Abstract

Rayleigh’s method is used in a numerical study of the light scattered from a one-dimensional, randomly rough surface on a metal illuminated by a plane wave whose direction of incidence is perpendicular to the grooves of the surface. In the regime of interest a significant component of the amplitude of the p-polarized light scattered in the far field may be attributed to the resonant interaction between the incident wave and surface polaritons. The dependence of the coherent and of the diffuse scattering on the incident wavelength, the roughness parameters, the polarization, and the angle of incidence or of scattering is considered. The conditions under which an enhanced backscattering peak may be observed are determined within the range of convergence of Rayleigh’s method. A random roughness superimposed upon a periodic grating may produce enhanced backscattering at wavelengths longer than twice the period of the grating. At the wavelength and the angle at which a grating anomaly is found, the diffuse scattering may display a band or a minimum, depending on the angle of incidence.

© 1994 Optical Society of America

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References

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  1. E. Kretschmann, E. Kröger, “Reflection and transmission of light by a rough surface, including results for surface-plasmon effects,” J. Opt. Soc. Am. 65, 150–154 (1975).
    [CrossRef]
  2. F. Toigo, A. Marvin, V. Celli, N. R. Hill, “Optical properties of rough surfaces: general theory and the small roughness limit,” Phys. Rev. B 15, 5618–5626 (1977).
    [CrossRef]
  3. A. A. Maradudin, “Iterative solutions for electromagnetic scattering by gratings,” J. Opt. Soc. Am. 73, 759–764 (1983).
    [CrossRef]
  4. G. Brown, V. Celli, H. Haller, A. A. Maradudin, A. Marvin, “Resonant light scattering from a randomly rough surface,” Phys. Rev. B 31, 4993–5005 (1985).
    [CrossRef]
  5. A. R. McGurn, A. A. Maradudin, V. Celli, “Localization effects in the scattering of light from a randomly rough grating,” Phys. Rev. B 31, 4866–4871 (1985).
    [CrossRef]
  6. A. R. McGurn, A. A. Maradudin, “Localization effects in the elastic scattering of light from a randomly rough surface,” J. Opt. Soc. Am. B 4, 910–926 (1987).
    [CrossRef]
  7. A. A. Maradudin, E. R. Méndez, “Enhanced backscattering of light from weakly rough, random metal surfaces,” Appl. Opt. 32, 3335–3343 (1993).
    [CrossRef] [PubMed]
  8. P. Tran, V. Celli, “Monte Carlo calculation of backscattering enhancement for a randomly rough grating,” J. Opt. Soc. Am. A 5, 1635–1637 (1988).
    [CrossRef]
  9. A. A. Maradudin, Jun Q. Lu, P. Tran, R. F. Wallis, V. Celli, Zu-Han Gu, A. R. McGurn, E. R. Méndez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 3, 343–397 (1992).
  10. For a review, see H. Raether, Surface Plasmons on Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).
  11. S. O. Sari, D. K. Cohen, K. D. Scherkoske, “Study of surface plasma-wave reflectance and roughness-induced scattering in silver foils,” Phys. Rev. B 21, 2162–2174 (1980).
    [CrossRef]
  12. V. Celli, A. A. Maradudin, A. M. Marvin, A. R. McGurn, “Some aspects of light scattering from a randomly rough metal surface,” J. Opt. Soc. Am. A 2, 2225–2239 (1985).
    [CrossRef]
  13. M. E. Knotts, T. R. Michel, K. A. O’Donnell, “Comparisons of theory and experiment in light scattering from a randomly rough surface,” J. Opt. Soc. Am. A 10, 928–941 (1993).
    [CrossRef]
  14. J. A. Sánchez-Gil, M. Nieto-Vesperinas, “Resonance effects in multiple scattering from statistically rough metallic surfaces,” Phys. Rev. B 45, 8623–8633 (1992).
    [CrossRef]
  15. A. A. Maradudin, E. R. Méndez, T. Michel, “Backscattering effects in the elastic scattering of p-polarized light from a large-amplitude random grating,” in Scattering in Volume and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (North-Holland, Amsterdam, 1990), pp. 157–174.
  16. A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (N.Y.) 203, 255–307 (1990).
    [CrossRef]
  17. See, for example, D. Maystre, “General study of grating anomalies from electromagnetic surface modes,” in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, New York, 1982), pp. 661–724.
  18. M. C. Hutley, V. M. Bird, “A detailed experimental study of the anomalies of a sinusoidal diffraction grating,” Opt. Acta 20, 771–782 (1973).
    [CrossRef]
  19. M. C. Hutley, D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun. 19, 431–436 (1976).
    [CrossRef]
  20. J. M. Simon, S. A. Ledesma, “Diffuse light bands from diffraction gratings: a correlation study,” Optik (Stuttgart) 89, 145–150 (1992).
  21. R. A. Depine, V. L. Brudny, “Speckle patterns generated by rough surfaces with a periodic component,” J. Mod. Opt. 38, 2281–2293 (1991).
    [CrossRef]
  22. V. L. Brudny, R. A. Depine, “Speckle pattern intensification in highly conducting microrough gratings,” J. Mod. Opt. 40, 427–439 (1993).
    [CrossRef]
  23. D. Maystre, “Rigorous vector theories of diffraction gratings,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. 11, pp. 1–68.
  24. K. A. O’Donnell, M. E. Knotts, “Polarization dependence of scattering from one-dimensional rough surface,” J. Opt. Soc. Am. A 8, 1126–1131 (1991).
    [CrossRef]
  25. N. R. Hill, V. Celli, “Limits of convergence of the Rayleigh method for surface scattering,” Phys. Rev. B 17, 2478–2481 (1978).
    [CrossRef]
  26. D. H. Berman, J. S. Perkins, “Rayleigh method for scattering from random and deterministic interfaces,” J. Acoust. Soc. Am. 88, 1032–1044 (1990).
    [CrossRef]
  27. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, New York, 1985),
  28. A. A. Maradudin, “Electromagnetic surface excitations on rough surfaces,” in Electromagnetic Surface Excitation, R. F. Wallis, G. I. Stegeman, eds. (Springer-Verlag, New York, 1986), pp. 57–131.
    [CrossRef]
  29. B. Laks, D. L. Mills, A. A. Maradudin, “Surface polaritons on large amplitude gratings,” Phys. Rev. B 23, 4965–4975 (1981).
    [CrossRef]
  30. G. S. Brown, “A stochastic Fourier transform approach to scattering from perfectly conducting randomly rough surfaces,” IEEE Trans. Antennas Propag. AP-30, 1135–1144 (1982).
    [CrossRef]
  31. S. Solimeno, B. Crosignani, P. DiPorto, Guiding, Diffraction, and Confinement of Optical Radiation (Academic, Orlando, Fla.1986), p. 210.
  32. N. E. Class, M. Weber, D. L. Mills, “Attenuation and dispersion of surface polaritons on gratings,” Phys. Rev. B 29, 6548–6559 (1984).
    [CrossRef]
  33. A. A. Maradudin, T. Michel, “The transverse correlation length for randomly rough surfaces,” J. Stat. Phys. 58, 485–501 (1990).
    [CrossRef]
  34. J. M. Soto-Crespo, M. Nieto-Vesperinas, A. T. Friberg, “Scattering from slightly rough random surfaces: a detailed study on the validity of the small perturbation method,” J. Opt. Soc. Am. A 7, 1185–1201 (1990).
    [CrossRef]
  35. C. Lopez, F. J. Yndurain, N. Garcia, “Iterative series for calculating the scattering of waves from a hard corrugated surface,” Phys. Rev. B 18, 970–972 (1978).
    [CrossRef]
  36. A. A. Maradudin, R. E. Luna, E. R. Méndez, “The Brewster effect for a one-dimensional random surface,” Waves Random Media 3, 51–60 (1993).
    [CrossRef]
  37. M. Salliard, “Randomly rough surfaces: numerical study of localized electromagnetic surface modes,” Appl. Opt. 32, 3354–3361 (1993).
    [CrossRef]
  38. M. Saillard, “Anderson localization for electromagnetic surface waves,” Opt. Commun. 96, 1–7 (1993).
    [CrossRef]

