Abstract

A perturbative expression up to fourth order in k0σ (k0 = 2π/λ; σ being the rms of the surface height and λ the wavelength) has been obtained for the mean diffuse intensity from a one-dimensional random rough surface that has normal statistics and a Gaussian correlation function for s polarization. For p polarization it is not possible to obtain this expression because of the existence of certain resonances; thus the calculations must be restricted to second order in k0σ. Perturbative calculations were derived from the Rayleigh hypothesis and also from the extinction theorem. The expression for the diffuse component of the mean scattered intensity was the same for p waves in both cases up to second order in k0σ. For s waves the equality was obtained up to fourth order in k0σ. Comparisons with exact numerical results and with those obtained by using the Kirchhoff approximation are made. This comparison allows us to establish assessments on the validity of the perturbative solution and to obtain some new interesting facts. In addition, the behavior of the diffuse halo at small σ/λ as a function of the correlation length T, the angle of incidence θ0, and the polarization is discussed. The validity of the Rayleigh hypothesis is also studied.

© 1990 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. G. Bass, I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, Oxford, 1979).
  2. G. S. Brown, “A comparison of approximate theories for scattering from rough surfaces,” Wave Motion 7, 195–205 (1985).
    [CrossRef]
  3. J. A. de Santo, G. S. Brown, “Analytical techniques for multiple scattering from rough surfaces,” in Progress in Optics XXIII, E. Wolf, ed. (North-Holland, Amsterdam, 1986), pp. 3–62.
  4. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, New York, 1963).
  5. S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces,” Commun. Pure Appl. Math. 4, 351–378 (1951).
    [CrossRef]
  6. M. Nieto-Vesperinas, “Depolarization of EM waves scattered from slightly rough random surfaces: a study by means of the extinction theorem,” J. Opt. Soc. Am. 72, 539–547 (1982).
    [CrossRef]
  7. G. R. Valenzuela, “Depolarization of EM waves by slightly rough surfaces,” IEEE Trans. Antennas Propag. AP-15, 552–557 (1967).
    [CrossRef]
  8. G. S. Agarwal, “Interaction of electromagnetic waves at rough dielectric surfaces,” Phys. Rev. B 15, 2371–2383 (1977).
    [CrossRef]
  9. 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]
  10. R. Schiffer, “Reflectivity of a slightly rough surfaces,” Appl. Opt. 26, 704–712 (1987).
    [CrossRef] [PubMed]
  11. N. García, V. Celli, M. Nieto-Vesperinas, “Exact multiple scattering of waves from random rough surfaces,” Opt. Commun. 30, 279–281 (1979).
    [CrossRef]
  12. M. Nieto-Vesperinas, N. García, “A detailed study of the scattering of scalar waves from random rough surfaces,” Opt. Acta 28, 1651–1672 (1981).
    [CrossRef]
  13. M. G. Kendall, A. Stuart, The Advanced Theory of Statistics (Hafner, New York, 1963).
  14. J. Shen, A. A. Maradudin, “Multiple scattering of waves from random rough surfaces,” Phys. Rev. B 22, 4234–4240 (1980).
    [CrossRef]
  15. D. P. Winebrener, A. Ishimaru, “Investigation of a surface field phase-perturbation technique for scattering from rough surfaces,” Radio. Sci. 20, 161–170 (1985).
    [CrossRef]
  16. D. P. Winebrener, A. Ishimaru, “Application of the phase-perturbation technique to randomly rough surfaces,” J. Opt. Soc. Am. A 2, 2285–2293 (1985).
    [CrossRef]
  17. C. Eftimiu, G. V. Welland, “The use of Padé approximants in rough surface scattering,” IEEE Trans. Antennas Propag. AP-35, 721–727 (1987).
    [CrossRef]
  18. M. Nieto-Vesperinas, J. M. Soto-Crespo, “Monte Carlo simulations for scattering of electromagnetic waves from perfectly conductive random rough surfaces,” Opt. Lett. 12, 979–981 (1987).
    [CrossRef] [PubMed]
  19. E. I. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 83, 78–92 (1988).
    [CrossRef]
  20. J. M. Soto-Crespo, M. Nieto-Vesperinas, “Electromagnetic scattering from very rough random surfaces and deep reflection gratings,” J. Opt. Soc. Am. A 6, 367–384 (1989).
    [CrossRef]
  21. A. A. Maradudin, E. R. Méndez, T. Michel, “Backscattering effects in the elastic scattering of p-polarized light from a large-amplitude random metallic grating,” Opt. Lett. 14, 151–153 (1989).
    [CrossRef] [PubMed]
  22. J. C. Leader, “The relationship between the Kirchhoff approach and small perturbation analysis in rough surface scattering theory,” IEEE Trans. Antennas Propag. AP-19, 786–788 (1981).
  23. G. R. Valenzuela, J. W. Wright, J. C. Leader, “Comments on the relationship between the Kirchhoff approach and small perturbation analysis in rough surface scattering theory,” IEEE Trans. Antennas Propag. AP-20, 536–539 (1972).
    [CrossRef]
  24. D. Holliday, “Resolution of a controversy surrounding the Kirchhoff approach and the small perturbation method in rough surface scattering theory,” IEEE Trans. Antennas Propag. AP-35, 120–122 (1987).
    [CrossRef]
  25. M. Nieto-Vesperinas, “Radiometry of rough surfaces,” Opt. Acta 29, 961–971 (1982).
    [CrossRef]
  26. V. M. Agranovich, D. L. Mills, eds., Surface Polaritons (North-Holland, Amsterdam, 1982).
  27. H. Raether, Surface Plasmons (Springer-Verlag, Berlin, 1988).
  28. 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]
  29. P. Tran, V. Celli, “Monte Carlo calculations of backscattering enhancement for a randomly rough grating,” J. Opt. Soc. Am. A 5, 1635–1637 (1988).
    [CrossRef]
  30. N. García, E. Stoll, “Monte Carlo calculation for electromagnetic-wave scattering from random rough surfaces,” Phys. Rev. Lett. 52, 1798–1801 (1984).
    [CrossRef]
  31. B. A. Lippmann, “Note on the theory of gratings,” J. Opt. Soc. Am. 43, 408–409 (1953).
    [CrossRef]
  32. J. L. Urestky, “The scattering of plane waves from periodic surfaces,” Ann. Phys. (NY) 33, 400–427 (1965).
    [CrossRef]
  33. R. Petit, M. Cadilhac, “Sur la diffraction d’une onde plane par un réseau infinement conducteur. Note,” C. R. Acad. Sci. B 262, 468–471 (1966).
  34. R. F. Millar, “On the Rayleigh assumption in scattering by a periodic surface,” Proc. Cambridge Philos. Soc. 65, 773–791 (1969).
    [CrossRef]
  35. R. F. Millar, “On the Rayleigh assumption in scattering by a periodic surface. II,” Proc. Cambridge Philos. Soc. 69, 217–224 (1971).
    [CrossRef]
  36. 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).
    [CrossRef]
  37. J. P. Rossi, D. Maystre, “Rigorous numerical study of speckle patterns for two dimensional, random microrough surfaces,” Opt. Eng. 25, 613–617 (1986).
    [CrossRef]
  38. A. Wirgin, “On Rayleigh’s theory of sinusoidal gratings,” Opt. Acta 27, 1671–1692 (1980).
    [CrossRef]
  39. A. Wirgin, “Scattering from sinusoidal gratings: an evaluation of the Kirchhoff approximation,” J. Opt.Soc. Am. 73, 1028–1041 (1983).
    [CrossRef]
  40. N. García, J. Ibañez, J. Solana, N. Cabrera, “On the ‘quantum rainbow’ in surface scattering,” Solid State Commun. 20, 1159–1163 (1976).
    [CrossRef]
  41. N. García, “The scattering of He atoms from a hard corrugated surface model using the GR method. I.” J. Chem. Phys. 67, 897–916 (1977).
    [CrossRef]
  42. N. García, N. Cabrera, “New methods for solving the scattering of waves from a periodic hard surface: solutions and numerical comparisons with the various formalisms,” Phys. Rev. B 18, 576–589 (1978).
    [CrossRef]
  43. A. Erdélyi, Asymptotic Expansions (Dover, New York, 1956), p. 11.
  44. E. T. Whittaker, G. N. Watson, A Course of Modern Analysis (Cambridge U. Press, London, 1973), pp. 150–159.
  45. J. A. Kong, Electromagnetic Wave Theory (Wiley, New York, 1986), p. 307.
  46. M. F. Chen, A. K. Fung, “A numerical study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models,” Radio Sci. 23, 163–170 (1988).
    [CrossRef]
  47. E. I. Thorsos, D. R. Jackson, “The validity of the pertubative approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 86, 261–277 (1989).
    [CrossRef]
  48. P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Vol. 1, p. 811.

1989

1988

M. F. Chen, A. K. Fung, “A numerical study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models,” Radio Sci. 23, 163–170 (1988).
[CrossRef]

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

E. I. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 83, 78–92 (1988).
[CrossRef]

1987

M. Nieto-Vesperinas, J. M. Soto-Crespo, “Monte Carlo simulations for scattering of electromagnetic waves from perfectly conductive random rough surfaces,” Opt. Lett. 12, 979–981 (1987).
[CrossRef] [PubMed]

R. Schiffer, “Reflectivity of a slightly rough surfaces,” Appl. Opt. 26, 704–712 (1987).
[CrossRef] [PubMed]

C. Eftimiu, G. V. Welland, “The use of Padé approximants in rough surface scattering,” IEEE Trans. Antennas Propag. AP-35, 721–727 (1987).
[CrossRef]

D. Holliday, “Resolution of a controversy surrounding the Kirchhoff approach and the small perturbation method in rough surface scattering theory,” IEEE Trans. Antennas Propag. AP-35, 120–122 (1987).
[CrossRef]

1986

J. P. Rossi, D. Maystre, “Rigorous numerical study of speckle patterns for two dimensional, random microrough surfaces,” Opt. Eng. 25, 613–617 (1986).
[CrossRef]

1985

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]

D. P. Winebrener, A. Ishimaru, “Application of the phase-perturbation technique to randomly rough surfaces,” J. Opt. Soc. Am. A 2, 2285–2293 (1985).
[CrossRef]

D. P. Winebrener, A. Ishimaru, “Investigation of a surface field phase-perturbation technique for scattering from rough surfaces,” Radio. Sci. 20, 161–170 (1985).
[CrossRef]

G. S. Brown, “A comparison of approximate theories for scattering from rough surfaces,” Wave Motion 7, 195–205 (1985).
[CrossRef]

1984

N. García, E. Stoll, “Monte Carlo calculation for electromagnetic-wave scattering from random rough surfaces,” Phys. Rev. Lett. 52, 1798–1801 (1984).
[CrossRef]

1983

A. Wirgin, “Scattering from sinusoidal gratings: an evaluation of the Kirchhoff approximation,” J. Opt.Soc. Am. 73, 1028–1041 (1983).
[CrossRef]

1982

1981

J. C. Leader, “The relationship between the Kirchhoff approach and small perturbation analysis in rough surface scattering theory,” IEEE Trans. Antennas Propag. AP-19, 786–788 (1981).

M. Nieto-Vesperinas, N. García, “A detailed study of the scattering of scalar waves from random rough surfaces,” Opt. Acta 28, 1651–1672 (1981).
[CrossRef]

1980

J. Shen, A. A. Maradudin, “Multiple scattering of waves from random rough surfaces,” Phys. Rev. B 22, 4234–4240 (1980).
[CrossRef]

A. Wirgin, “On Rayleigh’s theory of sinusoidal gratings,” Opt. Acta 27, 1671–1692 (1980).
[CrossRef]

1979

N. García, V. Celli, M. Nieto-Vesperinas, “Exact multiple scattering of waves from random rough surfaces,” Opt. Commun. 30, 279–281 (1979).
[CrossRef]

1978

N. García, N. Cabrera, “New methods for solving the scattering of waves from a periodic hard surface: solutions and numerical comparisons with the various formalisms,” Phys. Rev. B 18, 576–589 (1978).
[CrossRef]

1977

N. García, “The scattering of He atoms from a hard corrugated surface model using the GR method. I.” J. Chem. Phys. 67, 897–916 (1977).
[CrossRef]

G. S. Agarwal, “Interaction of electromagnetic waves at rough dielectric surfaces,” Phys. Rev. B 15, 2371–2383 (1977).
[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]

1976

N. García, J. Ibañez, J. Solana, N. Cabrera, “On the ‘quantum rainbow’ in surface scattering,” Solid State Commun. 20, 1159–1163 (1976).
[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).
[CrossRef]

1972

G. R. Valenzuela, J. W. Wright, J. C. Leader, “Comments on the relationship between the Kirchhoff approach and small perturbation analysis in rough surface scattering theory,” IEEE Trans. Antennas Propag. AP-20, 536–539 (1972).
[CrossRef]

