Abstract

The Rayleigh hypothesis and the related method of diffraction analysis are revisited. It is shown that the Rayleigh method can be applied to deep grating modeling without numerical problems and that it gives any desired accuracy whatever the groove depth. This proves the validity of the Rayleigh hypothesis and rehabilitates the Rayleigh method.

© 2009 Optical Society of America

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  1. Lord Rayleigh (J. W. Strutt), "On the incidence of aerial and electromagnetic waves upon small obstacles in the form of ellipsoids or elliptic cylinders, and the passage of electric waves through a circular aperture in a conducting screen," Phil. Mag. 44, 28-52 (1897).
  2. Lord Rayleigh (J. W. Strutt), "On the dynamical theory of gratings," Proc. R. Soc. London Ser. A 79, 399-416 (1907).
  3. L. N. Deryugin, "Equations for coefficients of wave reflections from a periodically uneven surface," Dokl. Akad. Nauk SSSR 87,913-916 (1952).
  4. B. A. Lippmann, "Note on the theory of gratings," J. Opt. Soc. Am. 43,408 (1953).
    [CrossRef]
  5. J. L. Uretski, "The scattering of plane waves from periodic surfaces," Ann. Phys. 33, 400-427 (1965).
    [CrossRef]
  6. R. Petit, M. Cadilhac, "Sur la diffraction d’une onde plane par un réseau infinement conducteur, C. R. Acad. Sci. Paris 262B, 468-471 (1966).
  7. R. F. Millar, "On the Rayleigh assumption in scattering by a periodic surface, II," Proc. Cambridge Philos. Soc. 69,217-225 (1971).
    [CrossRef]
  8. J. Pavageau, "Sur la méthode des spectres d’ondes planes dans les problèmes de diffraction," C. R. Acad. Sci. Paris 266B, 135-138 (1968).
  9. R. H. T. Bates, "Analytic constraints on electromagnetic field computations," IEEE Trans. Microwave Theory and Tech. MTT-23, 605-623 (1975).
    [CrossRef]
  10. A. Wirgin, "On Rayleigh’s theory of sinusoidal diffraction gratings," Opt. Acta 27, 1671-1692 (1980).
  11. K. Yasuura and H. Ikuno, "On the modified Rayleigh hypothesis and the mode-matching method," in Summaries Int. Symp. Antennas and Propagation, Sendai, Japan, 173-174, (1971).
  12. P. C. Waterman, "Scattering by periodic surfaces," J. Acoust. Soc. Am. 57, 791 (1975).
    [CrossRef]
  13. J. B. Davies, "A least-squares boundary residual method for the numerical solution of scattering problems," IEEE Trans. Microwave Theory and Tech. MTT-21, 99-103 (1973).
    [CrossRef]
  14. V. I. Tatarskii, "Relation between the Rayleigh equation in diffraction theory and the equation based on Green’s formula, " J. Opt. Soc. Am. 12, 1254-1260 (1995).
    [CrossRef]
  15. J. Wauer, T. Rother, "Considerations to Rayleigh’s hypothesis," Opt. Commun. 282, 339 (2009).
    [CrossRef]
  16. L. Kazandjian, "Rayleigh methods applied to electromagnetic scattering from gratings in general homogeneous media," Phys. Rev. E 54, 6802-6815 (1996).
    [CrossRef]
  17. V. A. Sychugov and A. V. Tishchenko, "Light emission from a corrugated dielectric waveguide," Sov. J. Quantum Electron. 10, 186-189 (1980).
