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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 15, Iss. 10 — Oct. 1, 1998
  • pp: 2684–2697

Model with two roughness levels for diffraction gratings: the generalized Rayleigh expansion

R. Dusséaux  »View Author Affiliations

JOSA A, Vol. 15, Issue 10, pp. 2684-2697 (1998)

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A model with two roughness levels for the diffraction of a plane wave by a metallic grating with periodic imperfections is presented. The grating surface is the sum of a reference profile and a perturbation profile. First, the diffraction by the reference grating is treated. At this stage the Chandezon method is used. This method leads to the resolution of eigenvalue systems. Each eigensolution defines an elementary wave function that characterizes a propagating or an evanescent wave. Second, the periodic errors are taken into account and a Rayleigh hypothesis is expressed: Everywhere in space the diffracted fields can be written as a linear combination of reference wave functions. The boundary conditions on the perturbed grating allow the diffraction amplitudes to be determined and therefore lead to the energetic magnitudes (efficiencies). The domain of analytical validity of this hypothesis is not defined. In fact, this method is considered to be an approximation. The proposed numerical study leads to some utilization rules. With a plane as the reference surface, the electromagnetic fields are given by classical Rayleigh expansions. Here the reference profile is a grating, hence the term generalized Rayleigh expansion.

© 1998 Optical Society of America

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(050.1960) Diffraction and gratings : Diffraction theory
(240.6680) Optics at surfaces : Surface plasmons

Original Manuscript: January 29, 1998
Revised Manuscript: April 24, 1998
Manuscript Accepted: May 27, 1998
Published: October 1, 1998

R. Dusséaux, "Model with two roughness levels for diffraction gratings: the generalized Rayleigh expansion," J. Opt. Soc. Am. A 15, 2684-2697 (1998)

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  1. M. Breidne, D. Maystre, “Variational theory of diffraction gratings and its application to the study of ghosts,” J. Opt. Soc. Am. 72, 499–506 (1982). [CrossRef]
  2. N. A. Finkelstein, C. H. Brawley, R. J. Meltzer, “The reduction of ghosts on diffraction spectra,” J. Opt. Soc. Am. 42, 121–126 (1952). [CrossRef]
  3. R. Dusséaux, “Etude de la diffraction d’une onde plane par un réseau—équations de Maxwell covariantes et méthodes de perturbation,” Ph.D. dissertation (Université Blaise Pascal, Clermont-Ferrand, France, 1993).
  4. R. Dusséaux, C. Faure, J. Chandezon, F. Molinet, “New perturbation theory of diffraction gratings and its application to the study of ghosts,” J. Opt. Soc. Am. A 12, 1271–1282 (1995). [CrossRef]
  5. E. J. Post, Format Structure of Electromagnetic (North-Holland, Amsterdam, 1962).
  6. J. Chandezon, “Les équations de Maxwell sous forme covariante—application à l’étude de la propagation dans les guides périodiques et à la diffraction par les réseaux,” Ph.D. dissertation (Université Blaise Pascal, Clermont-Ferrand, France, 1979).
  7. J. Chandezon, D. Maystre, G. Raoult, “A new theoretical method for diffraction gratings and its numerical application,” J. Opt. (Paris) 11, 235–241 (1980). [CrossRef]
  8. J. M. Elson, R. H. Ritchie, “Photon interaction at a rough metal surface,” Phys. Rev. B 4, 4129–4138 (1971). [CrossRef]
  9. 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]
  10. L. Li, “Multilayer-coated diffraction gratings: differential method of Chandezon et al. revisited,” J. Opt. Soc. Am. A 11, 2816–2828 (1994). [CrossRef]
  11. T. W. Preist, N. P. Cotter, J. R. Sambles, “Periodic multilayer gratings of arbitrary shape,” J. Opt. Soc. Am. A 12, 1740–1748 (1995). [CrossRef]
  12. G. Granet, “Analysis of diffraction by crossed gratings using a non-orthogonal coordinate system,” Pure Appl. Opt. 4, 777–793 (1995). [CrossRef]
  13. L. Li, G. Granet, J. P. Plumey, J. Chandezon, “Some topics in extending the C method to multilayer-coated gratings of different profiles,” Pure Appl. Opt. 5, 141–156 (1996). [CrossRef]
  14. J. P. Plumey, G. Granet, J. Chandezon, “Differential covariant formalism for solving Maxwell’s equations in curvilinear coordinates: oblique scattering from lossy periodic surfaces,” IEEE Trans. Antennas Propag. 43, 835–842 (1995). [CrossRef]
  15. Lord Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. London, Ser. A 79, 399–416 (1907). [CrossRef]
  16. Lord Rayleigh, The Theory of Sound (Dover, New York, 1945), Vol. 2, pp. 89–96.
  17. R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Heidelberg, 1980).
  18. R. Petit, M. Cadilhac, “Sur la diffraction d’une onde plane par un réseau infiniment conducteur,” C. R. Acad. Sci., Ser. B 262, 468–471 (1966).
  19. R. F. Millar, “On the Rayleigh assumption in scattering by a periodic surface,” Proc. Cambridge Philos. Soc. 69, 773–791 (1971). [CrossRef]
  20. 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). [CrossRef]
  21. M. Nevière, M. Cadilhac, “Sur une nouvelle formulation du problème de la diffraction d’une onde plane par un réseau infiniment conducteur: cas général,” Opt. Commun. 3, 379–383 (1971). [CrossRef]
  22. P. M. van den Berg, J. T. Fokkema, “Rayleigh hypothesis in the theory of reflection by a grating,” J. Opt. Soc. Am. 69, 27–31 (1979). [CrossRef]
  23. P. M. van den Berg, “Reflection by a grating: Rayleigh methods,” J. Opt. Soc. Am. 71, 1224–1229 (1981). [CrossRef]
  24. J. P. Hugonin, R. Petit, M. Cadilhac, “Plane-wave expansions used to describe the field diffracted by a grating,” J. Opt. Soc. Am. 71, 593–598 (1981). [CrossRef]
  25. J. M. Soto-Crespo, M. Nieto Vesperinas, A. T. Friberg, “Scattering from slightly rough random surfaces: a detailed study on the validity of the small perturbation method,” J. Opt. Soc. Am. A 7, 1185–1201 (1990). [CrossRef]
  26. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988), Chap. 6 and Appendix 4.

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