1971

R. F. Millar, “On the Rayleigh assumption in scattering by a periodic surface. II,” Proc. Cambridge Philos. Soc. 69, 217–224 (1971).
[CrossRef]

1969

R. F. Millar, “On the Rayleigh assumption in scattering by a periodic surface,” Proc. Cambridge Philos. Soc. 65, 773–791 (1969).
[CrossRef]

1967

G. R. Valenzuela, “Depolarization of EM waves by slightly rough surfaces,” IEEE Trans. Antennas Propag. AP-15, 552–557 (1967).
[CrossRef]

1966

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

1965

J. L. Urestky, “The scattering of plane waves from periodic surfaces,” Ann. Phys. (NY) 33, 400–427 (1965).
[CrossRef]

1953

1951

S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces,” Commun. Pure Appl. Math. 4, 351–378 (1951).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal, “Interaction of electromagnetic waves at rough dielectric surfaces,” Phys. Rev. B 15, 2371–2383 (1977).
[CrossRef]

Bass, F. G.

F. G. Bass, I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, Oxford, 1979).

Beckmann, P.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, New York, 1963).

Brown, G. S.

G. S. Brown, “A comparison of approximate theories for scattering from rough surfaces,” Wave Motion 7, 195–205 (1985).
[CrossRef]

J. A. de Santo, G. S. Brown, “Analytical techniques for multiple scattering from rough surfaces,” in Progress in Optics XXIII, E. Wolf, ed. (North-Holland, Amsterdam, 1986), pp. 3–62.

Cabrera, N.

N. García, N. Cabrera, “New methods for solving the scattering of waves from a periodic hard surface: solutions and numerical comparisons with the various formalisms,” Phys. Rev. B 18, 576–589 (1978).
[CrossRef]

N. García, J. Ibañez, J. Solana, N. Cabrera, “On the ‘quantum rainbow’ in surface scattering,” Solid State Commun. 20, 1159–1163 (1976).
[CrossRef]

Cadilhac, M.

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

Celli, V.

P. Tran, V. Celli, “Monte Carlo calculations of backscattering enhancement for a randomly rough grating,” J. Opt. Soc. Am. A 5, 1635–1637 (1988).
[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. García, V. Celli, M. Nieto-Vesperinas, “Exact multiple scattering of waves from random rough surfaces,” Opt. Commun. 30, 279–281 (1979).
[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]

Chen, M. F.

M. F. Chen, A. K. Fung, “A numerical study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models,” Radio Sci. 23, 163–170 (1988).
[CrossRef]

de Santo, J. A.

J. A. de Santo, G. S. Brown, “Analytical techniques for multiple scattering from rough surfaces,” in Progress in Optics XXIII, E. Wolf, ed. (North-Holland, Amsterdam, 1986), pp. 3–62.

Eftimiu, C.

C. Eftimiu, G. V. Welland, “The use of Padé approximants in rough surface scattering,” IEEE Trans. Antennas Propag. AP-35, 721–727 (1987).
[CrossRef]

Erdélyi, A.

A. Erdélyi, Asymptotic Expansions (Dover, New York, 1956), p. 11.

Feshbach, H.

P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Vol. 1, p. 811.

Fuks, I. M.

F. G. Bass, I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, Oxford, 1979).

Fung, A. K.

M. F. Chen, A. K. Fung, “A numerical study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models,” Radio Sci. 23, 163–170 (1988).
[CrossRef]

García, N.

N. García, E. Stoll, “Monte Carlo calculation for electromagnetic-wave scattering from random rough surfaces,” Phys. Rev. Lett. 52, 1798–1801 (1984).
[CrossRef]

M. Nieto-Vesperinas, N. García, “A detailed study of the scattering of scalar waves from random rough surfaces,” Opt. Acta 28, 1651–1672 (1981).
[CrossRef]

N. García, V. Celli, M. Nieto-Vesperinas, “Exact multiple scattering of waves from random rough surfaces,” Opt. Commun. 30, 279–281 (1979).
[CrossRef]

N. García, N. Cabrera, “New methods for solving the scattering of waves from a periodic hard surface: solutions and numerical comparisons with the various formalisms,” Phys. Rev. B 18, 576–589 (1978).
[CrossRef]

N. García, “The scattering of He atoms from a hard corrugated surface model using the GR method. I.” J. Chem. Phys. 67, 897–916 (1977).
[CrossRef]

N. García, J. Ibañez, J. Solana, N. Cabrera, “On the ‘quantum rainbow’ in surface scattering,” Solid State Commun. 20, 1159–1163 (1976).
[CrossRef]

Hill, N. R.