    [CrossRef]
  18. V. A. Sychugov and A. V. Tishchenko, "Propagation and conversion of light in corrugated waveguide structures," Sov. J. Quantum Electron. 12, 923-926 (1982).
    [CrossRef]
  19. G. A. Golubenko, A. A. Svakhin, V. A. Sychugov, and A. V. Tishchenko, "Total reflection of light from a corrugated surface of a dielectric waveguide," Sov. J. Quantum Electron. 15, 886-887 (1985).
    [CrossRef]
  20. J. Turunen, "Diffraction theory of dielectric surface relief gratings," in Micro-optics, H.P. Herzig ed. (Taylor&Francis Inc., 1997).
  21. A. M. Prokhorov, V. A. Sychugov, A. V. Tishchenko, and A. A. Khakimov, "Kinetics of the rippling of a germanium surface bombarded by an intense laser beam," Sov. Tech. Phys. Lett. 8, 605-606 (1982).
  22. V. A. Sychugov, A. V. Tishchenko, N. M. Lyndin, and O. Parriaux, "Waveguide coupling gratings for high-sensitivity biochemical sensors," Sens. Actuators B 38-39 360-364 (1997).
    [CrossRef]
  23. I. F. Salakhutdinov, V. A. Sychugov, A. V. Tishchenko, B. A. Usievich, and F. A. Pudonin, "Anomalous light reflection at the surface of a corrugated thin metal film," IEEE J. Quantum Electron. 34, 1054-1060 (1998).
    [CrossRef]
  24. I. A. Avrutsky, V. A. Sychugov, and A. V. Tishchenko, "The study of excitation, radiation, and reflection processes in corrugated waveguides," in Waveguide Corrugated Structures in Integrated and Fiber Optics, IOFAN Proc. 34, 3-98 (Nauka, Moscow, 1991, in Russian).
  25. P. Sheng, R. S. Stepleman, and P. N. Sanda, "Exact eigenfunctions for square-wave gratings: Application to diffraction and surface-plasmon calculations," Phys. Rev. B 262907-2916 (1982).
    [CrossRef]
  26. J. Chandezon, D. Maystre, and G. Raoult, "A new theoretical method for diffraction gratings and its numerical application," J. Opt. Paris 11, 235-241 (1980).
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  28. G. H. Golub, C. F. Van Loan, Matrix computations, 3rd ed., (Johns Hopkins, Baltimore, 1996).
  29. P. M. van den Berg, "Reflection by a grating: Rayleigh methods," J. Opt. Soc. Am. 71, 1224-1229 (1981).
    [CrossRef]
  30. E. Popov, B. Chernov, M. Nevière, and N. Bonod, "Differential theory: Application to highly conducting gratings," J. Opt. Soc. Am. A 21, 199-206 (2004).
    [CrossRef]
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  32. M. G. Moharam and T. K. Gaylord, "Diffraction analysis of dielectric surface-relief gratings," J. Opt. Soc. Am. 72, 1385-1392 (1982).
    [CrossRef]
  33. A. G. Ramm, "Modified Rayleigh conjecture and applications," J. Phys. A 35, L357-L361 (2002).
    [CrossRef]
  34. J. A. Fawcett, "Modeling acousto-elastic waveguide/object scattering with the Rayleigh hypothesis," J. Acoust. Soc. Am. 106, 164-168 (1999).
    [CrossRef]
  35. N. Garcia, G. Armand, and J. Lapujoulade, "Diffraction intensities in helium scattering; Topographic curves," Surf. Sci. 68, 399-407 (1977).
  36. V. Pan, "Complexity of computations with matrices and polynomials," SIAM Rev. 34, 225-262 (1992).
    [CrossRef]

