Journal of the Optical Society of America B ( IF 2.284 ) Pub Date : 2019-12-24 , DOI: 10.1364/josab.37.000168

This work demonstrates how the crystal symmetry of photonic crystal defect waveguides interacts with simple, experimentally realizable parity-time (${\cal P}{\cal T}$) symmetric regions of chip-scale absorption and amplification to control the existence and location of exceptional points in the first Brillouin zone. Our analysis is based on Heesh–Shubnikov group theory and is generalizable to a large class of devices for which the symmetry groups can be identified. Transverse, longitudinal, and transverse–longitudinal hybrid ${\cal P}{\cal T}$ symmetries are considered, and for each, a triangular lattice photonic crystal waveguide with lattice-aligned and lattice-shifted cladding orientations is analyzed. We find that various symmetry combinations produce either strictly real-valued or strictly complex-valued eigenfrequencies at the Brillouin zone boundary. We also show how symmetry can be used to predict ${\cal P}{\cal T}$ transitions at accidental degeneracies in the waveguide bands. It is shown how symmetry can be used to design single-mode waveguides, and we discovered exceptional points whose propagation constants are highly sensitive to the non-Hermiticity factor.

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