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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. 13, Iss. 9 — Sep. 1, 1996
  • pp: 1870–1876

Use of Fourier series in the analysis of discontinuous periodic structures

Lifeng Li  »View Author Affiliations


JOSA A, Vol. 13, Issue 9, pp. 1870-1876 (1996)
http://dx.doi.org/10.1364/JOSAA.13.001870


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Abstract

The recent reformulation of the coupled-wave method by Lalanne and Morris [ J. Opt. Soc. Am. A 13, 779 ( 1996)] and by Granet and Guizal [ J. Opt. Soc. Am. A 13, 1019 ( 1996)], which dramatically improves the convergence of the method for metallic gratings in TM polarization, is given a firm mathematical foundation in this paper. The new formulation converges faster because it uniformly satisfies the boundary conditions in the grating region, whereas the old formulations do so only nonuniformly. Mathematical theorems that govern the factorization of the Fourier coefficients of products of functions having jump discontinuities are given. The results of this paper are applicable to any numerical work that requires the Fourier analysis of products of discontinuous periodic functions.

© 1996 Optical Society of America

History
Original Manuscript: November 20, 1995
Revised Manuscript: April 4, 1996
Manuscript Accepted: March 5, 1996
Published: September 1, 1996

Citation
Lifeng Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A 13, 1870-1876 (1996)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-13-9-1870


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References

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  13. See, for example, G. H. Golub, C. F. Van Loan, Matrix Computations (Johns Hopkins U. Press, Baltimore, Md., 1983), Chap. 5, Sec. 7, pp. 125–135, or G. Heinig, K. Rost, Algebraic Methods for Toeplitz-like Matrices and Operators (Birkhäuser Verlag, Basel, Switzerland, 1984), Chap. 1, pp. 14–33, and the references therein.

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