Classification of symmetry properties of waveguide modes in presence of gain/losses, anisotropy/bianisotropy, or continuous/discrete rotational symmetry

TL;DR

This paper develops a comprehensive framework to classify and identify symmetry properties of waveguide modes considering gain/losses, anisotropy, and rotational symmetries, aiding in understanding modal behaviors.

Contribution

It introduces a $4\times4$ waveguide Hamiltonian and criteria for symmetry classification, providing a systematic approach to analyze waveguide modal symmetries.

Findings

Classified chiral, time reversal, parity, and rotational symmetries for various waveguides.

Provided criteria for identifying symmetry operations in waveguides.

Illustrated symmetry classification with practical examples.

Abstract

We study the symmetric properties of waveguide modes in presence of gain/losses, anisotropy/bianisotropy, or continuous/discrete rotational symmetry. We provide a comprehensive approach to identity the modal symmetry by constructing a $4\times4$ waveguide Hamiltonian and searching the symmetric operation in association with the corresponding waveguides. We classify the chiral/time reversal/parity/parity time/rotational symmetry for different waveguides, and provide the criterion for the aforementioned symmetry operations. Lastly, we provide examples to illustrate how the symmetry operations can be used to classify the modal properties from the symmetric relation between modal profiles of several different waveguides.