Abstract

The assertion made by S. Kaushik in a recent paper [J. Opt. Soc. Am. A 14, 596 (1997)] that the S-matrix propagation algorithm that he derived is new and represents an improvement over the earlier research is apparently incorrect. A review of the literature shows that every feature of the algorithm as presented in the above reference has been known for many years.

© 1998 Optical Society of America

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References

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  1. S. Kaushik, “Vector Fresnel equations and Airy formula for one-dimensional multilayer and surface-relief gratings,” J. Opt. Soc. Am. A 14, 596–609 (1997).
    [CrossRef]
  2. L. Li, “Bremmer series, R-matrix propagation algorithm, and numerical modeling of diffraction gratings,” J. Opt. Soc. Am. A 11, 2829–2836 (1994). The S-matrix algorithm in this paper was mistakenly referred to as the R-matrix algorithm. I have acknowledged and corrected this error in Ref. 7 below.
    [CrossRef]
  3. B. L. N. Kennett, “Reflections, rays, and reverberations,” Bull. Seis. Soc. Am. 64, 1685–1696 (1974).
  4. J. B. Pendry, “Photonics band structures,” J. Mod. Opt. 41, 209–229 (1994).
    [CrossRef]
  5. C. Altman, H. Cory, “The generalized thin-film optical method in electromagnetic wave propagation,” Radio Sci. 4, 457–470 (1969).
  6. R. Redheffer, “Difference equations and functional equations in transmission-line theory,” in Modern Mathematics for the Engineer, 2nd ser., E. F. Beckenbach, ed. (McGraw-Hill, New York, 1961), Chap. 12, pp. 282–337.
  7. L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13, 1024–1035 (1996). This paper, published after Ref. 1 was submitted, gives an account of the recursion subsets for the R- and S-matrix propagation algorithms.
    [CrossRef]
  8. E. B. Stechel, R. B. Walker, J. C. Light, “R-matrix solution of coupled equations for inelastic scattering,” J. Chem. Phys. 69, 3518–3531 (1978).
    [CrossRef]
  9. D. M. Pai, K. A. Awada, “Analysis of dielectric gratings of arbitrary profiles and thicknesses,” J. Opt. Soc. Am. A 8, 755–762 (1991).
    [CrossRef]
  10. R. Petit, J. Y. Suratteau, M. Cadilhac, “On the numerical study of deep lamellar gratings in the resonance domain,” in Application, Theory, and Fabrication of Periodic Structures, Diffraction Gratings, and Moire Phenomena II, J. M. Lerner, ed., Proc. SPIE503, 160–167 (1984).
    [CrossRef]

1997 (1)

1996 (1)

1994 (2)

1991 (1)

1978 (1)

E. B. Stechel, R. B. Walker, J. C. Light, “R-matrix solution of coupled equations for inelastic scattering,” J. Chem. Phys. 69, 3518–3531 (1978).
[CrossRef]

1974 (1)

B. L. N. Kennett, “Reflections, rays, and reverberations,” Bull. Seis. Soc. Am. 64, 1685–1696 (1974).

1969 (1)

C. Altman, H. Cory, “The generalized thin-film optical method in electromagnetic wave propagation,” Radio Sci. 4, 457–470 (1969).

Altman, C.

C. Altman, H. Cory, “The generalized thin-film optical method in electromagnetic wave propagation,” Radio Sci. 4, 457–470 (1969).

Awada, K. A.

Cadilhac, M.

R. Petit, J. Y. Suratteau, M. Cadilhac, “On the numerical study of deep lamellar gratings in the resonance domain,” in Application, Theory, and Fabrication of Periodic Structures, Diffraction Gratings, and Moire Phenomena II, J. M. Lerner, ed., Proc. SPIE503, 160–167 (1984).
[CrossRef]

Cory, H.

C. Altman, H. Cory, “The generalized thin-film optical method in electromagnetic wave propagation,” Radio Sci. 4, 457–470 (1969).

Kaushik, S.

Kennett, B. L. N.

B. L. N. Kennett, “Reflections, rays, and reverberations,” Bull. Seis. Soc. Am. 64, 1685–1696 (1974).

Li, L.

Light, J. C.

E. B. Stechel, R. B. Walker, J. C. Light, “R-matrix solution of coupled equations for inelastic scattering,” J. Chem. Phys. 69, 3518–3531 (1978).
[CrossRef]

Pai, D. M.

Pendry, J. B.

J. B. Pendry, “Photonics band structures,” J. Mod. Opt. 41, 209–229 (1994).
[CrossRef]

Petit, R.

R. Petit, J. Y. Suratteau, M. Cadilhac, “On the numerical study of deep lamellar gratings in the resonance domain,” in Application, Theory, and Fabrication of Periodic Structures, Diffraction Gratings, and Moire Phenomena II, J. M. Lerner, ed., Proc. SPIE503, 160–167 (1984).
[CrossRef]

Redheffer, R.

R. Redheffer, “Difference equations and functional equations in transmission-line theory,” in Modern Mathematics for the Engineer, 2nd ser., E. F. Beckenbach, ed. (McGraw-Hill, New York, 1961), Chap. 12, pp. 282–337.

Stechel, E. B.

E. B. Stechel, R. B. Walker, J. C. Light, “R-matrix solution of coupled equations for inelastic scattering,” J. Chem. Phys. 69, 3518–3531 (1978).
[CrossRef]

Suratteau, J. Y.

R. Petit, J. Y. Suratteau, M. Cadilhac, “On the numerical study of deep lamellar gratings in the resonance domain,” in Application, Theory, and Fabrication of Periodic Structures, Diffraction Gratings, and Moire Phenomena II, J. M. Lerner, ed., Proc. SPIE503, 160–167 (1984).
[CrossRef]

Walker, R. B.

E. B. Stechel, R. B. Walker, J. C. Light, “R-matrix solution of coupled equations for inelastic scattering,” J. Chem. Phys. 69, 3518–3531 (1978).
[CrossRef]

Bull. Seis. Soc. Am. (1)

B. L. N. Kennett, “Reflections, rays, and reverberations,” Bull. Seis. Soc. Am. 64, 1685–1696 (1974).

J. Chem. Phys. (1)

E. B. Stechel, R. B. Walker, J. C. Light, “R-matrix solution of coupled equations for inelastic scattering,” J. Chem. Phys. 69, 3518–3531 (1978).
[CrossRef]

J. Mod. Opt. (1)

J. B. Pendry, “Photonics band structures,” J. Mod. Opt. 41, 209–229 (1994).
[CrossRef]

J. Opt. Soc. Am. A (4)

Radio Sci. (1)

C. Altman, H. Cory, “The generalized thin-film optical method in electromagnetic wave propagation,” Radio Sci. 4, 457–470 (1969).

Other (2)

R. Redheffer, “Difference equations and functional equations in transmission-line theory,” in Modern Mathematics for the Engineer, 2nd ser., E. F. Beckenbach, ed. (McGraw-Hill, New York, 1961), Chap. 12, pp. 282–337.

R. Petit, J. Y. Suratteau, M. Cadilhac, “On the numerical study of deep lamellar gratings in the resonance domain,” in Application, Theory, and Fabrication of Periodic Structures, Diffraction Gratings, and Moire Phenomena II, J. M. Lerner, ed., Proc. SPIE503, 160–167 (1984).
[CrossRef]

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Equations (10)

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Γ˜i+=γi+tiΓ˜i-1+ 11-γiΓ˜i-1+ti,
T˜i+=T˜i-1+ 11-γiΓ˜i-1+ti,
D(zj-1)=RD(zj-1)+TU(zj-1)D(zj)×[1-RU(zj-1)D(zj)]-1TD(zj-1),
TD(zj-1)=TD(zj)[1-RU(zj-1)D(zj)]-1TD(zj-1);
t+-(Lz+1)=t+-(z)+t++(z)t+-(Lz)[1-t-+(z)t+-(Lz)]-1t--(z),
t--(Lz+1)=t--(Lz)[1-t-+(z)t+-(Lz)]-1t--(z);
Rdu(j)=r˜du(j)+t˜dd(j)[1-Rdu(j-1)r˜ud(j)]-1Rdu(j-1)t˜uu(j),
Tuu(j)=Tuu(j-1)[1-r˜ud(j)Rdu(j-1)]-1t˜uu(j).
Rdu(j)=r˜du(j)+t˜dd(j)Rdu(j-1)[1-r˜ud(j)Rdu(j-1)]-1t˜uu(j),
Tuu(j)=Tuu(j-1)[1-r˜ud(j)Rdu(j-1)]-1t˜uu(j).

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