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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: Franco Gori
  • Vol. 28, Iss. 5 — May. 1, 2011
  • pp: 859–867

Perturbation approach applied to modal diffraction methods

Joerg Bischoff and Karl Hehl  »View Author Affiliations


JOSA A, Vol. 28, Issue 5, pp. 859-867 (2011)
http://dx.doi.org/10.1364/JOSAA.28.000859


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Abstract

Eigenvalue computation is an important part of many modal diffraction methods, including the rigorous coupled wave approach (RCWA) and the Chandezon method. This procedure is known to be computationally intensive, accounting for a large proportion of the overall run time. However, in many cases, eigenvalue information is already available from previous calculations. Some of the examples include adjacent slices in the RCWA, spectral- or angle-resolved scans in optical scatterometry and parameter derivatives in optimization. In this paper, we present a new technique that provides accurate and highly reliable solutions with significant improvements in computational time. The proposed method takes advantage of known eigensolution information and is based on perturbation method.

© 2011 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(050.1950) Diffraction and gratings : Diffraction gratings
(050.1960) Diffraction and gratings : Diffraction theory

ToC Category:
Diffraction and Gratings

History
Original Manuscript: February 16, 2011
Manuscript Accepted: February 17, 2011
Published: April 22, 2011

Citation
Joerg Bischoff and Karl Hehl, "Perturbation approach applied to modal diffraction methods," J. Opt. Soc. Am. A 28, 859-867 (2011)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-5-859


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References

  1. M. G. Moharam, D. A. Pommet, and E. B. Grann, “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]
  2. L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A 14, 2758–2767(1997). [CrossRef]
  3. J. Chandezon, D. Maystre, and G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. 11, 235–241 (1980). [CrossRef]
  4. G. Granet, “Analysis of diffraction by surface-relief crossed gratings with the use of the Chandezon method: application to multilayer crossed gratings,” J. Opt. Soc. Am. A 15, 1121–1130(1998). [CrossRef]
  5. L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13, 1024–1035 (1996). [CrossRef]
  6. C. Zhou and L. Li, “Formulation of the Fourier modal method for symmetric crossed gratings in symmetric mountings,” J. Opt. A 6, 43–50 (2004). [CrossRef]
  7. B. Bai and L. Li, “Group-theoretic approach to enhancing the Fourier modal method for crossed gratings with square symmetry,” J. Opt. Soc. Am. A 23, 572–580 (2006). [CrossRef]
  8. 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]
  9. T. Schuster, J. Ruoff, N. Kerwien, S. Raffler, 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]
  10. J. Bischoff, “Formulation of the normal vector RCWA for symmetric crossed gratings in symmetric mountings,” J. Opt. Soc. Am. A 27, pp. 1024–1031 (2010). [CrossRef]
  11. C. J. Raymond, S. S. H. Naqvi, and J. R. McNeil, “Resist and etched line profile characterization using scatterometry,” Proc. SPIE 3050, 476–486 (1997). [CrossRef]
  12. X. Niu, N. Jakatdar, J. Bao, C. Spanos, and S. Yedur, “Specular spectroscopic scatterometry in DUV lithography,” Proc. SPIE 3677, 159–168 (1999). [CrossRef]
  13. C. J. Raymond, M. R. Murnane, S. L. Prins, S. S. H. Naqvi, and J. R. McNeil, “Multiparameter grating metrology using optical scatterometry,” J. Vac. Sci. Technol. B 15, 361–368 (1997). [CrossRef]
  14. N. P. van der Aa and R. M. M. Mattheij, “Computing shape parameter sensitivity of the field of one-dimensional surface-relief gratings by using an analytical approach based on RCWA,” J. Opt. Soc. Am. A 24, 2692–2700 (2007). [CrossRef]
  15. J. Bischoff, K. Hehl, X. Niu, and W. Jin, “Approximating eigensolutions for use in determining the profile of a structure formed on a semiconductor wafer,” U.S. Patent 7,630,873 (8 December 2009).
  16. E. J. Hinch, Perturbation Methods, Cambridge Texts in Applied Mathematics (Cambridge University, 1992).
  17. K. Edee, J. P. Plumey, G. Granet, and J. Hazart, “Perturbation method for the rigorous coupled wave analysis of grating diffraction,” Opt. Express 18, 26274–26284 (2010). [CrossRef] [PubMed]

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