1993 (6)

A. A. Maradudin, E. R. Méndez, “Enhanced backscattering of light from weakly rough, random metal surfaces,” Appl. Opt. 32, 3335–3343 (1993).
[CrossRef] [PubMed]

M. E. Knotts, T. R. Michel, K. A. O’Donnell, “Comparisons of theory and experiment in light scattering from a randomly rough surface,” J. Opt. Soc. Am. A 10, 928–941 (1993).
[CrossRef]

V. L. Brudny, R. A. Depine, “Speckle pattern intensification in highly conducting microrough gratings,” J. Mod. Opt. 40, 427–439 (1993).
[CrossRef]

A. A. Maradudin, R. E. Luna, E. R. Méndez, “The Brewster effect for a one-dimensional random surface,” Waves Random Media 3, 51–60 (1993).
[CrossRef]

M. Salliard, “Randomly rough surfaces: numerical study of localized electromagnetic surface modes,” Appl. Opt. 32, 3354–3361 (1993).
[CrossRef]

M. Saillard, “Anderson localization for electromagnetic surface waves,” Opt. Commun. 96, 1–7 (1993).
[CrossRef]

1992 (3)

J. M. Simon, S. A. Ledesma, “Diffuse light bands from diffraction gratings: a correlation study,” Optik (Stuttgart) 89, 145–150 (1992).

J. A. Sánchez-Gil, M. Nieto-Vesperinas, “Resonance effects in multiple scattering from statistically rough metallic surfaces,” Phys. Rev. B 45, 8623–8633 (1992).
[CrossRef]

A. A. Maradudin, Jun Q. Lu, P. Tran, R. F. Wallis, V. Celli, Zu-Han Gu, A. R. McGurn, E. R. Méndez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 3, 343–397 (1992).

1991 (2)

R. A. Depine, V. L. Brudny, “Speckle patterns generated by rough surfaces with a periodic component,” J. Mod. Opt. 38, 2281–2293 (1991).
[CrossRef]

K. A. O’Donnell, M. E. Knotts, “Polarization dependence of scattering from one-dimensional rough surface,” J. Opt. Soc. Am. A 8, 1126–1131 (1991).
[CrossRef]

1990 (4)

D. H. Berman, J. S. Perkins, “Rayleigh method for scattering from random and deterministic interfaces,” J. Acoust. Soc. Am. 88, 1032–1044 (1990).
[CrossRef]

A. A. Maradudin, T. Michel, “The transverse correlation length for randomly rough surfaces,” J. Stat. Phys. 58, 485–501 (1990).
[CrossRef]

J. M. Soto-Crespo, M. Nieto-Vesperinas, A. T. Friberg, “Scattering from slightly rough random surfaces: a detailed study on the validity of the small perturbation method,” J. Opt. Soc. Am. A 7, 1185–1201 (1990).
[CrossRef]

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (N.Y.) 203, 255–307 (1990).
[CrossRef]

1988 (1)

1987 (1)

1985 (3)

