A Matrix Basis Formulation For The Green's Functions Of Maxwell's Equations And The Elastic Wave Equations In Layered Media

TL;DR

This paper introduces a matrix basis approach to represent Green's functions for Maxwell's and elastic wave equations in layered media, enabling decomposition into fundamental wave components for improved analysis.

Contribution

It presents a novel matrix basis formulation that decomposes Green's functions into independent wave components, applicable to electromagnetic, elastic, and acoustic waves in layered media.

Findings

Decomposition of Maxwell's Green's functions into TE and TM components.

Representation of elastic Green's functions into S-wave and P-wave components.

Application of vector basis to acoustic wave sources in fluid layers.

Abstract

A matrix basis formulation is introduced to represent the 3 x 3 dyadic Green's functions in the frequency domain for the Maxwell's equations and the elastic wave equation in layered media. The formulation can be used to decompose the Maxwell's Green's functions into independent TE and TM components, each satisfying a Helmholtz equation, and decompose the elastic wave Green's function into the S-wave and the P-wave components. In addition, a derived vector basis formulation is applied to the case for acoustic wave sources from a non-viscous fluid layer.