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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

  • Vol. 17, Iss. 3 — Mar. 1, 2000
  • pp: 456–457

Singularities and Rayleigh’s hypothesis for diffraction gratings

Joseph B. Keller  »View Author Affiliations


JOSA A, Vol. 17, Issue 3, pp. 456-457 (2000)
http://dx.doi.org/10.1364/JOSAA.17.000456


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Abstract

The foci or branch points are found for a sinusoidal boundary. It is shown how they determine the range of validity of Rayleigh’s hypothesis for diffraction gratings.

© 2000 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings

History
Original Manuscript: May 10, 1999
Revised Manuscript: November 9, 1999
Manuscript Accepted: November 23, 1999
Published: March 1, 2000

Citation
Joseph B. Keller, "Singularities and Rayleigh’s hypothesis for diffraction gratings," J. Opt. Soc. Am. A 17, 456-457 (2000)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-17-3-456


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References

  1. R. F. Millar, “On the Rayleigh assumption in scattering by a periodic surface,” Proc. Cambridge Philos. Soc. 65, 773–791 (1969). [CrossRef]
  2. R. F. Millar, “On the Rayleigh assumption in scattering by a periodic surface. II,” Proc. Cambridge Philos. Soc. 69, 217–225 (1971). [CrossRef]
  3. P. R. Garabedian, Partial Differential Equations (Wiley, New York, 1964), pp. 641–650.
  4. R. Petit, M. Cadilhac, “Sur la diffraction d’une onde plane par un réseau infiniment conducteur,” C. R. Acad. Sci. (Paris) Ser. A, B 262, 468–471 (1966).
  5. O. P. Bruno, F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries,” J. Opt. Soc. Am. A 10, 1168–1175 (1993). [CrossRef]
  6. O. P. Bruno, F. Reitich, “Numerical solution of diffraction problems: a method of variation of boundaries. II. Finitely conducting gratings, Padé approximants, and singularities,” J. Opt. Soc. Am. A 10, 2307–2316 (1993). [CrossRef]

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