2009

J. Wauer, T. Rother, "Considerations to Rayleigh’s hypothesis," Opt. Commun. 282, 339 (2009).
[CrossRef]

2004

2002

A. G. Ramm, "Modified Rayleigh conjecture and applications," J. Phys. A 35, L357-L361 (2002).
[CrossRef]

1999

J. A. Fawcett, "Modeling acousto-elastic waveguide/object scattering with the Rayleigh hypothesis," J. Acoust. Soc. Am. 106, 164-168 (1999).
[CrossRef]

1998

I. F. Salakhutdinov, V. A. Sychugov, A. V. Tishchenko, B. A. Usievich, and F. A. Pudonin, "Anomalous light reflection at the surface of a corrugated thin metal film," IEEE J. Quantum Electron. 34, 1054-1060 (1998).
[CrossRef]

1997

V. A. Sychugov, A. V. Tishchenko, N. M. Lyndin, and O. Parriaux, "Waveguide coupling gratings for high-sensitivity biochemical sensors," Sens. Actuators B 38-39 360-364 (1997).
[CrossRef]

1996

L. Kazandjian, "Rayleigh methods applied to electromagnetic scattering from gratings in general homogeneous media," Phys. Rev. E 54, 6802-6815 (1996).
[CrossRef]

1995

V. I. Tatarskii, "Relation between the Rayleigh equation in diffraction theory and the equation based on Green’s formula, " J. Opt. Soc. Am. 12, 1254-1260 (1995).
[CrossRef]

1992

V. Pan, "Complexity of computations with matrices and polynomials," SIAM Rev. 34, 225-262 (1992).
[CrossRef]

1985

G. A. Golubenko, A. A. Svakhin, V. A. Sychugov, and A. V. Tishchenko, "Total reflection of light from a corrugated surface of a dielectric waveguide," Sov. J. Quantum Electron. 15, 886-887 (1985).
[CrossRef]

1982

A. M. Prokhorov, V. A. Sychugov, A. V. Tishchenko, and A. A. Khakimov, "Kinetics of the rippling of a germanium surface bombarded by an intense laser beam," Sov. Tech. Phys. Lett. 8, 605-606 (1982).

P. Sheng, R. S. Stepleman, and P. N. Sanda, "Exact eigenfunctions for square-wave gratings: Application to diffraction and surface-plasmon calculations," Phys. Rev. B 262907-2916 (1982).
[CrossRef]

V. A. Sychugov and A. V. Tishchenko, "Propagation and conversion of light in corrugated waveguide structures," Sov. J. Quantum Electron. 12, 923-926 (1982).
[CrossRef]

M. G. Moharam and T. K. Gaylord, "Diffraction analysis of dielectric surface-relief gratings," J. Opt. Soc. Am. 72, 1385-1392 (1982).
[CrossRef]

1981

1980

J. Chandezon, D. Maystre, and G. Raoult, "A new theoretical method for diffraction gratings and its numerical application," J. Opt. Paris 11, 235-241 (1980).

V. A. Sychugov and A. V. Tishchenko, "Light emission from a corrugated dielectric waveguide," Sov. J. Quantum Electron. 10, 186-189 (1980).
[CrossRef]

A. Wirgin, "On Rayleigh’s theory of sinusoidal diffraction gratings," Opt. Acta 27, 1671-1692 (1980).

1977

N. Garcia, G. Armand, and J. Lapujoulade, "Diffraction intensities in helium scattering; Topographic curves," Surf. Sci. 68, 399-407 (1977).

1975

P. C. Waterman, "Scattering by periodic surfaces," J. Acoust. Soc. Am. 57, 791 (1975).
[CrossRef]

R. H. T. Bates, "Analytic constraints on electromagnetic field computations," IEEE Trans. Microwave Theory and Tech. MTT-23, 605-623 (1975).
[CrossRef]

1973

J. B. Davies, "A least-squares boundary residual method for the numerical solution of scattering problems," IEEE Trans. Microwave Theory and Tech. MTT-21, 99-103 (1973).
[CrossRef]

1971

R. F. Millar, "On the Rayleigh assumption in scattering by a periodic surface, II," Proc. Cambridge Philos. Soc. 69,217-225 (1971).
[CrossRef]

1968

J. Pavageau, "Sur la méthode des spectres d’ondes planes dans les problèmes de diffraction," C. R. Acad. Sci. Paris 266B, 135-138 (1968).

1966

R. Petit, M. Cadilhac, "Sur la diffraction d’une onde plane par un réseau infinement conducteur, C. R. Acad. Sci. Paris 262B, 468-471 (1966).

1965

J. L. Uretski, "The scattering of plane waves from periodic surfaces," Ann. Phys. 33, 400-427 (1965).
[CrossRef]

1953

1952

L. N. Deryugin, "Equations for coefficients of wave reflections from a periodically uneven surface," Dokl. Akad. Nauk SSSR 87,913-916 (1952).

1907

Lord Rayleigh (J. W. Strutt), "On the dynamical theory of gratings," Proc. R. Soc. London Ser. A 79, 399-416 (1907).

1897

Lord Rayleigh (J. W. Strutt), "On the incidence of aerial and electromagnetic waves upon small obstacles in the form of ellipsoids or elliptic cylinders, and the passage of electric waves through a circular aperture in a conducting screen," Phil. Mag. 44, 28-52 (1897).

Armand, G.

N. Garcia, G. Armand, and J. Lapujoulade, "Diffraction intensities in helium scattering; Topographic curves," Surf. Sci. 68, 399-407 (1977).

Avrutsky, I. A.

I. A. Avrutsky, V. A. Sychugov, and A. V. Tishchenko, "The study of excitation, radiation, and reflection processes in corrugated waveguides," in Waveguide Corrugated Structures in Integrated and Fiber Optics, IOFAN Proc. 34, 3-98 (Nauka, Moscow, 1991, in Russian).

Bates, R. H. T.

R. H. T. Bates, "Analytic constraints on electromagnetic field computations," IEEE Trans. Microwave Theory and Tech. MTT-23, 605-623 (1975).
[CrossRef]

Bonod, N.

Cadilhac, M.

R. Petit, M. Cadilhac, "Sur la diffraction d’une onde plane par un réseau infinement conducteur, C. R. Acad. Sci. Paris 262B, 468-471 (1966).

Chandezon, J.

J. Chandezon, D. Maystre, and G. Raoult, "A new theoretical method for diffraction gratings and its numerical application," J. Opt. Paris 11, 235-241 (1980).

Chernov, B.

Davies, J. B.

J. B. Davies, "A least-squares boundary residual method for the numerical solution of scattering problems," IEEE Trans. Microwave Theory and Tech. MTT-21, 99-103 (1973).
[CrossRef]

Deryugin, L. N.

L. N. Deryugin, "Equations for coefficients of wave reflections from a periodically uneven surface," Dokl. Akad. Nauk SSSR 87,913-916 (1952).

Fawcett, J. A.

J. A. Fawcett, "Modeling acousto-elastic waveguide/object scattering with the Rayleigh hypothesis," J. Acoust. Soc. Am. 106, 164-168 (1999).
[CrossRef]

Garcia, N.

N. Garcia, G. Armand, and J. Lapujoulade, "Diffraction intensities in helium scattering; Topographic curves," Surf. Sci. 68, 399-407 (1977).

Gaylord, T. K.

Golubenko, G. A.

G. A. Golubenko, A. A. Svakhin, V. A. Sychugov, and A. V. Tishchenko, "Total reflection of light from a corrugated surface of a dielectric waveguide," Sov. J. Quantum Electron. 15, 886-887 (1985).
[CrossRef]

Kazandjian, L.

L. Kazandjian, "Rayleigh methods applied to electromagnetic scattering from gratings in general homogeneous media," Phys. Rev. E 54, 6802-6815 (1996).
[CrossRef]

Khakimov, A. A.

A. M. Prokhorov, V. A. Sychugov, A. V. Tishchenko, and A. A. Khakimov, "Kinetics of the rippling of a germanium surface bombarded by an intense laser beam," Sov. Tech. Phys. Lett. 8, 605-606 (1982).

Lapujoulade, J.

N. Garcia, G. Armand, and J. Lapujoulade, "Diffraction intensities in helium scattering; Topographic curves," Surf. Sci. 68, 399-407 (1977).

