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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 28, Iss. 6 — Jun. 1, 2011
  • pp: 1191–1196

Boundary integral equation Neumann-to-Dirichlet map method for gratings in conical diffraction

Yumao Wu and Ya Yan Lu  »View Author Affiliations

JOSA A, Vol. 28, Issue 6, pp. 1191-1196 (2011)

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Boundary integral equation methods for diffraction gratings are particularly suitable for gratings with complicated material interfaces but are difficult to implement due to the quasi-periodic Green’s function and the singular integrals at the corners. In this paper, the boundary integral equation Neumann-to-Dirichlet map method for in-plane diffraction problems of gratings [Y. Wu and Y. Y. Lu, J. Opt. Soc. Am. A 26, 2444 (2009)] is extended to conical diffraction problems. The method uses boundary integral equations to calculate the so-called Neumann-to-Dirichlet maps for homogeneous subdomains of the grating, so that the quasi-periodic Green’s functions can be avoided. Since wave field components are coupled on material interfaces with the involvement of tangential derivatives, a least squares polynomial approximation technique is developed to evaluate tangential derivatives along these interfaces for conical diffraction problems. Numerical examples indicate that the method performs equally well for dielectric or metallic gratings.

© 2011 Optical Society of America

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(050.1960) Diffraction and gratings : Diffraction theory
(050.1755) Diffraction and gratings : Computational electromagnetic methods

ToC Category:
Diffraction and Gratings

Original Manuscript: March 8, 2011
Revised Manuscript: April 12, 2011
Manuscript Accepted: April 14, 2011
Published: May 23, 2011

Yumao Wu and Ya Yan Lu, "Boundary integral equation Neumann-to-Dirichlet map method for gratings in conical diffraction," J. Opt. Soc. Am. A 28, 1191-1196 (2011)

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