General Solution of EM Wave Propagation in Anisotropic Media

TL;DR

This paper derives a new analytical method for solving electromagnetic wave propagation in anisotropic media by reformulating Maxwell's equations, enabling decoupled equations solvable with tensor Green's functions.

Contribution

It introduces a novel manipulation of Maxwell's equations that results in decoupled wave equations, applicable to both anisotropic and isotropic media, facilitating analytical solutions.

Findings

Derived new wave equations for anisotropic media

Achieved decoupling of electric and magnetic fields

Provided analytical solutions using tensor Green's functions

Abstract

When anisotropy is involved, the wave equation becomes simultaneous partial differential equations that are not easily solved. Moreover, when the anisotropy occurs due to both permittivity and permeability, these equations are insolvable without a numerical or an approximate method. The problem is essentially due to the fact neither $\e$ nor $\m$ can be extracted from the curl term, when they are in it. The terms $\na\times {\bf E}$ (or ${\bf H})$ and $\na\times \e{\bf E}$ (or $\;\m{\bf H})$ are practically independent variables, and $\bf E$ and $\bf H$ are coupled to each other. However, if Maxwell's equations are manipulated in a different way, new wave equations are obtained. The obtained equations can be applied in anisotropic, as well as isotropic, cases. In addition, $\bf E$ and $\bf H$ are decoupled in the new equations, so the equations can be solved analytically by using tensor Green's functions.