G. Brown, V. Celli, H. Haller, A. A. Maradudin, A. Marvin, “Resonant light scattering from a randomly rough surface,” Phys. Rev. B 31, 4993–5005 (1985).
[CrossRef]

A. R. McGurn, A. A. Maradudin, V. Celli, “Localization effects in the scattering of light from a randomly rough grating,” Phys. Rev. B 31, 4866–4871 (1985).
[CrossRef]

V. Celli, A. A. Maradudin, A. M. Marvin, A. R. McGurn, “Some aspects of light scattering from a randomly rough metal surface,” J. Opt. Soc. Am. A 2, 2225–2239 (1985).
[CrossRef]

1984 (1)

N. E. Class, M. Weber, D. L. Mills, “Attenuation and dispersion of surface polaritons on gratings,” Phys. Rev. B 29, 6548–6559 (1984).
[CrossRef]

1983 (1)

1982 (1)

G. S. Brown, “A stochastic Fourier transform approach to scattering from perfectly conducting randomly rough surfaces,” IEEE Trans. Antennas Propag. AP-30, 1135–1144 (1982).
[CrossRef]

1981 (1)

B. Laks, D. L. Mills, A. A. Maradudin, “Surface polaritons on large amplitude gratings,” Phys. Rev. B 23, 4965–4975 (1981).
[CrossRef]

1980 (1)

S. O. Sari, D. K. Cohen, K. D. Scherkoske, “Study of surface plasma-wave reflectance and roughness-induced scattering in silver foils,” Phys. Rev. B 21, 2162–2174 (1980).
[CrossRef]

1978 (2)

N. R. Hill, V. Celli, “Limits of convergence of the Rayleigh method for surface scattering,” Phys. Rev. B 17, 2478–2481 (1978).
[CrossRef]

C. Lopez, F. J. Yndurain, N. Garcia, “Iterative series for calculating the scattering of waves from a hard corrugated surface,” Phys. Rev. B 18, 970–972 (1978).
[CrossRef]

1977 (1)

F. Toigo, A. Marvin, V. Celli, N. R. Hill, “Optical properties of rough surfaces: general theory and the small roughness limit,” Phys. Rev. B 15, 5618–5626 (1977).
[CrossRef]

1976 (1)

M. C. Hutley, D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun. 19, 431–436 (1976).
[CrossRef]

1975 (1)

1973 (1)

M. C. Hutley, V. M. Bird, “A detailed experimental study of the anomalies of a sinusoidal diffraction grating,” Opt. Acta 20, 771–782 (1973).
[CrossRef]

Berman, D. H.

D. H. Berman, J. S. Perkins, “Rayleigh method for scattering from random and deterministic interfaces,” J. Acoust. Soc. Am. 88, 1032–1044 (1990).
[CrossRef]

Bird, V. M.

M. C. Hutley, V. M. Bird, “A detailed experimental study of the anomalies of a sinusoidal diffraction grating,” Opt. Acta 20, 771–782 (1973).
[CrossRef]

Brown, G.

G. Brown, V. Celli, H. Haller, A. A. Maradudin, A. Marvin, “Resonant light scattering from a randomly rough surface,” Phys. Rev. B 31, 4993–5005 (1985).
[CrossRef]

Brown, G. S.

G. S. Brown, “A stochastic Fourier transform approach to scattering from perfectly conducting randomly rough surfaces,” IEEE Trans. Antennas Propag. AP-30, 1135–1144 (1982).
[CrossRef]

Brudny, V. L.

V. L. Brudny, R. A. Depine, “Speckle pattern intensification in highly conducting microrough gratings,” J. Mod. Opt. 40, 427–439 (1993).
[CrossRef]

R. A. Depine, V. L. Brudny, “Speckle patterns generated by rough surfaces with a periodic component,” J. Mod. Opt. 38, 2281–2293 (1991).
[CrossRef]

Celli, V.

A. A. Maradudin, Jun Q. Lu, P. Tran, R. F. Wallis, V. Celli, Zu-Han Gu, A. R. McGurn, E. R. Méndez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 3, 343–397 (1992).

P. Tran, V. Celli, “Monte Carlo calculation of backscattering enhancement for a randomly rough grating,” J. Opt. Soc. Am. A 5, 1635–1637 (1988).
[CrossRef]

A. R. McGurn, A. A. Maradudin, V. Celli, “Localization effects in the scattering of light from a randomly rough grating,” Phys. Rev. B 31, 4866–4871 (1985).
[CrossRef]

G. Brown, V. Celli, H. Haller, A. A. Maradudin, A. Marvin, “Resonant light scattering from a randomly rough surface,” Phys. Rev. B 31, 4993–5005 (1985).
[CrossRef]

V. Celli, A. A. Maradudin, A. M. Marvin, A. R. McGurn, “Some aspects of light scattering from a randomly rough metal surface,” J. Opt. Soc. Am. A 2, 2225–2239 (1985).
[CrossRef]

N. R. Hill, V. Celli, “Limits of convergence of the Rayleigh method for surface scattering,” Phys. Rev. B 17, 2478–2481 (1978).
[CrossRef]

F. Toigo, A. Marvin, V. Celli, N. R. Hill, “Optical properties of rough surfaces: general theory and the small roughness limit,” Phys. Rev. B 15, 5618–5626 (1977).
[CrossRef]

Class, N. E.

N. E. Class, M. Weber, D. L. Mills, “Attenuation and dispersion of surface polaritons on gratings,” Phys. Rev. B 29, 6548–6559 (1984).
[CrossRef]

Cohen, D. K.

