Introducing a general method for solving electromagnetic radiation problem in an arbitrary linear medium

TL;DR

This paper introduces a comprehensive method utilizing fundamental transfer matrices to analytically solve electromagnetic radiation problems in complex, non-homogeneous, anisotropic, and active or lossy linear media, including photonic crystal structures.

Contribution

It develops a general analytical approach based on fundamental transfer matrices for solving radiation problems in arbitrary linear media, extending previous numerical methods.

Findings

Analytic solutions for radiation in complex media

Application to photonic crystal models

Framework for active and lossy materials

Abstract

Numerical transfer matrices have been widely used in the study of wave propagation and scattering. These may be viewed as descretizations of a recently introduced fundamental notion of transfer matrix which admits a representation in terms of the evolution operator for an effective non-unitary quantum system. We use the fundamental transfer matrix to develop a general method for the solution of the problem of radiation of an oscillating source in an arbitrary, possibly non-homogenous, anisotropic, and active or lossy linear medium. This allows us to obtain an analytic solution of this problem for an oscillating source located in the vicinity of a planar collection of possibly anisotropic and active/lossy point scatterers such as those modeling a two-dimensional photonic crystal.