Spherical Representation of Parity-Time and Anti-Parity-Time States in Bragg Gratings

Parity-time (PT) symmetry and anti-PT symmetry are two unique types of non-Hermitian Hamiltonian systems. Bragg gratings with phase-shifted perturbations in both real and imaginary refractive index can capture a design space of different (anti-)PT symmetry states. A spherical graphical representation captures evolving (anti-)PT symmetry states of gratings with perturbations in real index only, imaginary index only, and satisfying (anti-)PT symmetry in unbroken, broken, and exceptional point states. Grating designs in different PT states have interesting and distinct properties leading to potential applications in sensing and lasing.