S. O. Sari, D. K. Cohen, K. D. Scherkoske, “Study of surface plasma-wave reflectance and roughness-induced scattering in silver foils,” Phys. Rev. B 21, 2162–2174 (1980).
[CrossRef]

Crosignani, B.

S. Solimeno, B. Crosignani, P. DiPorto, Guiding, Diffraction, and Confinement of Optical Radiation (Academic, Orlando, Fla.1986), p. 210.

Dainty, J. C.

A. A. Maradudin, Jun Q. Lu, P. Tran, R. F. Wallis, V. Celli, Zu-Han Gu, A. R. McGurn, E. R. Méndez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 3, 343–397 (1992).

Depine, R. A.

V. L. Brudny, R. A. Depine, “Speckle pattern intensification in highly conducting microrough gratings,” J. Mod. Opt. 40, 427–439 (1993).
[CrossRef]

R. A. Depine, V. L. Brudny, “Speckle patterns generated by rough surfaces with a periodic component,” J. Mod. Opt. 38, 2281–2293 (1991).
[CrossRef]

DiPorto, P.

S. Solimeno, B. Crosignani, P. DiPorto, Guiding, Diffraction, and Confinement of Optical Radiation (Academic, Orlando, Fla.1986), p. 210.

Friberg, A. T.

Garcia, N.

C. Lopez, F. J. Yndurain, N. Garcia, “Iterative series for calculating the scattering of waves from a hard corrugated surface,” Phys. Rev. B 18, 970–972 (1978).
[CrossRef]

Gu, Zu-Han

A. A. Maradudin, Jun Q. Lu, P. Tran, R. F. Wallis, V. Celli, Zu-Han Gu, A. R. McGurn, E. R. Méndez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 3, 343–397 (1992).

Haller, H.

G. Brown, V. Celli, H. Haller, A. A. Maradudin, A. Marvin, “Resonant light scattering from a randomly rough surface,” Phys. Rev. B 31, 4993–5005 (1985).
[CrossRef]

Hill, N. R.

N. R. Hill, V. Celli, “Limits of convergence of the Rayleigh method for surface scattering,” Phys. Rev. B 17, 2478–2481 (1978).
[CrossRef]

F. Toigo, A. Marvin, V. Celli, N. R. Hill, “Optical properties of rough surfaces: general theory and the small roughness limit,” Phys. Rev. B 15, 5618–5626 (1977).
[CrossRef]

Hutley, M. C.

M. C. Hutley, D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun. 19, 431–436 (1976).
[CrossRef]

M. C. Hutley, V. M. Bird, “A detailed experimental study of the anomalies of a sinusoidal diffraction grating,” Opt. Acta 20, 771–782 (1973).
[CrossRef]

Knotts, M. E.

Kretschmann, E.

Kröger, E.

Laks, B.

B. Laks, D. L. Mills, A. A. Maradudin, “Surface polaritons on large amplitude gratings,” Phys. Rev. B 23, 4965–4975 (1981).
[CrossRef]

Ledesma, S. A.

J. M. Simon, S. A. Ledesma, “Diffuse light bands from diffraction gratings: a correlation study,” Optik (Stuttgart) 89, 145–150 (1992).

Lopez, C.

C. Lopez, F. J. Yndurain, N. Garcia, “Iterative series for calculating the scattering of waves from a hard corrugated surface,” Phys. Rev. B 18, 970–972 (1978).
[CrossRef]

Lu, Jun Q.

A. A. Maradudin, Jun Q. Lu, P. Tran, R. F. Wallis, V. Celli, Zu-Han Gu, A. R. McGurn, E. R. Méndez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 3, 343–397 (1992).

Luna, R. E.

A. A. Maradudin, R. E. Luna, E. R. Méndez, “The Brewster effect for a one-dimensional random surface,” Waves Random Media 3, 51–60 (1993).
[CrossRef]

Maradudin, A. A.

A. A. Maradudin, R. E. Luna, E. R. Méndez, “The Brewster effect for a one-dimensional random surface,” Waves Random Media 3, 51–60 (1993).
[CrossRef]

A. A. Maradudin, E. R. Méndez, “Enhanced backscattering of light from weakly rough, random metal surfaces,” Appl. Opt. 32, 3335–3343 (1993).
[CrossRef] [PubMed]

A. A. Maradudin, Jun Q. Lu, P. Tran, R. F. Wallis, V. Celli, Zu-Han Gu, A. R. McGurn, E. R. Méndez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 3, 343–397 (1992).

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (N.Y.) 203, 255–307 (1990).
[CrossRef]

A. A. Maradudin, T. Michel, “The transverse correlation length for randomly rough surfaces,” J. Stat. Phys. 58, 485–501 (1990).
[CrossRef]

A. R. McGurn, A. A. Maradudin, “Localization effects in the elastic scattering of light from a randomly rough surface,” J. Opt. Soc. Am. B 4, 910–926 (1987).
[CrossRef]

A. R. McGurn, A. A. Maradudin, V. Celli, “Localization effects in the scattering of light from a randomly rough grating,” Phys. Rev. B 31, 4866–4871 (1985).
[CrossRef]

G. Brown, V. Celli, H. Haller, A. A. Maradudin, A. Marvin, “Resonant light scattering from a randomly rough surface,” Phys. Rev. B 31, 4993–5005 (1985).
[CrossRef]

V. Celli, A. A. Maradudin, A. M. Marvin, A. R. McGurn, “Some aspects of light scattering from a randomly rough metal surface,” J. Opt. Soc. Am. A 2, 2225–2239 (1985).
[CrossRef]

A. A. Maradudin, “Iterative solutions for electromagnetic scattering by gratings,” J. Opt. Soc. Am. 73, 759–764 (1983).
[CrossRef]

B. Laks, D. L. Mills, A. A. Maradudin, “Surface polaritons on large amplitude gratings,” Phys. Rev. B 23, 4965–4975 (1981).
[CrossRef]

A. A. Maradudin, “Electromagnetic surface excitations on rough surfaces,” in Electromagnetic Surface Excitation, R. F. Wallis, G. I. Stegeman, eds. (Springer-Verlag, New York, 1986), pp. 57–131.
[CrossRef]

A. A. Maradudin, E. R. Méndez, T. Michel, “Backscattering effects in the elastic scattering of p-polarized light from a large-amplitude random grating,” in Scattering in Volume and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (North-Holland, Amsterdam, 1990), pp. 157–174.

