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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

  • Editor: Stephen A. Burns
  • Vol. 25, Iss. 7 — Jul. 1, 2008
  • pp: 1564–1573

Longitudinal Legendre polynomial expansion of electromagnetic fields for analysis of arbitrary-shaped gratings

Amin Khavasi, Ali Kazemi Jahromi, and Khashayar Mehrany  »View Author Affiliations


JOSA A, Vol. 25, Issue 7, pp. 1564-1573 (2008)
http://dx.doi.org/10.1364/JOSAA.25.001564


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Abstract

The Legendre polynomial expansion method (LPEM), which has been successfully applied to homogenous and longitudinally inhomogeneous gratings [ J. Opt. Soc. Am. B 24, 2676 (2007) ], is now generalized for the efficient analysis of arbitrary-shaped surface relief gratings. The modulated region is cut into a few sufficiently thin arbitrary-shaped subgratings of equal spatial period, where electromagnetic field dependence is now smooth enough to be approximated by keeping fewer Legendre basis functions. The R-matrix propagation algorithm is then employed to match the Legendre polynomial expansions of the transverse electric and magnetic fields across the upper and lower interfaces of every slice. The proposed strategy then enhances the overall computational efficiency, reduces the required memory size, and permits the efficient study of arbitrary-shaped gratings. Here the rigorous approach is followed, and analytical formulas of the involved matrices are given.

© 2008 Optical Society of America

OCIS Codes
(000.3860) General : Mathematical methods in physics
(050.1950) Diffraction and gratings : Diffraction gratings
(050.2770) Diffraction and gratings : Gratings
(050.7330) Diffraction and gratings : Volume gratings

ToC Category:
Diffraction and Gratings

History
Original Manuscript: February 4, 2008
Revised Manuscript: April 9, 2008
Manuscript Accepted: April 13, 2008
Published: June 9, 2008

Citation
Amin Khavasi, Ali Kazemi Jahromi, and Khashayar Mehrany, "Longitudinal Legendre polynomial expansion of electromagnetic fields for analysis of arbitrary-shaped gratings," J. Opt. Soc. Am. A 25, 1564-1573 (2008)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-25-7-1564


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