Integral equation method for the electromagnetic wave propagation in stratified anisotropic dielectric-magnetic materials

TL;DR

This paper develops an integral equation method to analyze electromagnetic wave propagation in stratified anisotropic dielectric-magnetic materials, deriving key relations and revealing new forms of the extinction theorem, supported by numerical simulations.

Contribution

It introduces a novel integral equation approach that derives dispersion, Snell's law, and reflection/transmission coefficients for stratified anisotropic media, including new forms of the extinction theorem.

Findings

Derived a unified framework for wave propagation in stratified anisotropic materials.

Discovered two new forms of the generalized extinction theorem.

Validated results through numerical simulations.

Abstract

We investigate the propagation of electromagnetic waves in stratified anisotropic dielectric-magnetic materials using the integral equation method (IEM). Based on the superposition principle, we use Hertz vector formulations of radiated fields to study the interaction of wave with matter. We derive in a new way the dispersion relation, Snell's law and reflection/transmission coefficients by self-consistent analyses. Moreover, we find two new forms of the generalized extinction theorem. Applying the IEM, we investigate the wave propagation through a slab and disclose the underlying physics which are further verified by numerical simulations. The results lead to a unified framework of the IEM for the propagation of wave incident either from a medium or vacuum in stratified dielectric-magnetic materials.