Marvin, A.

G. Brown, V. Celli, H. Haller, A. A. Maradudin, A. Marvin, “Resonant light scattering from a randomly rough surface,” Phys. Rev. B 31, 4993–5005 (1985).
[CrossRef]

F. Toigo, A. Marvin, V. Celli, N. R. Hill, “Optical properties of rough surfaces: general theory and the small roughness limit,” Phys. Rev. B 15, 5618–5626 (1977).
[CrossRef]

Marvin, A. M.

Maystre, D.

M. C. Hutley, D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun. 19, 431–436 (1976).
[CrossRef]

See, for example, D. Maystre, “General study of grating anomalies from electromagnetic surface modes,” in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, New York, 1982), pp. 661–724.

D. Maystre, “Rigorous vector theories of diffraction gratings,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. 11, pp. 1–68.

McGurn, A. R.

A. A. Maradudin, Jun Q. Lu, P. Tran, R. F. Wallis, V. Celli, Zu-Han Gu, A. R. McGurn, E. R. Méndez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 3, 343–397 (1992).

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (N.Y.) 203, 255–307 (1990).
[CrossRef]

A. R. McGurn, A. A. Maradudin, “Localization effects in the elastic scattering of light from a randomly rough surface,” J. Opt. Soc. Am. B 4, 910–926 (1987).
[CrossRef]

A. R. McGurn, A. A. Maradudin, V. Celli, “Localization effects in the scattering of light from a randomly rough grating,” Phys. Rev. B 31, 4866–4871 (1985).
[CrossRef]

V. Celli, A. A. Maradudin, A. M. Marvin, A. R. McGurn, “Some aspects of light scattering from a randomly rough metal surface,” J. Opt. Soc. Am. A 2, 2225–2239 (1985).
[CrossRef]

Méndez, E. R.

A. A. Maradudin, E. R. Méndez, “Enhanced backscattering of light from weakly rough, random metal surfaces,” Appl. Opt. 32, 3335–3343 (1993).
[CrossRef] [PubMed]

A. A. Maradudin, R. E. Luna, E. R. Méndez, “The Brewster effect for a one-dimensional random surface,” Waves Random Media 3, 51–60 (1993).
[CrossRef]

A. A. Maradudin, Jun Q. Lu, P. Tran, R. F. Wallis, V. Celli, Zu-Han Gu, A. R. McGurn, E. R. Méndez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 3, 343–397 (1992).

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (N.Y.) 203, 255–307 (1990).
[CrossRef]

A. A. Maradudin, E. R. Méndez, T. Michel, “Backscattering effects in the elastic scattering of p-polarized light from a large-amplitude random grating,” in Scattering in Volume and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (North-Holland, Amsterdam, 1990), pp. 157–174.

Michel, T.

A. A. Maradudin, Jun Q. Lu, P. Tran, R. F. Wallis, V. Celli, Zu-Han Gu, A. R. McGurn, E. R. Méndez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 3, 343–397 (1992).

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (N.Y.) 203, 255–307 (1990).
[CrossRef]

A. A. Maradudin, T. Michel, “The transverse correlation length for randomly rough surfaces,” J. Stat. Phys. 58, 485–501 (1990).
[CrossRef]

A. A. Maradudin, E. R. Méndez, T. Michel, “Backscattering effects in the elastic scattering of p-polarized light from a large-amplitude random grating,” in Scattering in Volume and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (North-Holland, Amsterdam, 1990), pp. 157–174.

Michel, T. R.

Mills, D. L.

N. E. Class, M. Weber, D. L. Mills, “Attenuation and dispersion of surface polaritons on gratings,” Phys. Rev. B 29, 6548–6559 (1984).
[CrossRef]

B. Laks, D. L. Mills, A. A. Maradudin, “Surface polaritons on large amplitude gratings,” Phys. Rev. B 23, 4965–4975 (1981).
[CrossRef]

Nieto-Vesperinas, M.

J. A. Sánchez-Gil, M. Nieto-Vesperinas, “Resonance effects in multiple scattering from statistically rough metallic surfaces,” Phys. Rev. B 45, 8623–8633 (1992).
[CrossRef]

A. A. Maradudin, Jun Q. Lu, P. Tran, R. F. Wallis, V. Celli, Zu-Han Gu, A. R. McGurn, E. R. Méndez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 3, 343–397 (1992).

J. M. Soto-Crespo, M. Nieto-Vesperinas, A. T. Friberg, “Scattering from slightly rough random surfaces: a detailed study on the validity of the small perturbation method,” J. Opt. Soc. Am. A 7, 1185–1201 (1990).
[CrossRef]

O’Donnell, K. A.

Perkins, J. S.

D. H. Berman, J. S. Perkins, “Rayleigh method for scattering from random and deterministic interfaces,” J. Acoust. Soc. Am. 88, 1032–1044 (1990).
[CrossRef]

Raether, H.

For a review, see H. Raether, Surface Plasmons on Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).

