Reduction of computation time for crossed-grating problems: a group-theoretic approach.

A systematic approach based on group theory is established to deal with diffraction problems of crossed gratings by exploiting symmetries. With this approach, a problem in an asymmetrical incident mounting can be decomposed into a superposition of several symmetrical basis problems so that the computation efficiency is improved effectively. This methodology offers a convenient and succinct way to treat all possible symmetry cases by following only several mechanical steps instead of intricate mathematical considerations or physical intuition. It is also general, applicable to both scalar-wave and vector-wave problems and in principle can be easily adapted to any numerical method. A numerical example is presented to show its application and effectiveness.

[1]  M F Becker,et al.  Electromagnetic scattering of two-dimensional surface-relief dielectric gratings. , 1992, Applied optics.

[2]  David C. Dobson,et al.  Integral equation method for biperiodic diffraction structures , 1991, Optics & Photonics.

[3]  Fernando Reitich,et al.  Numerical solution of diffraction problems: a method of variation of boundaries , 1993 .

[4]  Lifeng Li,et al.  Fourier modal method for crossed anisotropic gratings with arbitrary permittivity and permeability tensors , 2003 .

[5]  J. Greffet,et al.  Diffraction of electromagnetic waves by crossed gratings: a series solution. , 1992, Optics letters.

[6]  J. R. Sambles,et al.  Optical response of bigratings , 1996 .

[7]  Ross C. McPhedran,et al.  Crossed gratings: A theory and its applications , 1979 .

[8]  Lifeng Li,et al.  New formulation of the Fourier modal method for crossed surface-relief gratings , 1997 .

[9]  Fernando Reitich,et al.  Calculation of electromagnetic scattering VIA boundary variations and analytic continuation , 1995 .

[10]  Fernando Reitich,et al.  Numerical solution of diffraction problems: a method of variation of boundaries. III. Doubly periodic gratings , 1993 .

[11]  Gérard Granet,et al.  Parametric formulation of the Fourier modal method for crossed surface-relief gratings , 2002 .

[12]  Chuanhong Zhou,et al.  Formulation of the Fourier modal method for symmetric crossed gratings in symmetric mountings , 2004 .

[13]  T. Hahn.  International tables for crystallography , 2002 .

[14]  R. McPhedran,et al.  Metallic crossed gratings , 1982 .

[15]  P. Vincent,et al.  A finite-difference method for dielectric and conducting crossed gratings , 1978 .

[16]  Stéphane Mainguy,et al.  Diffraction of electromagnetic waves by dielectric crossed gratings: a three- dimensional Rayleigh-Fourier solution , 1999 .

[17]  Gérard Granet,et al.  Analysis of diffraction by surface-relief crossed gratings with use of the Chandezon method: application to multilayer crossed gratings , 1998 .

[18]  Philippe Lalanne,et al.  On the effective medium theory of subwavelength periodic structures , 1996 .

[19]  Olof Bryngdahl,et al.  Electromagnetic diffraction analysis of two-dimensional gratings , 1993 .

[20]  Jari Turunen,et al.  Eigenmode method for electromagnetic synthesis of diffractive elements with three-dimensional profiles , 1994 .

[21]  D. Maystre,et al.  Electromagnetic theory of crossed gratings , 1978 .

[22]  P. Lalanne,et al.  Highly improved convergence of the coupled-wave method for TM polarization and conical mountings , 1996, Diffractive Optics and Micro-Optics.

[23]  Brahim Guizal,et al.  Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization , 1996 .

[24]  Philippe Lalanne,et al.  Improved formulation of the coupled-wave method for two-dimensional gratings , 1997 .

[25]  Lifeng Li,et al.  Use of Fourier series in the analysis of discontinuous periodic structures , 1996 .