Numerical study of electromagnetic wave propagation in twisted birefringent layers by the spectral moments method

Abstract

This paper presents a first attempt at using the spectral moments method (SMM) to solve Maxwell's equations in twisted anisotropic media in the presence of defects. This numerical method, previously developed in condensed matter physics, allows computation of Green functions for very large systems. The dynamic matrix of the discretized system is built from the medium parameters. Green functions, calculated for a given source, representing a point source at infinity and given receiver, are developed as a continued fraction whose coefficients are related to the moments and directly computed from the dynamic matrix. In this study we compute the light transmitted through thin surface-stabilized ferroelectric liquid crystal cells with a chevron structure and a twisted director distribution. The efficiency and accuracy of the method are analysed by comparing the results obtained by SMM with the analytical solution obtained using the Jones matrix formalism. Finally, we apply SMM to compute the transmitted light with different director configurations. We show, by comparisons with experimental data, that the simplest director configuration is certainly the most probable.

Computation of electromagnetic waves diffraction by spectral moments method

“…Comparison between the analytical solutions and the spectral moments-method results proves the accuracy of this method. Applications to the computation of radar cross sections and propagation in anisotropic heterogeneous media (such as liquid crystals [38]) are now being developed.…”

“…We conjecture that relation (36) holds for matrices involved in physical problems. The element can be written [using (32) and (36)] as (37) which corresponds to the operator given by (38) We want to determine this element (37) without having to compute the eigenvalues or eigenvectors of matrix . First, we introduce the following auxiliary function density: and are called the generalized moments.…”

Introduction of fractal absorbing boundary conditions in electromagnetic simulation by SMM

“…We terminate the computational domain with successive layers, with different conductivities (figure 2). We used the same method as described in Lakhliai et al (1996) to construct the matrix M. In the SMM, after discretization, the local physical properties of a point n of a medium are represented by six interaction matrices of (6 × 6) dimension. In three-dimensional space there is one matrix for every bond between site n and the six neighbouring sites.…”

“…It is a mixed method, both temporal and frequencial, which gives the result for all frequencies in one computation directly, and for any incident pulse. Some applications have already been reported: propagation in twisted birefringent layers with defects (Lakhliai et al 1996), electromagnetic wave diffraction by rectangular aperture in two and three dimensions (Chenouni et al 1998) and by a circular or a square dielectric cylinder (Poussigue et al 1996). In this latter application, no absorbing boundary condition was inserted in the very large domain.…”