Saillard, M.

M. Saillard, “Anderson localization for electromagnetic surface waves,” Opt. Commun. 96, 1–7 (1993).
[CrossRef]

Salliard, M.

Sánchez-Gil, J. A.

J. A. Sánchez-Gil, M. Nieto-Vesperinas, “Resonance effects in multiple scattering from statistically rough metallic surfaces,” Phys. Rev. B 45, 8623–8633 (1992).
[CrossRef]

Sant, A. J.

A. A. Maradudin, Jun Q. Lu, P. Tran, R. F. Wallis, V. Celli, Zu-Han Gu, A. R. McGurn, E. R. Méndez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 3, 343–397 (1992).

Sari, S. O.

S. O. Sari, D. K. Cohen, K. D. Scherkoske, “Study of surface plasma-wave reflectance and roughness-induced scattering in silver foils,” Phys. Rev. B 21, 2162–2174 (1980).
[CrossRef]

Scherkoske, K. D.

S. O. Sari, D. K. Cohen, K. D. Scherkoske, “Study of surface plasma-wave reflectance and roughness-induced scattering in silver foils,” Phys. Rev. B 21, 2162–2174 (1980).
[CrossRef]

Simon, J. M.

J. M. Simon, S. A. Ledesma, “Diffuse light bands from diffraction gratings: a correlation study,” Optik (Stuttgart) 89, 145–150 (1992).

Solimeno, S.

S. Solimeno, B. Crosignani, P. DiPorto, Guiding, Diffraction, and Confinement of Optical Radiation (Academic, Orlando, Fla.1986), p. 210.

Soto-Crespo, J. M.

Toigo, F.

F. Toigo, A. Marvin, V. Celli, N. R. Hill, “Optical properties of rough surfaces: general theory and the small roughness limit,” Phys. Rev. B 15, 5618–5626 (1977).
[CrossRef]

Tran, P.

A. A. Maradudin, Jun Q. Lu, P. Tran, R. F. Wallis, V. Celli, Zu-Han Gu, A. R. McGurn, E. R. Méndez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 3, 343–397 (1992).

P. Tran, V. Celli, “Monte Carlo calculation of backscattering enhancement for a randomly rough grating,” J. Opt. Soc. Am. A 5, 1635–1637 (1988).
[CrossRef]

Wallis, R. F.

A. A. Maradudin, Jun Q. Lu, P. Tran, R. F. Wallis, V. Celli, Zu-Han Gu, A. R. McGurn, E. R. Méndez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 3, 343–397 (1992).

Weber, M.

N. E. Class, M. Weber, D. L. Mills, “Attenuation and dispersion of surface polaritons on gratings,” Phys. Rev. B 29, 6548–6559 (1984).
[CrossRef]

Yndurain, F. J.

C. Lopez, F. J. Yndurain, N. Garcia, “Iterative series for calculating the scattering of waves from a hard corrugated surface,” Phys. Rev. B 18, 970–972 (1978).
[CrossRef]

Ann. Phys. (N.Y.) (1)

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (N.Y.) 203, 255–307 (1990).
[CrossRef]

Appl. Opt. (2)

IEEE Trans. Antennas Propag. (1)

G. S. Brown, “A stochastic Fourier transform approach to scattering from perfectly conducting randomly rough surfaces,” IEEE Trans. Antennas Propag. AP-30, 1135–1144 (1982).
[CrossRef]

J. Acoust. Soc. Am. (1)

D. H. Berman, J. S. Perkins, “Rayleigh method for scattering from random and deterministic interfaces,” J. Acoust. Soc. Am. 88, 1032–1044 (1990).
[CrossRef]

J. Mod. Opt. (2)

R. A. Depine, V. L. Brudny, “Speckle patterns generated by rough surfaces with a periodic component,” J. Mod. Opt. 38, 2281–2293 (1991).
[CrossRef]

V. L. Brudny, R. A. Depine, “Speckle pattern intensification in highly conducting microrough gratings,” J. Mod. Opt. 40, 427–439 (1993).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (5)

J. Opt. Soc. Am. B (1)

J. Stat. Phys. (1)

A. A. Maradudin, T. Michel, “The transverse correlation length for randomly rough surfaces,” J. Stat. Phys. 58, 485–501 (1990).
[CrossRef]

Opt. Acta (1)

M. C. Hutley, V. M. Bird, “A detailed experimental study of the anomalies of a sinusoidal diffraction grating,” Opt. Acta 20, 771–782 (1973).
[CrossRef]

Opt. Commun. (2)

M. C. Hutley, D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun. 19, 431–436 (1976).
[CrossRef]

M. Saillard, “Anderson localization for electromagnetic surface waves,” Opt. Commun. 96, 1–7 (1993).
[CrossRef]

Optik (Stuttgart) (1)

J. M. Simon, S. A. Ledesma, “Diffuse light bands from diffraction gratings: a correlation study,” Optik (Stuttgart) 89, 145–150 (1992).

