Singular optical propagation properties of two types of one-dimensional anti-$\mathcal{PT}$-symmetric periodic ring optical waveguide networks

Abstract

Two types of one-dimensional (1D) anti-$\mathcal{PT}$-symmetric periodic ring optical waveguide networks (APTPROWNS), consisting of gain and loss materials, respectively, are constructed in this study. The singular optical propagation properties of these networks are investigated. The results show that that system composed of gain materials exhibits characteristics of ultra-strong transmission and bidirectional reflection. Conversely, the system composed of loss materials demonstrates equal transmittance and reflectance at some frequency position. In both systems, a new type of total reflection phenomenon is observed. When the imaginary part of the refractive indices of waveguide segments is smaller than $10^{-5}$, the system shows bidirectional transparency with the transmittance tending to be 1and reflectivity be smaller than $10^{-8}$ at some bands, while when the refractive indices of the waveguide segments is real, the system will be bidirectional transparent at the full band. These findings may deepen the understanding of anti-$\mathcal{PT}$-symmetric optical systems and optical waveguide networks, and possess potential applications in efficient optical energy storage, ultra-sensitive optical filters, ultra-sensitive all-optical switches, integrated optical chips, stealth physics, and so on.