OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 27, Iss. 1 — Jan. 1, 2010
  • pp: 116–122

Fast diffraction computation schema for multilayer crossed gratings containing layers with 1D periodicity

Joerg Bischoff  »View Author Affiliations

JOSA A, Vol. 27, Issue 1, pp. 116-122 (2010)

View Full Text Article

Enhanced HTML    Acrobat PDF (216 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The diffraction computation of crossed gratings is very slow compared with that of line-space gratings of the same size when using a modal method such as rigorous coupled wave analysis (RCWA) or the Chandezon coordinate transformation method. It is well known that the main bottleneck in terms of computation speed is the solution of an eigenproblem for each RCWA slice or interface in the case of the C-method. Even if the crossed grating contains layers that are periodic only in one direction, usually the full 2D problem has to be solved for this layer in order to connect it to the full system solution. In this paper, a computation schema is presented that takes advantage of the 1D periodicity of layers inside a 2D multilayer grating. This results in a considerable acceleration of the formulation and solution of the eigenproblem for these layers. With this new computation schema the total time required for 1D layers in a 2D layer stack can be greatly reduced.

© 2009 Optical Society of America

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

ToC Category:
Diffraction and Gratings

Original Manuscript: September 21, 2009
Revised Manuscript: November 16, 2009
Manuscript Accepted: November 20, 2009
Published: December 23, 2009

Joerg Bischoff, "Fast diffraction computation schema for multilayer crossed gratings containing layers with 1D periodicity," J. Opt. Soc. Am. A 27, 116-122 (2010)

Sort:  Author  |  Year  |  Journal  |  Reset  


  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. I. C. Botten, M. S. Craig, R. C. McPhedran, L. Adams, and J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087-1102 (1981).
  3. J. Chandezon, D. Maystre, and G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. (Paris) 11, 235-241 (1980).
  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. J. Bischoff, “Beiträge zur theoretischen und experimentellen Untersuchung der Lichtbeugung an mikrostrukturierten Mehrschichtsystemen,” Habilitation thesis (Technical University Ilmenau, Germany, 2000).
  6. B. Gralak, M. de Doof, G. Tayeb, S. Enoch, and D. Maystre, “Theoretical study of photonic band gaps in woodpile crystals,” Phys. Rev. E 67, 066601 (2003). [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. 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]
  9. L. Li, “Note on the S-matrix propagation algorithm,” J. Opt. Soc. Am. A 20, 655-660 (2003). [CrossRef]
  10. http://www.netlib.org/lapack/

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited