Universal appearance tendency of modes at the finite periodic PT-symmetric structure

Abstract

We investigate the emergence of specific modes in finite periodic (FP) parity-time (PT) symmetric photonic structures using the transfer matrix (T-matrix) formalism. Three distinct resonant states are identified-the coherent perfect absorber-laser (McL), the unidirectional invisibility (MUI), and the anti-reflection (MAR) modes. We show that, unlike in a single-period PT bilayer-where the McL mode arises only once-FP structures support recurring McL modes as the number of periods increases. MAR modes appear between successive McL modes. The required imaginary part of the refractive index (n '') for the emergence of each mode is determined by the ratio l/N, where l is the mode order and N the number of periods. For small l/N, n '' increases linearly, whereas for large l/N, n '' approaches the PT critical point. Furthermore, the phase diagram shows that McL modes exist solely in the PT-broken phase, while MAR modes remain confined to the PT-symmetric phase. These findings are validated using photonic nanobeam simulations, demonstrating the systematic realization of the three modes in FP PT-symmetric photonic systems. (c) 2026 Optica Publishing Group. All rights, including for text and data mining (TDM), Artificial Intelligence (AI) training, and similar technologies, are reserved.