Abstract

A multimodal method based on a generalization of the admittance matrix is used to analyze wave propagation in heterogeneous two-dimensional anisotropic media. The heterogeneity of the medium can be due to the presence of anisotropic inclusions with arbitrary shapes, to a succession of anisotropic media with complex interfaces between them, or both. Using a modal expansion of the wave field, the problem is reduced to a system of two sets of first-order differential equations for the modal components of the field, similar to the system obtained in the rigorous coupled wave analysis. The system is solved numerically, using the admittance matrix, which leads to a stable numerical method, the basic properties of which are discussed. The convergence of the method is discussed, considering arrays of anisotropic inclusions with complex shapes, which tend to show that Li’s rules are not concerned within our approach. The method is validated by comparison with a subwavelength layered structure presenting an effective anisotropy at the wave scale.

© 2015 Optical Society of America

Transient electromagnetic wave propagation in anisotropic dispersive media

Jonas Fridén, Gerhard Kristensson, and Rodney D. Stewart
J. Opt. Soc. Am. A 10(12) 2618-2627 (1993)

Numerical scheme for the modal method based on subsectional Gegenbauer polynomial expansion: application to biperiodic binary grating

K. Edee and J. P. Plumey
J. Opt. Soc. Am. A 32(3) 402-410 (2015)

General polarized ray-tracing method for inhomogeneous uniaxially anisotropic media

Maarten Sluijter, Dick K. G. de Boer, and Joseph J. M. Braat
J. Opt. Soc. Am. A 25(6) 1260-1273 (2008)

Scattering by an infinite homogenous anisotropic elliptic cylinder in terms of Mathieu functions and Fourier series

Shi-Chun Mao and Zhen-Sen Wu
J. Opt. Soc. Am. A 25(12) 2925-2931 (2008)

Method of field expansions for vector electromagnetic scattering by layered periodic crossed gratings

David P. Nicholls
J. Opt. Soc. Am. A 32(5) 701-709 (2015)