Light transfer transitions beyond higher-order exceptional points in parity-time and anti-parity-time symmetric waveguide arrays

Abstract

We propose two non-Hermitian arrays consisting of N = 2l + 1 waveguides and exhibiting parity-time ( P T ) or anti- P T symmetry for investigating light transfer dynamics based on Nth-order exceptional points (EPs). The P T -symmetric array supports two Nth-order EPs separating an unbroken and a broken phase with real and imaginary eignvalues, respectively. Light transfer dynamics in this array exhibits radically different behaviors, i.e. a unidirectional oscillation behavior in the unbroken phase, an edge-towards localization behavior in the broken phase, and a center-towards localization behavior just at Nth-order EPs. The anti- P T -symmetric array supports also two Nth-order EPs separating an unbroken and a broken phase, which refer however to imaginary and real eigenvalues, respectively. Accordingly, light transfer dynamics in this array exhibits a center-towards localization behavior in the unbroken phase and an origin-centered oscillation behavior in the broken phase. These nontrivial light transfer behaviors and their controlled transitions are not viable for otherwise split lower-order EPs and depend on the underlying SU(2) symmetry of spin-l matrices.