Pseudo-Hermiticity and Electromagnetic Wave Propagation: The case of anisotropic and lossy media

TL;DR

This paper extends the application of pseudo-Hermitian operators to model electromagnetic wave propagation in anisotropic, lossy, or gain media, revealing new physical insights and mathematical properties of wave operators.

Contribution

It generalizes pseudo-Hermitian methods to anisotropic, lossy media and analyzes the physical implications, including non-diagonalizable operators and handedness of media.

Findings

Pseudo-Hermitian operators model wave propagation in complex media.

Uniaxial model exhibits non-diagonalizable wave operator.

Medium shows left-handedness with circular polarization solutions.

Abstract

Pseudo-Hermitian operators can be used in modeling electromagnetic wave propagation in stationary lossless media. We extend this method to a class of non-dispersive anisotropic media that may display loss or gain. We explore three concrete models to demonstrate the utility of our general results and reveal the physical meaning of pseudo-Hermiticity and quasi-Hermiticity of the relevant wave operator. In particular, we consider a uniaxial model where this operator is not diagonalizable. This implies left-handedness of the medium in the sense that only clockwise circularly polarized plane-wave solutions are bounded functions of time.