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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. 21, Iss. 11 — Nov. 1, 2004
  • pp: 2146–2153

Diffraction theory in TM polarization: application of the fast Fourier factorization method to cylindrical devices with arbitrary cross section

Philippe Boyer, Evgeni Popov, Michel Nevière, and Gérard Tayeb  »View Author Affiliations


JOSA A, Vol. 21, Issue 11, pp. 2146-2153 (2004)
http://dx.doi.org/10.1364/JOSAA.21.002146


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Abstract

The diffraction of an electromagnetic wave by a cylindrical object with arbitrary cross section is studied by taking advantage of recent progress in grating theories. The fast Fourier factorization method previously developed in Cartesian coordinates is extended to cylindrical coordinates thanks to the periodicity of both the diffracting object and the incident wave with respect to the polar angle θ. Thus Maxwell equations in a truncated Fourier space are derived and separated in TE and TM polarization cases. The new set of equations for TM polarization is resolved numerically with the S-matrix propagation algorithm. Examples of elliptic cross sections and cross sections including couples of nonconcentric circles show fast convergence of the results, for both dielectric and metallic materials, as well as good agreement with previous published results. Thus the method is suitable for an extension to conical (out-of-plane) diffraction, which will allow studying mode propagation along microstructured fibers.

© 2004 Optical Society of America

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(060.0060) Fiber optics and optical communications : Fiber optics and optical communications

History
Original Manuscript: April 16, 2004
Revised Manuscript: June 22, 2004
Manuscript Accepted: June 22, 2004
Published: November 1, 2004

Citation
Philippe Boyer, Evgeni Popov, Michel Nevière, and Gérard Tayeb, "Diffraction theory in TM polarization: application of the fast Fourier factorization method to cylindrical devices with arbitrary cross section," J. Opt. Soc. Am. A 21, 2146-2153 (2004)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-21-11-2146

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