Three-dimensional adaptive coordinate transformations for the Fourier modal method

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.