Frequency domain wave-splitting techniques for plane stratified bianisotropic media

Abstract

A plane harmonic electromagnetic wave obliquely incident on a plane stratified bianisotropic medium with multiple discontinuities in the parameters is considered. A covariant wave-splitting approach, based on the use of the formula of integration by parts for multiplicative integrals and the impedance concept, is presented. It encompasses various types of decomposition of the total internal field into two waves propagating in opposite directions, including the physical and vacuum wave splittings treated earlier in the literature, and provides a convenient means for both analytical investigation and numerical calculation of evolution operators (Green’s functions) and impedance tensors of split waves as well as characteristic matrices and reflection and transmission tensors of stratified bianisotropic media. The potentialities of the approach are illustrated by its application to the problems of reflection, transmission, and guided propagation, and by generalizing the method of multiple reflections to the case of stratified bianisotropic media.

Asymmetric transmission in planar chiral split-ring metamaterials: Microscopic Lorentz-theory approach

“…14 The transmission spectra of a CSR-based PCM are then calculated using the standard wave operator based extension of transfer-matrix methods. 30,31 In agreement with previous theoretical and experimental results, 10,12 the spectra show a difference with respect to whether the incident wave has left-or right-handed circular polarizations […”

“…The evolution operator of the metamaterial P can be derived by setting ε = ε eff in Eq. (31). On the other hand, the field at the output interface is the transmitted wave…”

“…The 4 × 4 matrix P (z) is called the evolution operator. Taking into account that in the medium surrounding the metamaterial layer (i.e., in air) the fields are related as q × E = ±I H depending on the propagation direction, 31 the incident and reflected waves at the input (air/PCM) boundary are related to the initial field W (0) as…”

“…For the details on this method, the reader is referred to previous publications. 30,31,38 We define a unit vector q = e z pointing in the propagation direction and write the Maxwell equations for a monochromatic normally incident wave in the form…”

Simple and versatile analytical approach for planar metamaterials

“…Since we deal now with more complex effective media where the full tensorial nature of the permittivity tensor has to be taken into account the standard transfer matrix algorithm cannot be applied. Hence, it is challenging to determine the scattering coefficients analytically 46 or even to invert them to retrieve effective parameters directly. Therefore we used an adapted Fourier Modal Method to determine the transmitted and reflected intensities 47 .…”