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

TL;DR

This paper investigates light transfer dynamics in parity-time and anti-parity-time symmetric waveguide arrays exhibiting higher-order exceptional points, revealing novel behaviors like unidirectional oscillations and localization, governed by underlying $SU(2)$ symmetry.

Contribution

It introduces two non-Hermitian waveguide arrays with $N$th-order exceptional points, demonstrating unique light transfer behaviors and phase transitions not seen in lower-order EPs.

Findings

Unidirectional oscillations in unbroken $ ext{PT}$ phase

Edge- and center-towards localization behaviors

Controlled transitions based on $SU(2)$ symmetry

Abstract

We propose two non-Hermitian arrays consisting of $N=2l+1$ waveguides and exhibiting parity-time ($\mathcal{PT}$) or anti-$\mathcal{PT}$ symmetry for investigating light transfer dynamics based on $N$th-order exceptional points (EPs). The $\mathcal{PT}$-symmetric array supports two $N$th-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 $N$th-order EPs. The anti-$\mathcal{PT}$-symmetric array supports also two $N$th-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.