Symmetry-engineered waveguide dispersion in $ {\cal P}{\cal T} $PT symmetric photonic crystal waveguides

Abstract

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