A detailed analysis of the B-spline Modal Method (BMM) for one- and two-dimensional diffraction gratings and a comparison to the Fourier Modal Method (FMM) is presented. Owing to its intrinsic capability to accurately resolve discontinuities, BMM avoids the notorious problems of FMM that are associated with the Gibbs phenomenon. As a result, BMM facilitates significantly more efficient eigenmode computations.

The concepts of adaptive coordinates and adaptive spatial resolution significantly enhance the performance of Fourier Modal Method for the simulation of periodic photonic structures, especially metallo-dielectric systems. We present several approaches for constructing different types of analytical coordinate transformations that are applicable to a great variety of structures. In addition, we analyze these meshes with an emphasis on the resulting convergence characteristics. This allows us to formulate general guidelines for the choice of mesh type and mesh parameters.