Abstract

We make a generalization of the integral method in the electromagnetic theory of gratings to study diffraction by echelles covered with dielectric lossless or absorbing layers. Numerical examples are given that show that, as in the resonance domain, the diffraction efficiency is more complicated than being a simple product of lossless diffraction efficiency curves and plane surface reflectivity.

© 1999 Optical Society of America

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  1. M. Nevière, G. Cerutti-Maori, M. Cadilhac, “Sur une nouvelle méthode de résolution du problème de la diffraction d’une onde plane par un réseau infiniment conducteur,” Opt. Commun. 3, 48–52 (1971).
    [CrossRef]
  2. 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]
  3. F. Montiel, M. Nevière, “Differential theory of gratings: extension to deep gratings of arbitrary profile and permittivity via the R-matrix propagation algorithm,” J. Opt. Soc. Am. A 12, 2672–2678 (1995).
    [CrossRef]
  4. M. G. Moharam, T. K. Gaylord, “Diffraction analysis of dielectric surface-relief gratings,” J. Opt. Soc. Am. 72, 1385–1392 (1982).
    [CrossRef]
  5. L. Li, “Multilayer modal method for diffraction gratings of arbitrary profile, depth, and permittivity,” J. Opt. Soc. Am. A 10, 2581–2591 (1993).
    [CrossRef]
  6. P. Lalanne, G. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779–784 (1996).
    [CrossRef]
  7. 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]
  8. J. Chandezon, M. T. Dupuis, G. Cornet, D. Maystre, “Multicoated gratings: a differential formalism applicable in the entire optical region,” J. Opt. Soc. Am. 72, 839–846 (1982).
    [CrossRef]
  9. J. P. Plumey, B. Guizal, J. Chandezon, “The coordinate transformation method as applied to asymmetric gratings with vertical facets,” J. Opt. Soc. Am. A 14, 610–617 (1997).
    [CrossRef]
  10. G. Granet, J. Chandezon, O. Coudert, “Extension of the C method to nonhomogeneous media: application to nonhomogeneous layers with parallel modulated faces and to inclined lamellar gratings,” J. Opt. Soc. Am. A 14, 1576–1582 (1997).
    [CrossRef]
  11. D. Maystre, “Integral method,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), Chap. 3.
  12. E. Loewen, D. Maystre, E. Popov, L. Tsonev, “Echelles: scalar, electromagnetic, and real-groove properties,” Appl. Opt. 34, 1707–1727 (1995).
    [CrossRef] [PubMed]
  13. E. Loewen, D. Maystre, E. Popov, L. Tsonev, “Diffraction efficiency of echelles working in extremely high orders,” Appl. Opt. 35, 1700–1704 (1996).
    [CrossRef] [PubMed]
  14. D. Maystre, “A new general integral theory for dielectric coated gratings,” J. Opt. Soc. Am. 68, 490–495 (1978).
    [CrossRef]
  15. D. Maystre, “A new theory for multiprofile, buried gratings,” Opt. Commun. 26, 127–132 (1978).
    [CrossRef]
  16. A. Pomp, “The integral method for coated gratings: computational cost,” J. Mod. Opt. 38, 109–120 (1991).
    [CrossRef]
  17. D. Maystre, “Electromagnetic study of photonic band gaps,” Pure Appl. Opt. 3, 975–993 (1994).
    [CrossRef]
  18. Lord Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. London Ser. A 79, 399–416 (1907).
    [CrossRef]
  19. R. F. Millar, “The Rayleigh hypothesis and a related least-squares solution to scattering problems for periodic surfaces and other scatterers,” Radio Sci. 8, 785–796 (1973); M. Nevière, M. Cadilhac, “Sur la validite du developpement de Rayleigh,” Opt. Commun. 2, 235–238 (1970).
    [CrossRef]
  20. A. Wirgin, “Sur la théorie de Rayleigh de la diffraction d’une onde par une surface sinusoidale,” C. R. Acad. Sci. Ser. B 288, 179–182 (1979).
  21. E. Popov, L. Mashev, “Convergence of Rayleigh Fourier method and rigorous differential method for relief diffraction gratings: nonsinusoidal profile,” J. Mod. Opt. 34, 155–158 (1987).
    [CrossRef]
  22. P. M. Van den Berg, “Reflection by a grating: Rayleigh methods,” J. Opt. Soc. Am. 71, 1224–1229 (1981).
    [CrossRef]
  23. See E. Loewen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997), Chap. 4.