Lippmann, B. A.

Lyndin, N. M.

V. A. Sychugov, A. V. Tishchenko, N. M. Lyndin, and O. Parriaux, "Waveguide coupling gratings for high-sensitivity biochemical sensors," Sens. Actuators B 38-39 360-364 (1997).
[CrossRef]

Maystre, D.

J. Chandezon, D. Maystre, and G. Raoult, "A new theoretical method for diffraction gratings and its numerical application," J. Opt. Paris 11, 235-241 (1980).

Millar, R. F.

R. F. Millar, "On the Rayleigh assumption in scattering by a periodic surface, II," Proc. Cambridge Philos. Soc. 69,217-225 (1971).
[CrossRef]

Moharam, M. G.

Nevière, M.

Pan, V.

V. Pan, "Complexity of computations with matrices and polynomials," SIAM Rev. 34, 225-262 (1992).
[CrossRef]

Parriaux, O.

V. A. Sychugov, A. V. Tishchenko, N. M. Lyndin, and O. Parriaux, "Waveguide coupling gratings for high-sensitivity biochemical sensors," Sens. Actuators B 38-39 360-364 (1997).
[CrossRef]

Pavageau, J.

J. Pavageau, "Sur la méthode des spectres d’ondes planes dans les problèmes de diffraction," C. R. Acad. Sci. Paris 266B, 135-138 (1968).

Petit, R.

R. Petit, M. Cadilhac, "Sur la diffraction d’une onde plane par un réseau infinement conducteur, C. R. Acad. Sci. Paris 262B, 468-471 (1966).

Popov, E.

Prokhorov, A. M.

A. M. Prokhorov, V. A. Sychugov, A. V. Tishchenko, and A. A. Khakimov, "Kinetics of the rippling of a germanium surface bombarded by an intense laser beam," Sov. Tech. Phys. Lett. 8, 605-606 (1982).

Pudonin, F. A.

I. F. Salakhutdinov, V. A. Sychugov, A. V. Tishchenko, B. A. Usievich, and F. A. Pudonin, "Anomalous light reflection at the surface of a corrugated thin metal film," IEEE J. Quantum Electron. 34, 1054-1060 (1998).
[CrossRef]

Ramm, A. G.

A. G. Ramm, "Modified Rayleigh conjecture and applications," J. Phys. A 35, L357-L361 (2002).
[CrossRef]

Raoult, G.

J. Chandezon, D. Maystre, and G. Raoult, "A new theoretical method for diffraction gratings and its numerical application," J. Opt. Paris 11, 235-241 (1980).

Rother, T.

J. Wauer, T. Rother, "Considerations to Rayleigh’s hypothesis," Opt. Commun. 282, 339 (2009).
[CrossRef]

Salakhutdinov, I. F.

I. F. Salakhutdinov, V. A. Sychugov, A. V. Tishchenko, B. A. Usievich, and F. A. Pudonin, "Anomalous light reflection at the surface of a corrugated thin metal film," IEEE J. Quantum Electron. 34, 1054-1060 (1998).
[CrossRef]

Sanda, P. N.

P. Sheng, R. S. Stepleman, and P. N. Sanda, "Exact eigenfunctions for square-wave gratings: Application to diffraction and surface-plasmon calculations," Phys. Rev. B 262907-2916 (1982).
[CrossRef]

Sheng, P.

P. Sheng, R. S. Stepleman, and P. N. Sanda, "Exact eigenfunctions for square-wave gratings: Application to diffraction and surface-plasmon calculations," Phys. Rev. B 262907-2916 (1982).
[CrossRef]

Stepleman, R. S.

P. Sheng, R. S. Stepleman, and P. N. Sanda, "Exact eigenfunctions for square-wave gratings: Application to diffraction and surface-plasmon calculations," Phys. Rev. B 262907-2916 (1982).
[CrossRef]

Svakhin, A. A.

