A B-Spline Modal Method in Comparison to the Fourier Modal Method

The Fourier modal method (FMM) is a common tool when transmittance or reflectance spectra of periodic structures are needed. In this work, we investigate an approach one could call the B‐spline modal method (BMM). We use an S‐matrix algorithm for connecting different layers but instead of a Fourier basis we use B‐splines to solve Maxwell’s equations in each layer. The advantage of B‐splines compared to plane waves is that they can represent discontinuities accurately. These discontinuities (naturally arising at interfaces between different materials) are problematic for the FMM since a finite Fourier series will always be smooth and one has to deal with Gibbs’ phenomenon. In this work, we present a comparison of the convergence behavior between FMM and BMM.