Optimizing bi-layered periodic structures: a closed-form transfer matrix method based on Pendry-MacKinnon’s discrete Maxwell’s equations

Abstract

The optimization procedure that we present is based on a closed-form exact analytical solution for the three-dimensional transfer matrix that we put forward in arXiv, arXiv:2303.06765 (2023)10.48550/arXiv.2303.06765. The analytical solution is valid for all modes, either propagative or evanescent, and any non-magnetic isotropic pattern with frequency-dependent permittivities. In this paper we exemplify the use of the transfer matrix elements to optimize a patterned bilaminar structure such that a subset of evanescent Bloch-Floquet modes (M x ,M y )≠0 acquire large scattering matrix elements at a specified frequency. Such an excited resonant mode propagates along the device’s surface at a frequency smaller than its Rayleigh frequency. These predictions are grouped into three categories. The first category, inspired by topological photonics, is related to robustness of the resonant modes with respect to the change of the dielectric constants, quantified as a map from the real to integer numbers. The second is based on resonant frequency identification, whereas the third is focused on high Q-factors and the use of a complex frequency plane to estimate the Fano-Lorentz spectral line shape for the resonant modes. All the predictions based on the proposed optimization were confirmed by a high-performance analysis software package [CST Studio Suite (2022)].