title: Vectorial thin-element approximation: a semirigorous determination of Kirchhoff's boundary conditions.
abstract: A semirigorous model is presented that bridges the gap between classical scalar diffraction theory on the one hand and fully rigorous simulation models on the other. It falls back on the basic ideas of scalar diffraction theory, especially the Kirchhoff approximation. In contrast to classical techniques, however, the boundary values are determined by rigorous methods of the stratified medium theory in the scope of a fully vectorial formulation. By this means the proposed approach takes vertical rigorous coupling effects inside the grating into account while neglecting the lateral ones. We therefore call this method semirigorous and use the name vectorial thin-element approximation. A direct comparison with rigorous coupled-wave analysis as a fully rigorous simulation model allows a detailed discussion of its range of validity and demonstrates a reduction of computation time of the order of 3 magnitudes. In addition, it also reveals deeper insight into the details of the electrodynamics inside diffracting structures. Some examples will demonstrate this benefit.
authors.affiliation: Institut für Technische Optik, Universität Stuttgart, Pfaffenwalring 9, 70569 Stuttgart, Germany. Kerwien@ito.uni-stuttgart.de
authors.forename: Norbert
authors.initials: N
authors.lastname: Kerwien
authors.forename: Thomas
authors.initials: T
authors.lastname: Schuster
authors.forename: Stephan
authors.initials: S
authors.lastname: Rafler
authors.forename: Wolfgang
authors.initials: W
authors.lastname: Osten
authors.forename: Michael
authors.initials: M
authors.lastname: Totzeck
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D020342:Finite Element Analysis; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008962:Models, Theoretical; D012031:Refractometry / Q000379:methods*; D012542:Scattering, Radiation