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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. 18, Iss. 11 — Nov. 1, 2001
  • pp: 2886–2894

Maxwell equations in Fourier space: fast-converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media

Evgeny Popov and Michel Nevière  »View Author Affiliations


JOSA A, Vol. 18, Issue 11, pp. 2886-2894 (2001)
http://dx.doi.org/10.1364/JOSAA.18.002886


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Abstract

We establish the most general differential equations that are satisfied by the Fourier components of the electromagnetic field diffracted by an arbitrary periodic anisotropic medium. The equations are derived by use of the recently published fast-Fourier-factorization (FFF) method, which ensures fast convergence of the Fourier series of the field. The diffraction by classic isotropic gratings arises as a particular case of the derived equations; the case of anisotropic classic gratings was published elsewhere. The equations can be resolved either through classic differential theory or through the modal method for particular groove profiles. The new equations improve both methods in the same way. Crossed gratings, among which are grids and two-dimensional arbitrarily shaped periodic surfaces, appear as particular cases of the theory, as do three-dimensional photonic crystals. The method can be extended to nonperiodic media through the use of a Fourier transform.

© 2001 Optical Society of America

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(050.1960) Diffraction and gratings : Diffraction theory
(070.2590) Fourier optics and signal processing : ABCD transforms
(260.2110) Physical optics : Electromagnetic optics

History
Original Manuscript: January 2, 2001
Revised Manuscript: March 23, 2001
Manuscript Accepted: April 23, 2001
Published: November 1, 2001

Citation
Evgeny Popov and Michel Nevière, "Maxwell equations in Fourier space: fast-converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media," J. Opt. Soc. Am. A 18, 2886-2894 (2001)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-11-2886

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