Abstract

The conclusion reached in a recent paper by Morf [ J. Opt. Soc. Am. A 12, 1043 ( 1995)], that the algorithm he proposed is several times faster than the R-matrix algorithm presented in an earlier paper of mine [ J. Opt. Soc. Am. A 10, 2581 ( 1993)], is erroneous. By providing operation count, I show that the R-matrix algorithm, when it is applied to the classical modal method, is as efficient as Morf’s algorithm.

© 1996 Optical Society of America

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References

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  1. R. H. Morf, “Exponentially convergent and numerically efficient solution of Maxwell’s equations for lamellar gratings,” J. Opt. Soc. Am. A 12, 1043–1056 (1995).
    [CrossRef]
  2. K. Knop, “Rigorous diffraction theory for transmission gratings with deep rectangular grooves,” J. Opt. Soc. Am. 68, 1206–1210 (1978).
    [CrossRef]
  3. M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1385–1392 (1982).
    [CrossRef]
  4. L. Li, “Multilayer modal method for diffraction gratings of arbitrary profile, depth, and permittivity,” J. Opt. Soc. Am. A 10, 2581–2591 (1993).
    [CrossRef]
  5. Since the writing of paper B, I have not investigated the real cause of the instability of the computer code under the condition described in the text. However, a new code that combines the classical modal method with the S-matrix algorithm is free of this type of instability.
  6. If the WEITEK SPARC POWER μPenhanced-performance CPU is used in a Sun SPARCstation 2, the clock frequency is doubled.
  7. The numbers in Fig. 9 of paper B include the times for reading input data, writing output data, and everything in between. An examination of the fitting polynomials reveals that the average time taken by the N3process for the four cases that used the first initialization method for N= 60 was approximately 175 s; therefore the estimate of 20 s per layer made by the author of paper A is reasonable.
  8. G. H. Golub, C. F. Van Loan, Matrix Computations (John Hopkins University Press, Baltimore, Md., 1983).

1995 (1)

1993 (1)

1982 (1)

1978 (1)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (2)

Other (4)

Since the writing of paper B, I have not investigated the real cause of the instability of the computer code under the condition described in the text. However, a new code that combines the classical modal method with the S-matrix algorithm is free of this type of instability.

If the WEITEK SPARC POWER μPenhanced-performance CPU is used in a Sun SPARCstation 2, the clock frequency is doubled.

The numbers in Fig. 9 of paper B include the times for reading input data, writing output data, and everything in between. An examination of the fitting polynomials reveals that the average time taken by the N3process for the four cases that used the first initialization method for N= 60 was approximately 175 s; therefore the estimate of 20 s per layer made by the author of paper A is reasonable.

G. H. Golub, C. F. Van Loan, Matrix Computations (John Hopkins University Press, Baltimore, Md., 1983).

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