G. A. Golubenko, A. A. Svakhin, V. A. Sychugov, and A. V. Tishchenko, "Total reflection of light from a corrugated surface of a dielectric waveguide," Sov. J. Quantum Electron. 15, 886-887 (1985).
[CrossRef]

Sychugov, V. A.

I. F. Salakhutdinov, V. A. Sychugov, A. V. Tishchenko, B. A. Usievich, and F. A. Pudonin, "Anomalous light reflection at the surface of a corrugated thin metal film," IEEE J. Quantum Electron. 34, 1054-1060 (1998).
[CrossRef]

V. A. Sychugov, A. V. Tishchenko, N. M. Lyndin, and O. Parriaux, "Waveguide coupling gratings for high-sensitivity biochemical sensors," Sens. Actuators B 38-39 360-364 (1997).
[CrossRef]

G. A. Golubenko, A. A. Svakhin, V. A. Sychugov, and A. V. Tishchenko, "Total reflection of light from a corrugated surface of a dielectric waveguide," Sov. J. Quantum Electron. 15, 886-887 (1985).
[CrossRef]

V. A. Sychugov and A. V. Tishchenko, "Propagation and conversion of light in corrugated waveguide structures," Sov. J. Quantum Electron. 12, 923-926 (1982).
[CrossRef]

A. M. Prokhorov, V. A. Sychugov, A. V. Tishchenko, and A. A. Khakimov, "Kinetics of the rippling of a germanium surface bombarded by an intense laser beam," Sov. Tech. Phys. Lett. 8, 605-606 (1982).

V. A. Sychugov and A. V. Tishchenko, "Light emission from a corrugated dielectric waveguide," Sov. J. Quantum Electron. 10, 186-189 (1980).
[CrossRef]

I. A. Avrutsky, V. A. Sychugov, and A. V. Tishchenko, "The study of excitation, radiation, and reflection processes in corrugated waveguides," in Waveguide Corrugated Structures in Integrated and Fiber Optics, IOFAN Proc. 34, 3-98 (Nauka, Moscow, 1991, in Russian).

Tatarskii, V. I.

V. I. Tatarskii, "Relation between the Rayleigh equation in diffraction theory and the equation based on Green’s formula, " J. Opt. Soc. Am. 12, 1254-1260 (1995).
[CrossRef]

Tishchenko, A. V.

I. F. Salakhutdinov, V. A. Sychugov, A. V. Tishchenko, B. A. Usievich, and F. A. Pudonin, "Anomalous light reflection at the surface of a corrugated thin metal film," IEEE J. Quantum Electron. 34, 1054-1060 (1998).
[CrossRef]

V. A. Sychugov, A. V. Tishchenko, N. M. Lyndin, and O. Parriaux, "Waveguide coupling gratings for high-sensitivity biochemical sensors," Sens. Actuators B 38-39 360-364 (1997).
[CrossRef]

G. A. Golubenko, A. A. Svakhin, V. A. Sychugov, and A. V. Tishchenko, "Total reflection of light from a corrugated surface of a dielectric waveguide," Sov. J. Quantum Electron. 15, 886-887 (1985).
[CrossRef]

V. A. Sychugov and A. V. Tishchenko, "Propagation and conversion of light in corrugated waveguide structures," Sov. J. Quantum Electron. 12, 923-926 (1982).
[CrossRef]

A. M. Prokhorov, V. A. Sychugov, A. V. Tishchenko, and A. A. Khakimov, "Kinetics of the rippling of a germanium surface bombarded by an intense laser beam," Sov. Tech. Phys. Lett. 8, 605-606 (1982).

V. A. Sychugov and A. V. Tishchenko, "Light emission from a corrugated dielectric waveguide," Sov. J. Quantum Electron. 10, 186-189 (1980).
[CrossRef]

I. A. Avrutsky, V. A. Sychugov, and A. V. Tishchenko, "The study of excitation, radiation, and reflection processes in corrugated waveguides," in Waveguide Corrugated Structures in Integrated and Fiber Optics, IOFAN Proc. 34, 3-98 (Nauka, Moscow, 1991, in Russian).

