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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Steven A. Burns
  • Vol. 24, Iss. 9 — Sep. 1, 2007
  • pp: 2880–2890

Normal vector method for convergence improvement using the RCWA for crossed gratings

Thomas Schuster, Johannes Ruoff, Norbert Kerwien, Stephan Rafler, and Wolfgang Osten  »View Author Affiliations


JOSA A, Vol. 24, Issue 9, pp. 2880-2890 (2007)
http://dx.doi.org/10.1364/JOSAA.24.002880


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Abstract

The rigorous coupled wave analysis (RCWA) is a widely used method for simulating diffraction from periodic structures. Since its recognized formulation by Moharam et al. [J. Opt. Soc. Am. A 12, 1068 and 1077 (1995)] , there still has been a discussion about convergence problems. Those problems are more or less solved for the diffraction from line gratings, but there remain different concurrent proposals about the convergence improvement for crossed gratings. We propose to combine Popov and Nevière's formulation of the differential method [Light Propagation in Periodic Media (Dekker, 2003) and J. Opt. Soc. Am. A 18, 2886 (2001)] with the classical RCWA. With a suitable choice of a normal vector field we obtain a better convergence than for the formulations that are known from the literature.

© 2007 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.1960) Diffraction and gratings : Diffraction theory
(260.0260) Physical optics : Physical optics
(260.1960) Physical optics : Diffraction theory

ToC Category:
Diffraction and Gratings

History
Original Manuscript: April 3, 2007
Revised Manuscript: May 21, 2007
Manuscript Accepted: May 23, 2007
Published: August 21, 2007

Citation
Thomas Schuster, Johannes Ruoff, Norbert Kerwien, Stephan Rafler, and Wolfgang Osten, "Normal vector method for convergence improvement using the RCWA for crossed gratings," J. Opt. Soc. Am. A 24, 2880-2890 (2007)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-24-9-2880


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References

  1. E. Popov and M. Nevière, Light Propagation in Periodic Media (Dekker, 2003).
  2. 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]
  3. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, "Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings," J. Opt. Soc. Am. A 12, 1068-1076 (1995). [CrossRef]
  4. M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, "Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach," J. Opt. Soc. Am. A 12, 1077-1086 (1995). [CrossRef]
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  7. L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A 13, 1870-1876 (1996). [CrossRef]
  8. E. Popov, B. Chernov, M. Nevière, and N. Bonod, "Differential theory: application to highly conducting gratings," J. Opt. Soc. Am. A 21, 199-206 (2004). [CrossRef]
  9. P. Lalanne, "Improved formulation of the coupled-wave method for two-dimensional gratings," J. Opt. Soc. Am. A 14, 1592-1598 (1997). [CrossRef]
  10. L. Li, "New formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. Soc. Am. A 14, 2758-2767 (1997). [CrossRef]
  11. E. Popov, M. Neviére, B. Gralak, and G. Tayeb, "Staircase approximation validity for arbitrary-shaped gratings," J. Opt. Soc. Am. A 19, 33-42 (2002). [CrossRef]
  12. T. Driscoll, "Schwarz-Christoffel toolbox for MATLAB," http://www.math.udel.edu/∼driscoll/software.
  13. I. Sneddon, Encylopaedic Dictionary of Mathematics for Engineers and Applied Scientists (Wheatons, 1976).

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