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arXiv · 1606.05044

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

Adam Mock
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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.

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Adam Mock. 2016-06-16. Characterization of Parity-Time Symmetry in Photonic Lattices Using Heesh-Shubnikov Group Theory. https://doi.org/10.1364/oe.24.022693

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