OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 38, Iss. 1 — Jan. 1, 1999
  • pp: 47–55

Integral method for echelles covered with lossless or absorbing thin dielectric layers

Evgeny Popov, Bozhan Bozhkov, Daniel Maystre, and John Hoose  »View Author Affiliations

Applied Optics, Vol. 38, Issue 1, pp. 47-55 (1999)

View Full Text Article

Enhanced HTML    Acrobat PDF (167 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We make a generalization of the integral method in the electromagnetic theory of gratings to study diffraction by echelles covered with dielectric lossless or absorbing layers. Numerical examples are given that show that, as in the resonance domain, the diffraction efficiency is more complicated than being a simple product of lossless diffraction efficiency curves and plane surface reflectivity.

© 1999 Optical Society of America

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

Original Manuscript: May 12, 1998
Revised Manuscript: September 9, 1998
Published: January 1, 1999

Evgeny Popov, Bozhan Bozhkov, Daniel Maystre, and John Hoose, "Integral method for echelles covered with lossless or absorbing thin dielectric layers," Appl. Opt. 38, 47-55 (1999)

Sort:  Author  |  Year  |  Journal  |  Reset  


  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. 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]
  3. F. Montiel, M. Nevière, “Differential theory of gratings: extension to deep gratings of arbitrary profile and permittivity via the R-matrix propagation algorithm,” J. Opt. Soc. Am. A 12, 2672–2678 (1995). [CrossRef]
  4. M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1385–1392 (1982). [CrossRef]
  5. L. Li, “Multilayer modal method for diffraction gratings of arbitrary profile, depth, and permittivity,” J. Opt. Soc. Am. A 10, 2581–2591 (1993). [CrossRef]
  6. P. Lalanne, G. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779–784 (1996). [CrossRef]
  7. G. Granet, B. Guizal, “Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization,” J. Opt. Soc. Am. A 13, 1019–1023 (1996). [CrossRef]
  8. J. Chandezon, M. T. Dupuis, G. Cornet, D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region,” J. Opt. Soc. Am. 72, 839–846 (1982). [CrossRef]
  9. J. P. Plumey, B. Guizal, J. Chandezon, “The coordinate transformation method as applied to asymmetric gratings with vertical facets,” J. Opt. Soc. Am. A 14, 610–617 (1997). [CrossRef]
  10. G. Granet, J. Chandezon, O. Coudert, “Extension of the C method to nonhomogeneous media: application to nonhomogeneous layers with parallel modulated faces and to inclined lamellar gratings,” J. Opt. Soc. Am. A 14, 1576–1582 (1997). [CrossRef]
  11. D. Maystre, “Integral method,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), Chap. 3. [CrossRef]
  12. E. Loewen, D. Maystre, E. Popov, L. Tsonev, “Echelles: scalar, electromagnetic, and real-groove properties,” Appl. Opt. 34, 1707–1727 (1995). [CrossRef] [PubMed]
  13. E. Loewen, D. Maystre, E. Popov, L. Tsonev, “Diffraction efficiency of echelles working in extremely high orders,” Appl. Opt. 35, 1700–1704 (1996). [CrossRef] [PubMed]
  14. D. Maystre, “A new general integral theory for dielectric coated gratings,” J. Opt. Soc. Am. 68, 490–495 (1978). [CrossRef]
  15. D. Maystre, “A new theory for multiprofile, buried gratings,” Opt. Commun. 26, 127–132 (1978). [CrossRef]
  16. A. Pomp, “The integral method for coated gratings: computational cost,” J. Mod. Opt. 38, 109–120 (1991). [CrossRef]
  17. D. Maystre, “Electromagnetic study of photonic band gaps,” Pure Appl. Opt. 3, 975–993 (1994). [CrossRef]
  18. Lord Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. London Ser. A 79, 399–416 (1907). [CrossRef]
  19. R. F. Millar, “The Rayleigh hypothesis and a related least-squares solution to scattering problems for periodic surfaces and other scatterers,” Radio Sci. 8, 785–796 (1973); M. Nevière, M. Cadilhac, “Sur la validite du developpement de Rayleigh,” Opt. Commun. 2, 235–238 (1970). [CrossRef]
  20. A. Wirgin, “Sur la théorie de Rayleigh de la diffraction d’une onde par une surface sinusoidale,” C. R. Acad. Sci. Ser. B 288, 179–182 (1979).
  21. E. Popov, L. Mashev, “Convergence of Rayleigh Fourier method and rigorous differential method for relief diffraction gratings: nonsinusoidal profile,” J. Mod. Opt. 34, 155–158 (1987). [CrossRef]
  22. P. M. Van den Berg, “Reflection by a grating: Rayleigh methods,” J. Opt. Soc. Am. 71, 1224–1229 (1981). [CrossRef]
  23. See E. Loewen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997), Chap. 4.

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