OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 21, Iss. 2 — Feb. 1, 2004
  • pp: 199–206

Differential theory: application to highly conducting gratings

Evgeny Popov, Boris Chernov, Michel Nevière, and Nicolas Bonod  »View Author Affiliations


JOSA A, Vol. 21, Issue 2, pp. 199-206 (2004)
http://dx.doi.org/10.1364/JOSAA.21.000199


View Full Text Article

Enhanced HTML    Acrobat PDF (352 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The recently developed fast Fourier factorization method, which has greatly improved the application range of the differential theory of gratings, suffers from numerical instability when applied to metallic gratings with very low losses. This occurs when the real part of the refractive index is small, in particular, smaller than 0.1–0.2, for example, when silver and gold gratings are analyzed in the infrared region. This failure can be attributed to Li’s “inverse rule” [LiL., J. Opt. Soc. Am. A 13, 1870 (1996)] as shown by studying the condition number of matrices that have to be inverted. Two ways of overcoming the difficulty are explored: first, an additional truncation of the matrices containing the coefficients of the differential system, which reduces the numerical problems in some cases, and second, an introduction of lossier material inside the bulk, thus leaving only a thin layer of the highly conducting metal. If the layer is sufficiently thick, this does not change the optical properties of the system but significantly improves the convergence of the differential theory, including the rigorous coupled-wave method, for various types of grating profiles.

© 2004 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(050.1940) Diffraction and gratings : Diffraction
(050.1950) Diffraction and gratings : Diffraction gratings
(050.1960) Diffraction and gratings : Diffraction theory
(050.2770) Diffraction and gratings : Gratings
(260.1960) Physical optics : Diffraction theory
(260.2110) Physical optics : Electromagnetic optics

History
Original Manuscript: June 23, 2003
Revised Manuscript: September 12, 2003
Manuscript Accepted: September 24, 2003
Published: February 1, 2004

Citation
Evgeny Popov, Boris Chernov, Michel Nevière, and Nicolas Bonod, "Differential theory: application to highly conducting gratings," J. Opt. Soc. Am. A 21, 199-206 (2004)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-21-2-199


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. M. Nevière, G. Cerutti-Maori, M. Cadilhac, “Sur une nouvelle méthode de résolution du problème de la diffraction d’une onde plane par un réseau infiniment conducteur,” Opt. Commun. 3, 48–52 (1971). [CrossRef]
  2. M. Nevière, R. Petit, M. Cadilhac, “About the theory of optical grating coupler-waveguide systems,” Opt. Commun. 8, 113–117 (1973). [CrossRef]
  3. M. Nevière, P. Vincent, R. Petit, M. Cadilhac, “Systematic study of resonances of holographic thin film couplers,” Opt. Commun. 9, 48–53 (1973). [CrossRef]
  4. M. Nevière, P. Vincent, R. Petit, “Sur la théorie du réseau conducteur et ses applications à l’optique,” Nouv. Rev. Opt. 5, 65–77 (1974).
  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. M. Nevière, E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (Marcel Dekker, New York, 2003).
  7. E. Popov, M. Nevière, “Grating theory: New equations in Fourier space leading to fast converging results for TM polarization,” J. Opt. Soc. Am. A 17, 1773–1784 (2000). [CrossRef]
  8. E. Popov, M. Nevière, “Maxwell equations in Fourier space: Fast converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media,” J. Opt. Soc. Am. A 17, 1773 (2001). [CrossRef]
  9. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876 (1996). [CrossRef]
  10. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The dielectric lamellar diffraction grating,” Opt. Acta 28, 413–428 (1981). [CrossRef]
  11. C. Botten, M. S. Craig, R. C. McPhedran, J. L. Adams, J. R. Andrewartha, “The finitely conducting lamellar diffraction grating,” Opt. Acta 28, 1087–1102 (1981). [CrossRef]
  12. J. R. Andrewartha, G. H. Derrick, R. C. McPhedran, “A general modal theory for reflection gratings,” Opt. Acta 28, 1501–1516 (1981). [CrossRef]
  13. S. T. Peng, T. Tamir, H. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975). [CrossRef]
  14. M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981). [CrossRef]
  15. M. G. Moharam, T. K. Gaylord, “Rigorous coupled-wave analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1385–1392 (1982). [CrossRef]
  16. M. G. Moharam, D. A. Pommet, E. B. Grann, T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmission matrix approach,” J. Opt. Soc. Am. A 12, 1077–1086 (1995). [CrossRef]
  17. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in Fortran: The Art of Scientific Computing, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

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.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited