Use of Fourier series in the analysis of discontinuous periodic structures

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 13, Issue 9, 1996, Pages 1870-1876

  Li, Lifeng ^a  

^a UNIVERSITY OF ARIZONA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; FOURIER TRANSFORMS; LIGHT POLARIZATION; MAXWELL EQUATIONS; PERMITTIVITY;

COUPLED WAVE METHOD; DISCONTINUOUS PERIODIC STRUCTURES; FACTORIZATION; JUMP DISCONTINUITIES; LAURENT RULE;

DIFFRACTION GRATINGS;

EID: 0030241250     PISSN: 10847529     EISSN: 15208532     Source Type: Journal    
DOI: 10.1364/JOSAA.13.001870     Document Type: Article

References (14)

1. K. Knop, “Rigorous diffraction theory for transmission phase gratings with deep rectangular grooves,” J. Opt. Soc. Am. 68, 1206–1210 (1978).
2. M. G. Moharam and T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1385–1392 (1982).
3. L. Li and C. W. Haggans, “Convergence of the coupled-wave method for metallic lamellar diffraction gratings,” J. Opt. Soc. Am. A 10, 1184–1189 (1993).
4. P. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779–784 (1996).
5. G. Granet and B. Guizal, “Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization,” J. Opt. Soc. Am. A 13, 1019–1023 (1996).
6. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
7. L. Li, “Fourier factorization of a product of discontinuous periodic functions,” submitted to SIAM J. Anal. Math.
8. A. Zygmund, Trigonometric Series (Cambridge U. Press, Cambridge, 1977), Vol. 1, Chap. 4, Sec. 8, p. 159.
9. G. H. Hardy, Divergent Series (Oxford U. Press, London, 1949), Chap. 10, Secs. 12–15, pp. 239–246.
10. P. Vincent, “Differential methods,” in Electromagnetic Theory of Gratings, Vol. 22 of Topics in Current Physics, R. Petit, ed. (Springer-Verlag, Berlin, 1980), pp. 101–121.
11. J. Chandezon, M. T. Dupuis, G. Cornet, and D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region,” J. Opt. Soc. Am. 72, 839–846 (1982).
12. L. Li and J. Chandezon, “Improvement of the coordinate transformation method for surface-relief gratings with sharp edges,” J. Opt. Soc. Am. A (to be published).
13. G. H. Golub and C. F. Van Loan, Matrix Computations (Johns Hopkins U. Press, Baltimore, Md., 1983), Chap. 5, Sec. 7, pp. 125–135
14. G. Heinig and K. Rost, Algebraic Methods for Toeplitz-like Matrices and Operators (Birkhauser Verlag, Basel, Switzerland, 1984), Chap. 1, pp. 14–33, and the references therein.