Characterization of parity-time symmetry in photonic lattices using Heesh-Shubnikov group theory

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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.

Original languageEnglish
Pages (from-to)22693-22707
Number of pages15
JournalOptics Express
Issue number20
StatePublished - Oct 3 2016


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