Scattering of TE and TM waves and quantum dynamics generated by non-Hermitian Hamiltonians

TL;DR

This paper develops a dynamical formulation for scattering of TE and TM electromagnetic waves in inhomogeneous media, linking it to non-Hermitian quantum systems and simplifying the analysis through Riccati equations.

Contribution

It introduces a novel transfer matrix approach using non-unitary quantum evolution to analyze wave scattering in complex media.

Findings

Extended transfer matrix technique to inhomogeneous media

Reduced scattering problem to Riccati initial-value problem

Identified media that do not reflect specific wave modes

Abstract

The study of the scattering of electromagnetic waves by a linear isotropic medium with planar symmetry can be reduced to that of their TE and TM modes. For situations where the medium consists of parallel homogeneous slabs, one may use the standard transfer matrix technique to address the scattering problem for these modes. We extend the utility of this technique to inhomogeneous permittivity and permeability profiles by proposing a dynamical formulation of the scattering of TE and TM waves in which the transfer matrix for the medium is given in terms of the evolution operator for an effective non-unitary quantum system. This leads to a system of dynamical equations for the reflection and transmission amplitudes. Decoupling these equations we reduce the solution of the scattering problem for TE and TM modes to that of an initial-value problem for a Riccati equation. We discuss the application of this observation in identifying media that do not reflect TE or TM waves with given wavenumber and incidence angle.