title: B-spline modal method: a polynomial approach compared to the Fourier modal method.
abstract: 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. With regard to BMM-based transmission and reflection computations, it is demonstrated that a novel Galerkin approach (in conjunction with a scattering-matrix algorithm) allows for an improved field matching between different layers. This approach is superior relative to the traditional point-wise field matching. Moreover, only this novel Galerkin approach allows for an competitive extension of BMM to the case of two-dimensional diffraction gratings. These improvements will be very useful for high-accuracy grating computations in general and for the analysis of associated electromagnetic field profiles in particular.
authors.affiliation: Institut für Theoretische Festkörperphysik (TFP) and DFG-Center for Functional Nanostructures (CFN), Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Str. 1, 76131 Karlsruhe, Germany.
authors.forename: Michael
authors.initials: M
authors.lastname: Walz
authors.forename: Thomas
authors.initials: T
authors.lastname: Zebrowski
authors.forename: Jens
authors.initials: J
authors.lastname: Küchenmeister
authors.forename: Kurt
authors.initials: K
authors.lastname: Busch
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D017076:Computer-Aided Design; D005583:Fourier Analysis; D008027:Light; D008962:Models, Theoretical; D009716:Numerical Analysis, Computer-Assisted; D012031:Refractometry / Q000295:instrumentation*; D012542:Scattering, Radiation