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

• URL: http://arxiv.org/abs/2205.07566v1
• Date: Mon, 16 May 2022 10:51:38 GMT
• Title: Light transfer transitions beyond higher-order exceptional points in parity-time and anti-parity-time symmetric waveguide arrays
• Authors: Chuanxun Du, Gang Wang, Yan Zhang, and Jin-Hui Wu
• Abstract summary: Two non-Hermitian arrays are proposed for investigating light transfer dynamics based on $N$th-order exceptional points (EPs) The $mathcalPT$-symmetric array supports two $N$th-order EPs separating an unbroken and a broken phase with real and imaginary eignvalues, respectively. The anti-$mathcalPT$-symmetric array supports also two $N$th-order EPs separating an unbroken and a broken phase, which refer however to imaginary and real eignvalues, respectively.
• Score: 7.21172766653517
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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