Scattering theory for stationary materials with $\mathcal{PT}$ symmetry

TL;DR

This paper develops a theoretical framework for scalar wave scattering in stationary media with $ ext{PT}$-symmetry, revealing two distinct mechanisms of symmetry breaking in the statistical properties of scattered radiation.

Contribution

It introduces a novel scattering theory for stationary $ ext{PT}$-symmetric media, extending previous deterministic models to statistical media with complex correlation functions.

Findings

Two mechanisms of symmetry breaking identified

Stationary $ ext{PT}$-symmetry affects scattering statistics

Framework applicable to complex media with $ ext{PT}$-symmetry

Abstract

A theoretical framework is developed for scattering of scalar radiation from stationary, three-dimensional media with correlation functions of scattering potentials obeying $\mathcal{PT}$-symmetry. It is illustrated that unlike in scattering from deterministic $\mathcal{PT}$-symmetric media, its stationary generalization involves two mechanisms leading to symmetry breaking in the statistics of scattered radiation, one stemming from the complex-valued medium realizations and the other - from the complex-valued degree of medium's correlation.