Geometry-dependent skin effects in reciprocal photonic crystals

TL;DR

This paper proposes a design for a reciprocal 2D photonic crystal that exhibits a geometry-dependent skin effect driven by non-Hermitian topology, expanding the understanding and potential applications of skin effects in photonic systems.

Contribution

It introduces a novel design strategy linking eigenvalue topology of exceptional points to skin effects in reciprocal 2D photonic crystals, demonstrating the effect through simulations.

Findings

Successful design of a 2D PhC with nonzero eigenvalue winding numbers.

Demonstration of the skin effect at specific crystalline interfaces.

Time-domain simulations vividly illustrate the skin effect phenomenon.

Abstract

Skin effect that all eigenmodes within a frequency range become edge states is dictated by the topological properties of complex eigenvalues unique in non-Hermitian systems. The prevailing attempts to realize such a fascinating effect are confined to either one-dimensional or nonreciprocal systems exhibiting asymmetric couplings. Here, inspired by a recent model Hamiltonian theory, we propose a realistic reciprocal two-dimensional (2D) photonic crystal (PhC) system that shows the desired skin effect. Specifically, we establish a routine for designing such non-Hermitian systems via revealing the inherent connections between the non-trivial eigenvalue topology of order-2 exceptional points (EPs) and the skin effects. Guided by the proposed strategy, we successfully design a 2D PhC that possesses the EPs with nonzero eigenvalue winding numbers. The spectral area along a specific wavevector direction is then formed by leveraging the symmetry of the macroscopic geometry and the unit cell. The projected-band-structure calculations are performed to demonstrate that the desired skin effect exists at the specific crystalline interfaces. We finally employ time-domain simulations to vividly illustrate this phenomenon by exciting a pulse at the center of a finite-sized PhC. Our results form a solid basis for further experimental confirmations and applications of the skin effect.