Abstract

The inverse rule that is described in a recent paper [J. Opt. Soc. Am. A 17, 491 (2000)] is not a multiplication rule for multiplying two infinite series, because it does not address how the terms of two series being multiplied are combined to form the product series. Furthermore, it is not the one that is being used in numerical practice. Therefore the insight that the paper provides into why the inverse rule yields correct results at the points of complementary discontinuities is questionable.

© 2002 Optical Society of America

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References

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  1. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876 (1996).
    [CrossRef]
  2. L. Li, “Mathematical reflections on the Fourier modal method in grating theory,” in Mathematical Modeling in Optical Science, G. Bao, L. Cowsar, W. Masters, eds. SIAM Frontiers in Applied Mathematics Series (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 2001), Chap. 4, pp. 111–139.
  3. P. P. Banerjee, J. M. Jarem, “Convergence of electromagnetic field components across discontinuous permittivity profiles,” J. Opt. Soc. Am. A 17, 491–492 (2000).
    [CrossRef]
  4. Ph. Lalanne, G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779–784 (1996).
    [CrossRef]
  5. G. Granet, 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).
    [CrossRef]
  6. G. H. Hardy, Divergent Series (Oxford U. Press, London, 1949).

2000 (1)

1996 (3)

Banerjee, P. P.

Granet, G.

Guizal, B.

Hardy, G. H.

G. H. Hardy, Divergent Series (Oxford U. Press, London, 1949).

Jarem, J. M.

Lalanne, Ph.

Li, L.

L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876 (1996).
[CrossRef]

L. Li, “Mathematical reflections on the Fourier modal method in grating theory,” in Mathematical Modeling in Optical Science, G. Bao, L. Cowsar, W. Masters, eds. SIAM Frontiers in Applied Mathematics Series (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 2001), Chap. 4, pp. 111–139.

Morris, G. M.

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f(xp)g(xp)h(xp)
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hT(2)(x)=1fTRECgT(x),

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