Three-dimensional adaptive coordinate transformations for the Fourier modal method

Abstract

Abstract:The concepts of adaptive coordinates and adaptive spatial resolution have proved to be a valuable tool to improve the convergence characteristics of the Fourier Modal Method (FMM), especially for metallo-dielectric systems. Yet, only two-dimensional adaptive coordinates were used so far. This paper presents the first systematic construction of three-dimensional adaptive coordinate and adaptive spatial resolution transformations in the context of the FMM. For that, the construction of a three-dimensional mesh for a periodic system consisting of two layers of mutually rotated, metallic crosses is discussed. The main impact of this method is that it can be used with any classic FMM code that is able to solve the large FMM eigenproblem. Since the transformation starts and ends in a Cartesian mesh, only the transformed material tensors need to be computed and entered into an existing FMM code.

Generalization and modularization of two-dimensional adaptive coordinate transformations for the Fourier modal method

“…Since this is not the first publication on this topic, I keep the section short and use the notation already used in [9][10][11][12][13]. The type of system considered in this paper in displayed in Fig.…”

“…Using the formulation from Section 3.2, the mesh in panel (c) can be constructed. The sketches are taken from [12] where the construction principle presented in Section 3.2 was already applied.…”

“…When both are combined, a great variety of structures can be reliably treated with the FMM [6][7][8]. In the last years, different concepts were found for the construction of the corresponding meshes in two [9][10][11] and even in three dimensions [12].…”