Abstract

In a recent paper [J. Opt. Soc. Am. A 14, 596 (1997)], S. Kaushik describes a modal theory of diffraction in which a number of features from scalar optics are generalized. The paper describes an S-matrix propagation algorithm that is characterized as being new and an improvement over earlier work. In a response to this paper, L. Li [J. Opt. Soc. Am. A. 15, 1006 (1998)] disputes this claim and claims that the algorithm is well known and presents no significant improvement over earlier work. These criticisms are addressed in this reply. Specifically, it is shown that unlike earlier work cited by Li, the method described by Kaushik is a genuine S-matrix method since energy balance is automatically guaranteed for dielectric gratings, irrespective of truncation order. Further, it is shown that the algorithm is easier to relate to scalar optics and is computationally more efficient than the specific algorithms cited by Li.

© 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, “Vector Fresnel equations and Airy formula for one-dimensional multilayer and surface-relief gratings: comment,” J. Opt. Soc. Am. A 15, 1006–1008 (1998).
    [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. L. Li, “Bremmer series, R-matrix propagation algorithm, and numerical modeling of diffraction grating,” J. Opt. Soc. Am. A 11, 2829–2836 (1994).
    [CrossRef]
  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).
    [CrossRef]
  8. L. C. Botten, M. S. Craig, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1103–1106 (1981).
    [CrossRef]
  9. 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]
  10. N. F. Mott, H. S. W. Massey, The Theory of Atomic Collisions (Oxford Science Publications, New York, 1933).
  11. A. Messiah, Quantum Mechanics: Vol. II (WileyNew York, 1958).
  12. J. Choma, Electrical Networks: Theory and Analysis (Wiley, New York, 1985).
  13. J. C. Light, R. B. Walker, “An R-matrix approach to the solution of coupled equations for atom-molecule reactive scattering,” J. Chem. Phys. 65, 4272–4282 (1976).
    [CrossRef]
  14. M. V. Klein, T. E. Furtak, Optics (Wiley, New York, 1986).
  15. S. T. Peng, T. Tamir, H. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).
    [CrossRef]
  16. T. Tamir, S. Zhang, “Modal transmission-line theory of multilayer grating structures,” J. Lightwave Technol. 14, 914–927 (1996).
    [CrossRef]
  17. 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]

1998

1997

1996

T. Tamir, S. Zhang, “Modal transmission-line theory of multilayer grating structures,” J. Lightwave Technol. 14, 914–927 (1996).
[CrossRef]

L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13, 1024–1035 (1996).
[CrossRef]

1994

1991

1981

L. C. Botten, M. S. Craig, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1103–1106 (1981).
[CrossRef]

1976

J. C. Light, R. B. Walker, “An R-matrix approach to the solution of coupled equations for atom-molecule reactive scattering,” J. Chem. Phys. 65, 4272–4282 (1976).
[CrossRef]

1975

S. T. Peng, T. Tamir, H. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).
[CrossRef]

1974

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

1969

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.

Bertoni, H.

S. T. Peng, T. Tamir, H. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).
[CrossRef]

Botten, L. C.

L. C. Botten, M. S. Craig, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1103–1106 (1981).
[CrossRef]

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]

Choma, J.

J. Choma, Electrical Networks: Theory and Analysis (Wiley, New York, 1985).

Cory, H.

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

Craig, M. S.

L. C. Botten, M. S. Craig, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1103–1106 (1981).
[CrossRef]

Furtak, T. E.

M. V. Klein, T. E. Furtak, Optics (Wiley, New York, 1986).

Kaushik, S.

Kennett, B. L. N.

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

Klein, M. V.

M. V. Klein, T. E. Furtak, Optics (Wiley, New York, 1986).

Li, L.

Light, J. C.

J. C. Light, R. B. Walker, “An R-matrix approach to the solution of coupled equations for atom-molecule reactive scattering,” J. Chem. Phys. 65, 4272–4282 (1976).
[CrossRef]

Massey, H. S. W.

N. F. Mott, H. S. W. Massey, The Theory of Atomic Collisions (Oxford Science Publications, New York, 1933).

Messiah, A.

A. Messiah, Quantum Mechanics: Vol. II (WileyNew York, 1958).

Mott, N. F.

N. F. Mott, H. S. W. Massey, The Theory of Atomic Collisions (Oxford Science Publications, New York, 1933).

Pai, D. M.

Pendry, J. B.

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

Peng, S. T.

S. T. Peng, T. Tamir, H. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).
[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]

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]

Tamir, T.

T. Tamir, S. Zhang, “Modal transmission-line theory of multilayer grating structures,” J. Lightwave Technol. 14, 914–927 (1996).
[CrossRef]

S. T. Peng, T. Tamir, H. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).
[CrossRef]

Walker, R. B.

J. C. Light, R. B. Walker, “An R-matrix approach to the solution of coupled equations for atom-molecule reactive scattering,” J. Chem. Phys. 65, 4272–4282 (1976).
[CrossRef]

Zhang, S.

T. Tamir, S. Zhang, “Modal transmission-line theory of multilayer grating structures,” J. Lightwave Technol. 14, 914–927 (1996).
[CrossRef]

Bull. Seis. Soc. Am.

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

IEEE Trans. Microwave Theory Tech.

S. T. Peng, T. Tamir, H. Bertoni, “Theory of periodic dielectric waveguides,” IEEE Trans. Microwave Theory Tech. MTT-23, 123–133 (1975).
[CrossRef]

J. Chem. Phys.

J. C. Light, R. B. Walker, “An R-matrix approach to the solution of coupled equations for atom-molecule reactive scattering,” J. Chem. Phys. 65, 4272–4282 (1976).
[CrossRef]

J. Lightwave Technol.

T. Tamir, S. Zhang, “Modal transmission-line theory of multilayer grating structures,” J. Lightwave Technol. 14, 914–927 (1996).
[CrossRef]

J. Mod. Opt.

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

J. Opt. Soc. Am. A

Opt. Acta

L. C. Botten, M. S. Craig, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1103–1106 (1981).
[CrossRef]

Radio Sci.

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

Other

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]

N. F. Mott, H. S. W. Massey, The Theory of Atomic Collisions (Oxford Science Publications, New York, 1933).

A. Messiah, Quantum Mechanics: Vol. II (WileyNew York, 1958).

J. Choma, Electrical Networks: Theory and Analysis (Wiley, New York, 1985).

M. V. Klein, T. E. Furtak, Optics (Wiley, New York, 1986).

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