Hybrid finite element method and boundary element method for analysis of light diffraction on diffraction gratings
D.V. Nesterenko, V.V. Kotlyar

Image Processing Systems Institute of the Russian Academy of Sciences,
S.P. Korolyov Samara State Aerospace University

Full text of article: Russian language.

Abstract:
The hybrid finite element method and boundary element method realization for the simulation of the diffraction by periodical optical elements is an efficient numerical tool in case of complex geometry elements. The implementation of the hybrid method is discussed. As example we present the comparison with RCWA method of the simulations of binary dielectric gratings which demonstrates the efficiency of our approach.

Key words:
diffraction, diffraction grating, finite element method, boundary element method.

Citation: Nesterenko DV, Kotlyar VV. Hybrid finite element method and boundary element method for analysis of light diffraction on diffraction gratings. Computer Optics 2008; 32(3): 238-45.

References:

  1. Petit R. Electromagnetic Theory of Gratings: Topics in current physics. N.Y.: Springer-Verlag, 1980.
  2. Moharam MG. Rigorous coupled wave analysis of planar grating diffraction. J. Opt. Soc. A 1981; 71: 811–818.
  3. Chandezon J. A new theoretical method for diffraction gratings and its applications. J. Opt. (Paris) 1980; 11: 235–241.
  4. Urbach HP. Convergence of the Galerkin method for two-dimensional electromagnetic problems. SIAM J. Numer. Anal. 1991; 28: 697–710.
  5. Bao G. Finite element approximation of time harmonic waves in periodic structures. SIAM J. Numer. Anal. 1995; 32: 1155–1169.
  6. Elschner J. Finite element solution of conical diffraction problems. Advances in Comp. Math. 2002; 16: 139–156.
  7. Prather DW. Boundary integral methods to the analysis of diffractive optical elements. J. Opt. Soc. Am. A 1997; 14: 34–42.
  8. Yee K. Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Trans. Antennas Propag. 1966; AP-14: 302–307.
  9. Saj WM. FDTD simulations of 2D plasmon waveguide on silver nanorods in hexagonal lattice. Opt. Express 2005; 13:4818–4827.
  10. GSolver, rigorous diffraction grating analysis. URL:  http://www.gsolver.com. – Grating Solver Development Company.
  11. Soifer VA, ed. Methods of Computer Optics [In Russian]. Moscow: “Fizmatlit” Publisher; 2000: 688 p.
  12. Neganov VA, Raevsky SB, Yarovoy GP. Linear microscopic electrodynamics [In Russian]. Moscow: “Radio i svyaz” Publisher 2000; 509 p.
  13. Methods For Computer Design of Diffractive Optical Elements. Ed by Soifer VA. N.Y.: Wiley-Inter-science Publication John Wiley & Sons, Inc., 2002.
  14. Moharam MG. Formulation for Stable and Efficient Implementation of the Rigorous Coupled-Wave Analysis of Binary Gratings. J. Opt. Soc. A 1995; 12(5): 1068-1076.
  15. Nesterenko DV, Kotlyar VV. Light scattering in a dielectric cylinder consisting of metallic nanorod arrays [In Russian]. Computer Optics 2008; 32(1): 23-28.

© 2009, ИСОИ РАН
Россия, 443001, Самара, ул. Молодогвардейская, 151; электронная почта: ko@smr.ru ; тел: +7 (846) 332-56-22, факс: +7 (846 2) 332-56-20