On the computation of the dyadic Green's functions of Maxwell's equations in layered media

TL;DR

This paper presents two formulations for computing dyadic Green's functions in layered media, simplifying the derivation of a recent vector potential-based method and demonstrating its equivalence to the traditional TE/TM approach.

Contribution

It simplifies the derivation of a vector potential-based formulation and proves its equivalence to the well-known TE/TM decomposition for Maxwell's equations in layered media.

Findings

The second formulation is equivalent to the first but easier to derive.

The matrix basis separates non-symmetric factors, aiding far-field approximation derivation.

The approach extends to elastic wave Green's functions in layered media.

Abstract

In this paper, two formulations for the computation of the dyadic Green's functions of Maxwell's equations in layered media are presented in details. The first formulation derived using TE/TM decomposition is well-known and intensively used in engineering community while the second formulation derived using vector potential and a matrix basis is recently used in establishing a fast multipole method. We significantly simplify the derivation of second formulation and show that it is equivalent to the first one while the derivation is more straightforward as the interface conditions are directly decoupled using the vector potential. The matrix basis is designed to split out all non-symmetric factors in the density functions which facilitates the derivation of far-field approximations for the dyadic Green's functions. Moreover, it can be applied to the computation of the dyadic Green's functions of elastic wave equation in layered media.