for fields in gradient index metamaterials with different loss factors in negative and positive refractive index segments

Mariana Dalarsson; Martin Norgren; Tatjana Asenov; Nebojsa Doncov; Zoran Jaksic

doi:10.1117/1.JNP.7.073086

19 August 2013 Exact analytical solution for fields in gradient index metamaterials with different loss factors in negative and positive refractive index segments

Mariana Dalarsson, Martin Norgren, Tatjana Asenov, Nebojsa Doncov, Zoran Jaksic

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Journal of Nanophotonics, Vol. 7, Issue 1, 073086 (August 2013). https://doi.org/10.1117/1.JNP.7.073086

Abstract

Gradient refractive index metamaterials are of interest for various applications of transformation optics. Wave propagation through gradient index metamaterials using an exact analytical approach is investigated. Composite materials containing constituents with negative real and positive real indexes of refraction are considered. An exact analytical solution for the field distribution is obtained for the sinusoidal spatial variation of complex effective permittivity and permeability along a fixed direction, under the assumption that the wave impedance remains spatially uniform across the structure. Loss factors in the constituent materials can be different from each other corresponding to the realistic situations. Temporal dispersion can be arbitrary subject to the physical limitations imposed by the Kramers-Kronig relations. A numerical model based on the Z -transform is developed to verify the analytical results. The approach can be applied to arbitrary periodic refractive index profiles using the Fourier series method.

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Mariana Dalarsson, Martin Norgren, Tatjana Asenov, Nebojsa Doncov, and Zoran Jaksic "Exact analytical solution for fields in gradient index metamaterials with different loss factors in negative and positive refractive index segments," Journal of Nanophotonics 7(1), 073086 (19 August 2013). https://doi.org/10.1117/1.JNP.7.073086

Published: 19 August 2013

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