Turunen, J.

J. Turunen, "Diffraction theory of dielectric surface relief gratings," in Micro-optics, H.P. Herzig ed. (Taylor&Francis Inc., 1997).

Uretski, J. L.

J. L. Uretski, "The scattering of plane waves from periodic surfaces," Ann. Phys. 33, 400-427 (1965).
[CrossRef]

Usievich, B. A.

I. F. Salakhutdinov, V. A. Sychugov, A. V. Tishchenko, B. A. Usievich, and F. A. Pudonin, "Anomalous light reflection at the surface of a corrugated thin metal film," IEEE J. Quantum Electron. 34, 1054-1060 (1998).
[CrossRef]

van den Berg, P. M.

Waterman, P. C.

P. C. Waterman, "Scattering by periodic surfaces," J. Acoust. Soc. Am. 57, 791 (1975).
[CrossRef]

Wauer, J.

J. Wauer, T. Rother, "Considerations to Rayleigh’s hypothesis," Opt. Commun. 282, 339 (2009).
[CrossRef]

Wirgin, A.

A. Wirgin, "On Rayleigh’s theory of sinusoidal diffraction gratings," Opt. Acta 27, 1671-1692 (1980).

Ann. Phys.

J. L. Uretski, "The scattering of plane waves from periodic surfaces," Ann. Phys. 33, 400-427 (1965).
[CrossRef]

C. R. Acad. Sci. Paris

R. Petit, M. Cadilhac, "Sur la diffraction d’une onde plane par un réseau infinement conducteur, C. R. Acad. Sci. Paris 262B, 468-471 (1966).

J. Pavageau, "Sur la méthode des spectres d’ondes planes dans les problèmes de diffraction," C. R. Acad. Sci. Paris 266B, 135-138 (1968).

Dokl. Akad. Nauk SSSR

L. N. Deryugin, "Equations for coefficients of wave reflections from a periodically uneven surface," Dokl. Akad. Nauk SSSR 87,913-916 (1952).

IEEE J. Quantum Electron.

I. F. Salakhutdinov, V. A. Sychugov, A. V. Tishchenko, B. A. Usievich, and F. A. Pudonin, "Anomalous light reflection at the surface of a corrugated thin metal film," IEEE J. Quantum Electron. 34, 1054-1060 (1998).
[CrossRef]

IEEE Trans. Microwave Theory and Tech.

R. H. T. Bates, "Analytic constraints on electromagnetic field computations," IEEE Trans. Microwave Theory and Tech. MTT-23, 605-623 (1975).
[CrossRef]

J. B. Davies, "A least-squares boundary residual method for the numerical solution of scattering problems," IEEE Trans. Microwave Theory and Tech. MTT-21, 99-103 (1973).
[CrossRef]

J. Acoust. Soc. Am.

P. C. Waterman, "Scattering by periodic surfaces," J. Acoust. Soc. Am. 57, 791 (1975).
[CrossRef]

J. A. Fawcett, "Modeling acousto-elastic waveguide/object scattering with the Rayleigh hypothesis," J. Acoust. Soc. Am. 106, 164-168 (1999).
[CrossRef]

J. Opt. Paris

J. Chandezon, D. Maystre, and G. Raoult, "A new theoretical method for diffraction gratings and its numerical application," J. Opt. Paris 11, 235-241 (1980).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Phys. A

A. G. Ramm, "Modified Rayleigh conjecture and applications," J. Phys. A 35, L357-L361 (2002).
[CrossRef]

Opt. Acta

A. Wirgin, "On Rayleigh’s theory of sinusoidal diffraction gratings," Opt. Acta 27, 1671-1692 (1980).

Opt. Commun.

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