Matched coordinate technique in the analysis of self-assembled cylinders

Abstract

This paper explores the utilization of matched coordinates for the comprehensive analysis of self-assembled cylinders, specifically focusing on a crossed grating with circular cross section within a hexagonal lattice. By incorporating the matched coordinate technique into the Fourier modal method (FMM), the paper addresses the limitations associated with staircase approximations when solving Maxwell’s equations in a curvilinear coordinate system. The study demonstrates that the proposed transformation significantly enhances the efficiency and speed of FMM, particularly in extracting optical characteristics such as reflection and transmission coefficients. Through a comparative analysis of a hexagonal lattice comprising air-suspended cylindrical resonators with a dielectric constant of 2, the proposed technique is shown to achieve comparable accuracy while utilizing only \(40\%\) of the harmonics required by conventional methods. As a result, this approach offers substantial computational cost reductions of up to an order of magnitude.