Abstract

Early formulations of the RCWA yield, implicated by the erroneous application of factorization rules to discrete Fourier transformations, poor convergence in certain cases. An explanation for this finding and an approach to overcome the problem for crossed gratings was first given by Li [J. Opt. Soc. Am. A 13, 1870 (1996) and 14, 2758 (1997)]. A further improvement was achieved by Schuster et al. [J. Opt. Soc. Am. A 24, 2880 (2007)], using a structure dependent normal vector (NV) field. While it is trivial to create those NV fields for simple geometrical shapes, to our knowledge an appropriate algorithm for arbitrary shapes does not exist, yet. In this work we present such an algorithm.

© 2008 Optical Society of America

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  1. M. G. Moharam and T. K. Gaylord, "Rigorous coupled-wave analysis of planar-grating diffraction," J. Opt. Soc. Am. 71, 811-818 (1981).
  2. L. Li and C. W. Haggans, "Convergence of the coupled-wave method for metallic lamellar diffraction gratings," J. Opt. Soc. Am. A 10, 1184-1189 (1993).
  3. P. Lalanne and M. Morris, "Highly improved convergence of the coupled-wave method for TM polarization," J. Opt. Soc. Am. A 13, 779-784 (1996).
    [CrossRef]
  4. G. Granet and B. Guizal, "Efficient implemenation of the coupled-wave method for metallic lamellar grating in TM polarization," J. Opt. Soc. Am. A 13, 1019-1023 (1996).
  5. L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A 13, 1870-1876 (1996).
  6. P. Lalanne, "Improved formulation of the coupled-wave method for two-dimensional gratings," J. Opt. Soc. Am. A 14, 1592-1598 (1997).
    [CrossRef]
  7. L. Li, "New formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. Soc. Am. A 14, 2758-2767 (1997).
    [CrossRef]
  8. T. Schuster, J. Ruoff, N. Kerwien, S. Rafler, and W. Osten, "Normal vector method for convergence improvement using the RCWA for crossed gratings," J. Opt. Soc. Am. A 24, 2880-2890 (2007).
    [CrossRef]
  9. M. Nevière and E. Popov, Light Propagation in Periodic Media - Differential Theory and Design (Marcel Dekker, Inc., New York, 2003).
  10. E. Popov and M. Nevière, "Maxwell equations in Fourier space: fast-converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media," J. Opt. Soc. Am. A 18, 2886-2894 (2001).
    [CrossRef]
  11. D. Shepard, "A two-dimensional interpolation function for irregularly-spaced data," pp. 517-524 (ACM National Conference, 1968).
  12. R. Franke, "Scattered Data Interpolation: Tests of Some Methods," Math. Comput. 38, 181-200 (1982).
    [CrossRef]
  13. M. G. Moharam, T. K. Gaylord, E. B. Grann, and D. A. Pommet, "Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings," J. Opt. Soc. Am. A 12, 1068-1076 (1995).
  14. R. Bräuer and O. Bryngdahl, "Electromagnetic diffraction analysis of two-dimensional gratings" Opt. Commun. 100, 1-5 (1993).
    [CrossRef]
  15. P. Götz, "Simulation von Lichtbeugung mit der Normalenvektormethode," Diploma thesis, Universität Stuttgart, Germany (2008).

2007

2001

1997

1996

1995

1993

R. Bräuer and O. Bryngdahl, "Electromagnetic diffraction analysis of two-dimensional gratings" Opt. Commun. 100, 1-5 (1993).
[CrossRef]

L. Li and C. W. Haggans, "Convergence of the coupled-wave method for metallic lamellar diffraction gratings," J. Opt. Soc. Am. A 10, 1184-1189 (1993).

1982

R. Franke, "Scattered Data Interpolation: Tests of Some Methods," Math. Comput. 38, 181-200 (1982).
[CrossRef]

1981

Bräuer, R.

R. Bräuer and O. Bryngdahl, "Electromagnetic diffraction analysis of two-dimensional gratings" Opt. Commun. 100, 1-5 (1993).
[CrossRef]

Bryngdahl, O.

R. Bräuer and O. Bryngdahl, "Electromagnetic diffraction analysis of two-dimensional gratings" Opt. Commun. 100, 1-5 (1993).
[CrossRef]

Franke, R.

R. Franke, "Scattered Data Interpolation: Tests of Some Methods," Math. Comput. 38, 181-200 (1982).
[CrossRef]

Gaylord, T. K.

Granet, G.

Grann, E. B.

Guizal, B.

Haggans, C. W.

Kerwien, N.

Lalanne, P.

Li, L.

Moharam, M. G.

Morris, M.

Nevière, M.

Osten, W.

Pommet, D. A.

Popov, E.

Rafler, S.

Ruoff, J.

Schuster, T.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

E. Popov and M. Nevière, "Maxwell equations in Fourier space: fast-converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media," J. Opt. Soc. Am. A 18, 2886-2894 (2001).
[CrossRef]

T. Schuster, J. Ruoff, N. Kerwien, S. Rafler, and W. Osten, "Normal vector method for convergence improvement using the RCWA for crossed gratings," J. Opt. Soc. Am. A 24, 2880-2890 (2007).
[CrossRef]

P. Lalanne, "Improved formulation of the coupled-wave method for two-dimensional gratings," J. Opt. Soc. Am. A 14, 1592-1598 (1997).
[CrossRef]

L. Li, "New formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. Soc. Am. A 14, 2758-2767 (1997).
[CrossRef]

L. Li and C. W. Haggans, "Convergence of the coupled-wave method for metallic lamellar diffraction gratings," J. Opt. Soc. Am. A 10, 1184-1189 (1993).

P. Lalanne and M. Morris, "Highly improved convergence of the coupled-wave method for TM polarization," J. Opt. Soc. Am. A 13, 779-784 (1996).
[CrossRef]

G. Granet and B. Guizal, "Efficient implemenation of the coupled-wave method for metallic lamellar grating in TM polarization," J. Opt. Soc. Am. A 13, 1019-1023 (1996).

L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A 13, 1870-1876 (1996).

M. G. Moharam, T. K. Gaylord, E. B. Grann, and D. A. Pommet, "Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings," J. Opt. Soc. Am. A 12, 1068-1076 (1995).

Math. Comput.

R. Franke, "Scattered Data Interpolation: Tests of Some Methods," Math. Comput. 38, 181-200 (1982).
[CrossRef]

Opt. Commun.

R. Bräuer and O. Bryngdahl, "Electromagnetic diffraction analysis of two-dimensional gratings" Opt. Commun. 100, 1-5 (1993).
[CrossRef]

Other

P. Götz, "Simulation von Lichtbeugung mit der Normalenvektormethode," Diploma thesis, Universität Stuttgart, Germany (2008).

M. Nevière and E. Popov, Light Propagation in Periodic Media - Differential Theory and Design (Marcel Dekker, Inc., New York, 2003).

D. Shepard, "A two-dimensional interpolation function for irregularly-spaced data," pp. 517-524 (ACM National Conference, 1968).

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