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]

Holliday, D.

D. Holliday, “Resolution of a controversy surrounding the Kirchhoff approach and the small perturbation method in rough surface scattering theory,” IEEE Trans. Antennas Propag. AP-35, 120–122 (1987).
[CrossRef]

Ibañez, J.

N. García, J. Ibañez, J. Solana, N. Cabrera, “On the ‘quantum rainbow’ in surface scattering,” Solid State Commun. 20, 1159–1163 (1976).
[CrossRef]

Ishimaru, A.

D. P. Winebrener, A. Ishimaru, “Investigation of a surface field phase-perturbation technique for scattering from rough surfaces,” Radio. Sci. 20, 161–170 (1985).
[CrossRef]

D. P. Winebrener, A. Ishimaru, “Application of the phase-perturbation technique to randomly rough surfaces,” J. Opt. Soc. Am. A 2, 2285–2293 (1985).
[CrossRef]

Jackson, D. R.

E. I. Thorsos, D. R. Jackson, “The validity of the pertubative approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 86, 261–277 (1989).
[CrossRef]

Kendall, M. G.

M. G. Kendall, A. Stuart, The Advanced Theory of Statistics (Hafner, New York, 1963).

Kong, J. A.

J. A. Kong, Electromagnetic Wave Theory (Wiley, New York, 1986), p. 307.

Leader, J. C.

J. C. Leader, “The relationship between the Kirchhoff approach and small perturbation analysis in rough surface scattering theory,” IEEE Trans. Antennas Propag. AP-19, 786–788 (1981).

G. R. Valenzuela, J. W. Wright, J. C. Leader, “Comments on the relationship between the Kirchhoff approach and small perturbation analysis in rough surface scattering theory,” IEEE Trans. Antennas Propag. AP-20, 536–539 (1972).
[CrossRef]

Lippmann, B. A.

Maradudin, A. A.

Marvin, A.

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.

J. P. Rossi, D. Maystre, “Rigorous numerical study of speckle patterns for two dimensional, random microrough surfaces,” Opt. Eng. 25, 613–617 (1986).
[CrossRef]

McGurn, A. R.

Méndez, E. R.

Michel, T.

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).
[CrossRef]

R. F. Millar, “On the Rayleigh assumption in scattering by a periodic surface. II,” Proc. Cambridge Philos. Soc. 69, 217–224 (1971).
[CrossRef]

R. F. Millar, “On the Rayleigh assumption in scattering by a periodic surface,” Proc. Cambridge Philos. Soc. 65, 773–791 (1969).
[CrossRef]

Morse, P. M.

P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Vol. 1, p. 811.

Nieto-Vesperinas, M.

Petit, R.

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

Raether, H.

H. Raether, Surface Plasmons (Springer-Verlag, Berlin, 1988).

Rice, S. O.

S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces,” Commun. Pure Appl. Math. 4, 351–378 (1951).
[CrossRef]

Rossi, J. P.

J. P. Rossi, D. Maystre, “Rigorous numerical study of speckle patterns for two dimensional, random microrough surfaces,” Opt. Eng. 25, 613–617 (1986).
[CrossRef]

Schiffer, R.

Shen, J.

J. Shen, A. A. Maradudin, “Multiple scattering of waves from random rough surfaces,” Phys. Rev. B 22, 4234–4240 (1980).
[CrossRef]

Solana, J.

N. García, J. Ibañez, J. Solana, N. Cabrera, “On the ‘quantum rainbow’ in surface scattering,” Solid State Commun. 20, 1159–1163 (1976).
[CrossRef]

Soto-Crespo, J. M.

Spizzichino, A.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, New York, 1963).

Stoll, E.

N. García, E. Stoll, “Monte Carlo calculation for electromagnetic-wave scattering from random rough surfaces,” Phys. Rev. Lett. 52, 1798–1801 (1984).
[CrossRef]

Stuart, A.

M. G. Kendall, A. Stuart, The Advanced Theory of Statistics (Hafner, New York, 1963).

Thorsos, E. I.

