Singular Transmission Properties of Electromagnetic Waves in One-Dimensional PT-symmetric Triangular Optical Waveguide Networks

In this paper, the singular transmission properties of electromagnetic waves in one-dimensional PT-symmetric triangular finite periodic optical waveguide networks are investigated. We find that the transmission properties of electromagnetic waves differ significantly depending on whether the imaginary part of the system’s Bloch phase is zero or non-zero. Based on this, the generalized passbands and bandgaps of the PT-symmetric optical waveguide network are defined, and its generalized band structure is presented. Furthermore, we discover that electromagnetic waves incident within the frequency range of generalized bandgaps, where transmittance approaches zero, exhibit a reciprocal relationship between left and right reflectance. The system can generate interesting phenomena such as bidirectional total reflection, unidirectional super reflection, and unidirectional no reflection at these frequencies. It is also demonstrated that the frequency positions of these phenomena can be flexibly controlled by adjusting the length of the PT-symmetric waveguide and the imaginary part of its refractive index. These research findings offer a scientific basis for developing highly sensitive and multifunctional optical filters and laser reflectors.