1997

1996

1995

1994

D. Maystre, “Electromagnetic study of photonic band gaps,” Pure Appl. Opt. 3, 975–993 (1994).
[CrossRef]

1993

1991

A. Pomp, “The integral method for coated gratings: computational cost,” J. Mod. Opt. 38, 109–120 (1991).
[CrossRef]

1987

E. Popov, L. Mashev, “Convergence of Rayleigh Fourier method and rigorous differential method for relief diffraction gratings: nonsinusoidal profile,” J. Mod. Opt. 34, 155–158 (1987).
[CrossRef]

1982

1981

1979

A. Wirgin, “Sur la théorie de Rayleigh de la diffraction d’une onde par une surface sinusoidale,” C. R. Acad. Sci. Ser. B 288, 179–182 (1979).

1978

D. Maystre, “A new theory for multiprofile, buried gratings,” Opt. Commun. 26, 127–132 (1978).
[CrossRef]

D. Maystre, “A new general integral theory for dielectric coated gratings,” J. Opt. Soc. Am. 68, 490–495 (1978).
[CrossRef]

1973

R. F. Millar, “The Rayleigh hypothesis and a related least-squares solution to scattering problems for periodic surfaces and other scatterers,” Radio Sci. 8, 785–796 (1973); M. Nevière, M. Cadilhac, “Sur la validite du developpement de Rayleigh,” Opt. Commun. 2, 235–238 (1970).
[CrossRef]

1971

M. Nevière, G. Cerutti-Maori, M. Cadilhac, “Sur une nouvelle méthode de résolution du problème de la diffraction d’une onde plane par un réseau infiniment conducteur,” Opt. Commun. 3, 48–52 (1971).
[CrossRef]

1907

Lord Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. London Ser. A 79, 399–416 (1907).
[CrossRef]

Cadilhac, M.

M. Nevière, G. Cerutti-Maori, M. Cadilhac, “Sur une nouvelle méthode de résolution du problème de la diffraction d’une onde plane par un réseau infiniment conducteur,” Opt. Commun. 3, 48–52 (1971).
[CrossRef]

Cerutti-Maori, G.

M. Nevière, G. Cerutti-Maori, M. Cadilhac, “Sur une nouvelle méthode de résolution du problème de la diffraction d’une onde plane par un réseau infiniment conducteur,” Opt. Commun. 3, 48–52 (1971).
[CrossRef]

Chandezon, J.

Cornet, G.

Coudert, O.

Dupuis, M. T.

Gaylord, T. K.

Granet, G.

Guizal, B.

Lalanne, P.

Li, L.

Loewen, E.

Mashev, L.

E. Popov, L. Mashev, “Convergence of Rayleigh Fourier method and rigorous differential method for relief diffraction gratings: nonsinusoidal profile,” J. Mod. Opt. 34, 155–158 (1987).
[CrossRef]

Maystre, D.

Millar, R. F.

R. F. Millar, “The Rayleigh hypothesis and a related least-squares solution to scattering problems for periodic surfaces and other scatterers,” Radio Sci. 8, 785–796 (1973); M. Nevière, M. Cadilhac, “Sur la validite du developpement de Rayleigh,” Opt. Commun. 2, 235–238 (1970).
[CrossRef]

Moharam, M. G.

Montiel, F.