E. I. Thorsos, D. R. Jackson, “The validity of the pertubative approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 86, 261–277 (1989).
[CrossRef]

E. I. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 83, 78–92 (1988).
[CrossRef]

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.

Urestky, J. L.

J. L. Urestky, “The scattering of plane waves from periodic surfaces,” Ann. Phys. (NY) 33, 400–427 (1965).
[CrossRef]

Valenzuela, G. R.

G. R. Valenzuela, J. W. Wright, J. C. Leader, “Comments on the relationship between the Kirchhoff approach and small perturbation analysis in rough surface scattering theory,” IEEE Trans. Antennas Propag. AP-20, 536–539 (1972).
[CrossRef]

G. R. Valenzuela, “Depolarization of EM waves by slightly rough surfaces,” IEEE Trans. Antennas Propag. AP-15, 552–557 (1967).
[CrossRef]

Watson, G. N.

E. T. Whittaker, G. N. Watson, A Course of Modern Analysis (Cambridge U. Press, London, 1973), pp. 150–159.

Welland, G. V.

C. Eftimiu, G. V. Welland, “The use of Padé approximants in rough surface scattering,” IEEE Trans. Antennas Propag. AP-35, 721–727 (1987).
[CrossRef]

Whittaker, E. T.

E. T. Whittaker, G. N. Watson, A Course of Modern Analysis (Cambridge U. Press, London, 1973), pp. 150–159.

Winebrener, D. P.

D. P. Winebrener, A. Ishimaru, “Investigation of a surface field phase-perturbation technique for scattering from rough surfaces,” Radio. Sci. 20, 161–170 (1985).
[CrossRef]

D. P. Winebrener, A. Ishimaru, “Application of the phase-perturbation technique to randomly rough surfaces,” J. Opt. Soc. Am. A 2, 2285–2293 (1985).
[CrossRef]

Wirgin, A.

A. Wirgin, “Scattering from sinusoidal gratings: an evaluation of the Kirchhoff approximation,” J. Opt.Soc. Am. 73, 1028–1041 (1983).
[CrossRef]

A. Wirgin, “On Rayleigh’s theory of sinusoidal gratings,” Opt. Acta 27, 1671–1692 (1980).
[CrossRef]

Wright, J. W.

G. R. Valenzuela, J. W. Wright, J. C. Leader, “Comments on the relationship between the Kirchhoff approach and small perturbation analysis in rough surface scattering theory,” IEEE Trans. Antennas Propag. AP-20, 536–539 (1972).
[CrossRef]

Ann. Phys. (NY)

J. L. Urestky, “The scattering of plane waves from periodic surfaces,” Ann. Phys. (NY) 33, 400–427 (1965).
[CrossRef]

Appl. Opt.

C. R. Acad. Sci. B

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

Commun. Pure Appl. Math.

S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces,” Commun. Pure Appl. Math. 4, 351–378 (1951).
[CrossRef]

IEEE Trans. Antennas Propag.

G. R. Valenzuela, “Depolarization of EM waves by slightly rough surfaces,” IEEE Trans. Antennas Propag. AP-15, 552–557 (1967).
[CrossRef]

C. Eftimiu, G. V. Welland, “The use of Padé approximants in rough surface scattering,” IEEE Trans. Antennas Propag. AP-35, 721–727 (1987).
[CrossRef]

J. C. Leader, “The relationship between the Kirchhoff approach and small perturbation analysis in rough surface scattering theory,” IEEE Trans. Antennas Propag. AP-19, 786–788 (1981).

G. R. Valenzuela, J. W. Wright, J. C. Leader, “Comments on the relationship between the Kirchhoff approach and small perturbation analysis in rough surface scattering theory,” IEEE Trans. Antennas Propag. AP-20, 536–539 (1972).
[CrossRef]

D. Holliday, “Resolution of a controversy surrounding the Kirchhoff approach and the small perturbation method in rough surface scattering theory,” IEEE Trans. Antennas Propag. AP-35, 120–122 (1987).
[CrossRef]

J. Acoust. Soc. Am.

E. I. Thorsos, D. R. Jackson, “The validity of the pertubative approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 86, 261–277 (1989).
[CrossRef]

E. I. Thorsos, “The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum,” J. Acoust. Soc. Am. 83, 78–92 (1988).
[CrossRef]

J. Chem. Phys.

N. García, “The scattering of He atoms from a hard corrugated surface model using the GR method. I.” J. Chem. Phys. 67, 897–916 (1977).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Opt.Soc. Am.

