Group-theoretic approach to the enhancement of the Fourier modal method for crossed gratings: C2 symmetry case

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 22, Issue 4, 2005, Pages 654-661

  Bai, Benfeng ^a   Li, Lifeng ^a  

^a TSINGHUA UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; CRYSTAL LATTICES; CRYSTALLOGRAPHY; FOURIER OPTICS; FOURIER TRANSFORMS; MATHEMATICAL MODELS; MODAL ANALYSIS; PERMITTIVITY;

COMPUTATION EFFICIENCY; CROSSED GRATINGS; FOURIER MODAL METHOD; LITTROW MOUNTED LATTICE; TRUNCATED RECIPROCAL LATTICE;

DIFFRACTION GRATINGS;

EID: 17644363317     PISSN: 10847529     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAA.22.000654     Document Type: Article

References (18)

1. R. Bräuer and O. Bryngdahl, "Electromagnetic diffraction analysis of two-dimensional gratings," Opt. Commun. 100, 1-5 (1993).
2. E. Noponen and J. Turunen, "Eigenmode method for electromagnetic synthesis of diffractive elements with three-dimensional profiles," J. Opt. Soc. Am. A 11, 2494-2502 (1994).
3. L. Li, "New formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. Soc. Am. A 14, 2758-2767 (1997).
4. L. Li, "Fourier modal method for crossed anisotropic gratings with arbitrary permittivity and permeability tensors," J. Opt. A, Pure Appl. Opt. 5, 345-355 (2003).
5. G. Granet and J. Plumey, "Parametric formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. A, Pure Appl. Opt. (Suppl.) 4, S145-S149 (2002).
6. Ph. Lalanne and D. Lemercier-Lalanne, "On the effective medium theory of subwavelength periodic structures," J. Mod. Opt. 43, 2063-2085 (1996).
7. Ph. Lalanne, "Improved formulation of the coupled-wave method for two-dimensional gratings," J. Opt. Soc. Am. A 14, 1592-1598 (1997).
8. C. Zhou and L. Li, "Formulation of Fourier modal method of symmetric crossed gratings in symmetric mountings," J. Opt. A, Pure Appl. Opt. 6, 43-50 (2004).
9. B. Bai and L. Li, "Reduction of computation time for crossed-grating problems: a group-theoretic approach," J. Opt. Soc. Am. A 21, 1886-1894 (2004).
10. W. Ludwig and C. Falter, Symmetries in Physics: Group Theory Applied to Physical Problems (Springer, Berlin, 1988).
11. J. V. Smith, Geometrical and Structural Crystallography (Wiley, New York, 1982).
12. See, for example, J. F. Cornwell, ed., Group Theory in Physics: an Introduction (Academic, San Diego, Calif., 1997), App. C, pp. 299-318.
13. L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A 13, 1870-1876 (1996).
14. See, for example, R. C. Wrede, Introduction to Vector and Tensor Analysis (Dover, New York, 1972), Chap. 1.
15. . The derivation of matrix G in Ref. 3, in the case of ζ ≠ 0, depended on the validity of an unproven hypothesis. In Ref. 4 a different form of matrix G was rigorously derived. However, the numerical examples reported in Ref. 4 showed that the two forms of matrix G have more or less the same convergence rate. Here for simplicity we use the old form.
16. L. Li, "Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings," J. Opt. Soc. Am. A 13 1024-1035 (1996).
17. L. Li, "Note on the S-matrix propagation algorithm," J. Opt. Soc. Am. A 20, 655-660 (2003).
18. A. Sentenac, Ph. Lalanne, and D. Maystre, "Symmetry properties of the field transmitted by inductive grids," J. Mod. Opt. 47, 2323-2333 (2000).