Searching spectral singularities in non-Hermitian multi-layer structures based on the particle swarm optimization algorithm

Spectral singularity refers to a point in the spectrum where the transmittance or reflectance is infinitely high, typically occurring in non-Hermitian systems. How to quickly find the conditions of spectral singularities in complex optical structures is an important issue. In this paper, we propose a method to quickly obtain the parameters that are required for spectral singularities in non-Hermitian structures by particle swarm optimization (PSO) algorithm. Specifically, for a multi-layer film structure with alternating loss-neutral-gain-neutral materials, we first obtain the relation between the transmittance/reflectance and the material parameters using the transfer matrix method, then apply the PSO algorithm to quickly search the spectral singularity and the required condition. These results are confirmed by traditional analytical calculations through the calculation of the eigenvalues of the scattering matrix. In this process, it is found that the spectral singularities are highly sensitive to the system parameters, such as the real and imaginary parts of the refractive indices, demonstrating the potential applications of non-Hermitian multi-layer structures in sensing and detection. Our research demonstrates the effectiveness of the PSO algorithm in searching critical optical properties in complex non-Hermitian optical systems.