Symmetry-engineered waveguide dispersion in PT symmetric photonic crystal waveguides

This work demonstrates how the crystal symmetry of photonic crystal defect waveguides interacts with simple, experimentally realizable parity-time (PT ) 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 PT 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 PT 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.