A. Wirgin, “Scattering from sinusoidal gratings: an evaluation of the Kirchhoff approximation,” J. Opt.Soc. Am. 73, 1028–1041 (1983).
[CrossRef]

Opt. Acta

M. Nieto-Vesperinas, “Radiometry of rough surfaces,” Opt. Acta 29, 961–971 (1982).
[CrossRef]

A. Wirgin, “On Rayleigh’s theory of sinusoidal gratings,” Opt. Acta 27, 1671–1692 (1980).
[CrossRef]

M. Nieto-Vesperinas, N. García, “A detailed study of the scattering of scalar waves from random rough surfaces,” Opt. Acta 28, 1651–1672 (1981).
[CrossRef]

Opt. Commun.

N. García, V. Celli, M. Nieto-Vesperinas, “Exact multiple scattering of waves from random rough surfaces,” Opt. Commun. 30, 279–281 (1979).
[CrossRef]

Opt. Eng.

J. P. Rossi, D. Maystre, “Rigorous numerical study of speckle patterns for two dimensional, random microrough surfaces,” Opt. Eng. 25, 613–617 (1986).
[CrossRef]

Opt. Lett.

Phys. Rev. B

N. García, N. Cabrera, “New methods for solving the scattering of waves from a periodic hard surface: solutions and numerical comparisons with the various formalisms,” Phys. Rev. B 18, 576–589 (1978).
[CrossRef]

G. S. Agarwal, “Interaction of electromagnetic waves at rough dielectric surfaces,” Phys. Rev. B 15, 2371–2383 (1977).
[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]

J. Shen, A. A. Maradudin, “Multiple scattering of waves from random rough surfaces,” Phys. Rev. B 22, 4234–4240 (1980).
[CrossRef]

Phys. Rev. Lett.

N. García, E. Stoll, “Monte Carlo calculation for electromagnetic-wave scattering from random rough surfaces,” Phys. Rev. Lett. 52, 1798–1801 (1984).
[CrossRef]

Proc. Cambridge Philos. Soc.

R. F. Millar, “On the Rayleigh assumption in scattering by a periodic surface,” Proc. Cambridge Philos. Soc. 65, 773–791 (1969).
[CrossRef]

R. F. Millar, “On the Rayleigh assumption in scattering by a periodic surface. II,” Proc. Cambridge Philos. Soc. 69, 217–224 (1971).
[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).
[CrossRef]

M. F. Chen, A. K. Fung, “A numerical study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models,” Radio Sci. 23, 163–170 (1988).
[CrossRef]

Radio. Sci.

D. P. Winebrener, A. Ishimaru, “Investigation of a surface field phase-perturbation technique for scattering from rough surfaces,” Radio. Sci. 20, 161–170 (1985).
[CrossRef]

Solid State Commun.

N. García, J. Ibañez, J. Solana, N. Cabrera, “On the ‘quantum rainbow’ in surface scattering,” Solid State Commun. 20, 1159–1163 (1976).
[CrossRef]

Wave Motion

G. S. Brown, “A comparison of approximate theories for scattering from rough surfaces,” Wave Motion 7, 195–205 (1985).
[CrossRef]

Other

J. A. de Santo, G. S. Brown, “Analytical techniques for multiple scattering from rough surfaces,” in Progress in Optics XXIII, E. Wolf, ed. (North-Holland, Amsterdam, 1986), pp. 3–62.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, New York, 1963).

F. G. Bass, I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, Oxford, 1979).

M. G. Kendall, A. Stuart, The Advanced Theory of Statistics (Hafner, New York, 1963).

P. M. Morse, H. Feshbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Vol. 1, p. 811.

V. M. Agranovich, D. L. Mills, eds., Surface Polaritons (North-Holland, Amsterdam, 1982).

H. Raether, Surface Plasmons (Springer-Verlag, Berlin, 1988).

A. Erdélyi, Asymptotic Expansions (Dover, New York, 1956), p. 11.

E. T. Whittaker, G. N. Watson, A Course of Modern Analysis (Cambridge U. Press, London, 1973), pp. 150–159.

J. A. Kong, Electromagnetic Wave Theory (Wiley, New York, 1986), p. 307.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Metrics