Phys. Rev. B (9)

N. R. Hill, V. Celli, “Limits of convergence of the Rayleigh method for surface scattering,” Phys. Rev. B 17, 2478–2481 (1978).
[CrossRef]

C. Lopez, F. J. Yndurain, N. Garcia, “Iterative series for calculating the scattering of waves from a hard corrugated surface,” Phys. Rev. B 18, 970–972 (1978).
[CrossRef]

B. Laks, D. L. Mills, A. A. Maradudin, “Surface polaritons on large amplitude gratings,” Phys. Rev. B 23, 4965–4975 (1981).
[CrossRef]

N. E. Class, M. Weber, D. L. Mills, “Attenuation and dispersion of surface polaritons on gratings,” Phys. Rev. B 29, 6548–6559 (1984).
[CrossRef]

S. O. Sari, D. K. Cohen, K. D. Scherkoske, “Study of surface plasma-wave reflectance and roughness-induced scattering in silver foils,” Phys. Rev. B 21, 2162–2174 (1980).
[CrossRef]

J. A. Sánchez-Gil, M. Nieto-Vesperinas, “Resonance effects in multiple scattering from statistically rough metallic surfaces,” Phys. Rev. B 45, 8623–8633 (1992).
[CrossRef]

G. Brown, V. Celli, H. Haller, A. A. Maradudin, A. Marvin, “Resonant light scattering from a randomly rough surface,” Phys. Rev. B 31, 4993–5005 (1985).
[CrossRef]

A. R. McGurn, A. A. Maradudin, V. Celli, “Localization effects in the scattering of light from a randomly rough grating,” Phys. Rev. B 31, 4866–4871 (1985).
[CrossRef]

F. Toigo, A. Marvin, V. Celli, N. R. Hill, “Optical properties of rough surfaces: general theory and the small roughness limit,” Phys. Rev. B 15, 5618–5626 (1977).
[CrossRef]

Rev. Mex. Fis. (1)

A. A. Maradudin, Jun Q. Lu, P. Tran, R. F. Wallis, V. Celli, Zu-Han Gu, A. R. McGurn, E. R. Méndez, T. Michel, M. Nieto-Vesperinas, J. C. Dainty, A. J. Sant, “Enhanced backscattering from one- and two-dimensional random surfaces,” Rev. Mex. Fis. 3, 343–397 (1992).

Waves Random Media (1)

A. A. Maradudin, R. E. Luna, E. R. Méndez, “The Brewster effect for a one-dimensional random surface,” Waves Random Media 3, 51–60 (1993).
[CrossRef]

Other (7)

S. Solimeno, B. Crosignani, P. DiPorto, Guiding, Diffraction, and Confinement of Optical Radiation (Academic, Orlando, Fla.1986), p. 210.

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, New York, 1985),

A. A. Maradudin, “Electromagnetic surface excitations on rough surfaces,” in Electromagnetic Surface Excitation, R. F. Wallis, G. I. Stegeman, eds. (Springer-Verlag, New York, 1986), pp. 57–131.
[CrossRef]

D. Maystre, “Rigorous vector theories of diffraction gratings,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1976), Vol. 11, pp. 1–68.

For a review, see H. Raether, Surface Plasmons on Rough Surfaces and on Gratings (Springer-Verlag, Berlin, 1988).

A. A. Maradudin, E. R. Méndez, T. Michel, “Backscattering effects in the elastic scattering of p-polarized light from a large-amplitude random grating,” in Scattering in Volume and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (North-Holland, Amsterdam, 1990), pp. 157–174.

See, for example, D. Maystre, “General study of grating anomalies from electromagnetic surface modes,” in Electromagnetic Surface Modes, A. D. Boardman, ed. (Wiley, New York, 1982), pp. 661–724.

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Figures (12)

Fig. 1
Fig. 1

Intensities Ip(θs), Is(θs), and I+(θs) and the Stokes matrix elements S33(θs) and S34(θs) for +45° -polarized light incident upon a one-dimensional, randomly rough surface on silver. The parameters are λ = 0.4579 μm, θ0 = 20°, a = 0.1 μm, δ = 0.005 μm, = −7.5 + 0.24i, Np = 2000, Nx = 3000, Nk = 700, Δκ = 0.458 × 10−2, and M = 4. The solid curves are the leading-order terms from perturbation theory; these curves are indistinguishable from the numerical results for Is, S33, and S34. The dashed curve is the result for Ip according to the multiple-scattering theory of Ref. 5.

Fig. 2
Fig. 2

Same as Fig. 1 for the intensities Ip(θs), Is(θs), and I+(θs) but with δ = 0.016 μm. The computation parameters differing from those of Fig. 1 are Δκ = 0.602 × 10−2, M = 8, and Np = 1000.

Fig. 3
Fig. 3

Dependence of the intensity I+(θs) on the angle of incidence θ0 (0°, 20°, 40°, and 60°) for +45°-polarized light incident upon a one-dimensional, randomly rough surface on silver [Eq. (3.1)]. The parameters are a = 0.1 μm, δ = 0.016 μm, λ = 0.482 /μm, Np = 400, Nx = 2400, Nk = 700, Δκ = 0.635 × 10−2, and M = 8.

Fig. 4
Fig. 4

Dependence of the intensities Ip(θs), Is(θs), and I+(θs) on the correlation length a [(a) a = 0.1 μm, (b) a = 0.2 μm, and (c) a = 0.3 μm] for +45°-polarized incident light. The slope parameter is δ/a = 0.1 in all the cases. The incident wavelength is λ = 0.482 μm, and is given by Eq. (3.1). The parameters used in the computations are (a) Np = 1000, Nx = 2400, Nk = 700, Δκ = 0.689 × 10−2, and M = 6; (b) Np = 800, Nx = 2000, Nk = 700, Δκ = 0.548 × 10−2, and M = 10; and (c) Np = 420, Nx = 1000, Nk = 700, Δκ = 0.574 × 10−2, and M = 16.