Morris, G.

Nevière, M.

F. Montiel, M. Nevière, “Differential theory of gratings: extension to deep gratings of arbitrary profile and permittivity via the R-matrix propagation algorithm,” J. Opt. Soc. Am. A 12, 2672–2678 (1995).
[CrossRef]

M. Nevière, G. Cerutti-Maori, M. Cadilhac, “Sur une nouvelle méthode de résolution du problème de la diffraction d’une onde plane par un réseau infiniment conducteur,” Opt. Commun. 3, 48–52 (1971).
[CrossRef]

Plumey, J. P.

Pomp, A.

A. Pomp, “The integral method for coated gratings: computational cost,” J. Mod. Opt. 38, 109–120 (1991).
[CrossRef]

Popov, E.

E. Loewen, D. Maystre, E. Popov, L. Tsonev, “Diffraction efficiency of echelles working in extremely high orders,” Appl. Opt. 35, 1700–1704 (1996).
[CrossRef] [PubMed]

E. Loewen, D. Maystre, E. Popov, L. Tsonev, “Echelles: scalar, electromagnetic, and real-groove properties,” Appl. Opt. 34, 1707–1727 (1995).
[CrossRef] [PubMed]

E. Popov, L. Mashev, “Convergence of Rayleigh Fourier method and rigorous differential method for relief diffraction gratings: nonsinusoidal profile,” J. Mod. Opt. 34, 155–158 (1987).
[CrossRef]

See E. Loewen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997), Chap. 4.

Rayleigh, Lord

Lord Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. London Ser. A 79, 399–416 (1907).
[CrossRef]

Tsonev, L.

Van den Berg, P. M.

Wirgin, A.

A. Wirgin, “Sur la théorie de Rayleigh de la diffraction d’une onde par une surface sinusoidale,” C. R. Acad. Sci. Ser. B 288, 179–182 (1979).

Appl. Opt.

C. R. Acad. Sci. Ser. B

A. Wirgin, “Sur la théorie de Rayleigh de la diffraction d’une onde par une surface sinusoidale,” C. R. Acad. Sci. Ser. B 288, 179–182 (1979).

J. Mod. Opt.

E. Popov, L. Mashev, “Convergence of Rayleigh Fourier method and rigorous differential method for relief diffraction gratings: nonsinusoidal profile,” J. Mod. Opt. 34, 155–158 (1987).
[CrossRef]

A. Pomp, “The integral method for coated gratings: computational cost,” J. Mod. Opt. 38, 109–120 (1991).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

D. Maystre, “A new theory for multiprofile, buried gratings,” Opt. Commun. 26, 127–132 (1978).
[CrossRef]

M. Nevière, G. Cerutti-Maori, M. Cadilhac, “Sur une nouvelle méthode de résolution du problème de la diffraction d’une onde plane par un réseau infiniment conducteur,” Opt. Commun. 3, 48–52 (1971).
[CrossRef]

Proc. R. Soc. London Ser. A

Lord Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. London Ser. A 79, 399–416 (1907).
[CrossRef]

Pure Appl. Opt.

D. Maystre, “Electromagnetic study of photonic band gaps,” Pure Appl. Opt. 3, 975–993 (1994).
[CrossRef]

Radio Sci.

R. F. Millar, “The Rayleigh hypothesis and a related least-squares solution to scattering problems for periodic surfaces and other scatterers,” Radio Sci. 8, 785–796 (1973); M. Nevière, M. Cadilhac, “Sur la validite du developpement de Rayleigh,” Opt. Commun. 2, 235–238 (1970).
[CrossRef]

Other

See E. Loewen, E. Popov, Diffraction Gratings and Applications (Marcel Dekker, New York, 1997), Chap. 4.

D. Maystre, “Integral method,” in Electromagnetic Theory of Gratings, R. Petit, ed. (Springer-Verlag, Berlin, 1980), Chap. 3.

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