Efficient calculation of the optical properties of stacked metamaterials with a Fourier modal method

In its original formulation the Fourier modal method provides a very fast convergence for one- and two-dimensional dielectric structures, but owing to the Gibbs phenomenon the convergence is poor for a high contrast of the permittivity function, especially for metal-dielectric structures. The scheme has been improved by methods such as factorization rules and adaptive spatial resolution. We are going to discuss the combination of these methods in a covariant formulation, including a new method to calculate the homogeneous sub- and superstrates in the adaptive coordinate system. We use it to obtain the optical properties of split-ring resonators. Additionally, we will show how the spectra of stacked structures can be derived very efficiently.