Characterization of Parity-Time Symmetry in Photonic Lattices Using Heesh-Shubnikov Group Theory

TL;DR

This paper uses Heesh-Shubnikov group theory to analyze parity-time symmetric photonic lattices, revealing how antiunitary symmetries influence eigenmodes and enabling better design of photonic devices.

Contribution

It introduces a novel application of Heesh-Shubnikov group theory to classify eigenmodes in PT-symmetric photonic structures, including high-symmetry points.

Findings

Identification of corepresentations at symmetry points

Correlation between corepresentations and PT transition thresholds

General applicability to various dimensions of photonic lattices

Abstract

We investigate the properties of parity-time symmetric periodic photonic structures using Heesh-Shubnikov group theory. Classical group theory cannot be used to categorize the symmetry of the eigenmodes because the time-inversion operator is antiunitary. Fortunately, corepresentations of Heesh-Shubnikov groups have been developed to characterize the effect of antiunitary operators on eigenfunctions. Using the example structure of a one-dimensional photonic lattice, we identify the corepresentations of eigenmodes at both low and high symmetry points in the photonic band diagram. We find that thresholdless parity-time transitions are associated with particular classes of corepresentations. The approach is completely general and can be applied to parity-time symmetric photonic lattices of any dimension. The predictive power of this approach provides a powerful design tool for parity-time symmetric photonic device design.