Fig. 5
Fig. 5

Dependence of the intensity Ip(θs) on the wavelength λ for +45°-polarized light incident on a one-dimensional, randomly rough surface on silver [Eq. (3.1)]. The four wavelengths are A, λ = 0.547 μm; B, λ = 0.482 μm; C, λ = 0.449 μm; and D, λ = 0.386 μm. a = 0.1 μm and δ = 0.01 μm in all the cases. The computation parameters are A, Np = 1000, Nk = 800, and Δκ = 0.610 × 10−2; B, Np = 1000, Nk = 700, and Δκ = 0.689 × 10−2; C, Np = 860, Nk = 800, and Δκ = 0.749 × 10−2; D, Np = 1200, Nk = 800, and Δκ = 0.772 × 10−2; and in all the cases Nx = 2400 and M = 6.

Fig. 6
Fig. 6

Dependence on the angle of incidence θ0 of the coherent component Jν,coh and of the total diffuse component Jν (ν = p, s) of the p-polarized (open symbols) and of the s-polarized (filled symbols) intensities scattered from two different randomly rough surfaces on silver [Eq. (3.1)]. Both surfaces have a = 0.1 μm, and the roughnesses are δ = 0.01 μm (circles) and δ = 0.016 μm (squares). The parameters are λ = 0.547 μm, Np = 180, Nk = 800, Δκ = 0.610 × 10−2, Nx = 2400, and M = 6. Averages are taken over different sets of independent surface realizations at angles θ0 separated by 1°. The dashed curves are the leading terms from perturbation theory for the coherent component Jν,coh (symbols) and for the Fresnel reflection coefficients (no symbols).

Fig. 7
Fig. 7

Dispersion curve for surface polaritons propagating on a sinusoidal grating h cos(2πx1/b) on silver [Eq. (3.1)]. The period is b = 0.2 μm, and the amplitude is h = 0.1 μm. Nk = 13 momentum values were kept in the calculation. The upper (lower) right-hand curve gives the values of Ki corresponding to the upper (lower) branch of the dispersion curve.

Fig. 8
Fig. 8

For the same random component of the roughness and for three of the wavelengths used in Fig. 5 the intensity IP(θS) when a sinusoidal grating h cos(2πx1/b) is added to the surface profile (b = 0.2 μm and h = 0.1 μm). The wavelengths are B, λ= 0.482 μm; C, λ = 0.449 μm; and D, λ = 0.386 μm. The computation parameters are B, Np = 1460; Nk = 700, and Δκ= 0.893 ×10−2; C, Np = 940; Nk = 800, and Δκ = 0.899 × 10−2; and D, Np = 1000; Nk = 800, and Δκ = 0.919 × 10−2; and in all the cases Nx = 2400 and M = 6.

Fig. 9
Fig. 9

Dependence of Ip(θs) on the angle of incidence for a height of the random roughness on the periodic grating ten times smaller than that in curve D of Fig. 8. The parameters describing the surface are a = 0.1 μm, δ = 0.001 μm, b = 0.2 μm, and h = 0.1μm. The wavelength is λ = 0.386 μm. The angles of incidence are θ1 = 20°, θ2 = 37°, and θ3 = 60°. The top figure presents the results of the numerical simulations: Nk = 700, Δκ = 0.919 ×10−2, Nx = 2000, M = 4, and (θ1) Np = 470, (θ2) Np = 520, and (θ3) Np = 430. The bottom figure presents the leading-order term in an expansion of Ip in powers of the roughness δ; the dashed curve is for θ3.

Fig. 10
Fig. 10

Dependence on the angle of incidence θ0 of the coherent component Jp, coh and of the total diffuse component Jp the p-polarized intensity scattered for three different random roughnesses on the surface of a periodic grating on silver [Eq. (3.1)]; Jp, tot is the total scattered intensity. The parameters are a = 0.1 μm, δ = 0.001 μm (squares), δ = 0.005 μm (circles), δ = 0.01 μm (triangles), b = 0.2 μm, h = 0.01 μm, λ = 0.386 μm, Np = 80, Nk = 800, Δκ = 0.610 × 10−2, Nx = 2400, and M = 6. Averages are taken over different sets of independent surface realizations at every angle θ0 separated by 1°.

Fig. 11
Fig. 11

Modulus squared of the scattering amplitude Rp evaluated in the evanescent channels and averaged over the ensemble of surface realizations, 〈|RP|2〉. The top figure corresponds to calculations presented in Figs. 1 and 2 (circles). The middle figure corresponds to Fig. 5. The bottom figure corresponds to Fig. 8.

Fig. 12
Fig. 12

For three of the cases considered in Fig. 5 (top figure) and in Fig. 8 (bottom figure) the normalized autocovariance function of the Poynting vector fluctuations Δ S 1 s p ( x 1 ) evaluated in the plane x3 = 4δ.

Equations (8)

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Φ ν , sc ( x 1 , x 3 ) = n = R n ν exp [ i ω c ( κ n x 1 + α n > x 3 ) ] ,
n = A m n ( α m < α n > ) ( κ m κ n + α m < α n > ) σ α m < α n > R n ν = A m ( α m < + α n > ) ( κ m κ 0 α m < α 0 > ) σ 2 ( α m < + α 0 > ) ,
A m ( α ) = 1 L L / 2 L / 2 d x 1 exp { i ω c [ m λ L x 1 + α ζ ( x 1 ) ] } .
ê n + = 1 2 ( ê n p + ê n s ) , ê n R = 1 2 ( ê n p i ê n s ) ,
ê n = 1 2 ( ê n p ê n s ) , ê n L = 1 2 ( ê n p + i ê n s ) .
n ν = α n > α 0 > | R n ν | 2 ,
I ν ( θ n ) = L cos θ n λ n ν = L cos 2 θ n λ cos θ 0 | R n ν | 2 ,
( ω ) = [ 1 1 ω ω p ( ω ω p + i γ ) ] .

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