Abstract

The scattering of linearly polarized electromagnetic waves incident from a dielectric from a rough surface separating the dielectric from a vacuum is studied by using the extinction theorem. The angular distributions of the ensemble average of intensity of the reflected and transmitted fields are calculated numerically for several values of the angle of incidence, the surface statistical parameters, and the dielectric permittivity. To determine the effect of the corrugation on the transmitted evanescent waves, we also obtain the angular spectrum of the transmitted field as a function of the momentum parallel to the surface in the nonradiative zone. The total mean reflected and transmitted energies (reflectance and transmittance), as well as their incoherent parts in the case of slight corrugations, are derived by integrating the angular intensity distribution over the angle of observation. This permits the analysis of the influence of the corrugation and of the phenomenon of total internal reflection within two different systems of surface correlation length T namely, for T larger and smaller than the wavelength. In particular, enhanced backscattering and forward transmission are predicted for surfaces with both T and the rms deviation greater σ than the wavelength of the incident light.

© 1992 Optical Society of America

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References

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  1. E. R. Méndez, K. A. O’Donnell, “Observation of depolarization and backscattering enhancement in light scattering from Gaussian random surfaces,” Opt. Commun. 61, 91–95 (1987).
    [CrossRef]
  2. K. A. O’Donnell, E. R. Méndez, “Experimental study of scattering from characterized random surfaces,” J. Opt. Soc. Am. A 4, 1194–1205 (1987).
    [CrossRef]
  3. A. J. Sant, J. C. Dainty, M. J. Kim, “Comparison of surface scattering between identical, randomly rough metal and dielectric diffusers,” Opt. Lett. 14, 1183–1185 (1989).
    [CrossRef] [PubMed]
  4. M.-J. Kim, J. C. Dainty, A. T. Friberg, A. J. Sant, “Experimental study of enhanced backscattering from one- and two-dimensional random rough surfaces,” J. Opt. Soc. Am. A 7, 569–577 (1990).
    [CrossRef]
  5. 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]
  6. 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]
  7. 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]
  8. 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]
  9. A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 203, 255–307 (1990).
    [CrossRef]
  10. M. Saillard, D. Maystre, “Scattering from metallic and dielectric surfaces,” J. Opt. Soc. Am. A 7, 982–990 (1990).
    [CrossRef]
  11. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Macmillan, New York, 1963).
  12. P. Beckmann, “Scattering of light by rough surfaces,” in Progress in Optics VI, E. Wolf, ed. (North Holland, Amsterdam, 1961), pp. 51–69.
  13. F. G. Bass, I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, Oxford1979).
  14. S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces,” Commun. Pure Appl. Math. 4, 4808–4816 (1951).
    [CrossRef]
  15. G. R. Valenzuela, “Depolarization of electromagnetic waves by slightly rough surfaces,”IEEE Trans. Antennas Propag. AP-15, 552–557 (1967).
    [CrossRef]
  16. V. Celli, A. Marvin, F. Toigo, “Light scattering from rough surfaces,” Phys. Rev. B 11, 1779–1786 (1975).
    [CrossRef]
  17. R. Toigo, A. Marvin, V. Celli, N. R. Hill, “Optical properties of rough surfaces: general theory and small roughness limit,” Phys. Rev. B 15, 5618–5626 (1977).
    [CrossRef]
  18. G. S. Agarwal, “Interaction of EM waves at rough dielectric surfaces,” Phys. Rev. B 15, 2371–2383 (1977).
    [CrossRef]
  19. N. Garcia, V. Celli, M. Nieto-Vesperinas, “Exact multiple scattering of waves from random rough surfaces,” Opt. Commun. 30, 279–281 (1979).
    [CrossRef]
  20. M. Nieto-Vesperinas, N. Garcia, “A detailed study of the scattering of a scalar wave from random rough surfaces,” Opt. Acta 28, 1651–1672 (1981).
    [CrossRef]
  21. M. Nieto-Vesperinas, “Depolarization of electromagnetic waves scattered from slightly rough random surfaces: a study by means of the extinction theorem,”J. Opt. Soc. Am. 72, 539–547 (1982).
    [CrossRef]
  22. J. Shen, A. A. Maradudin, “Multiple scattering of waves from random rough surfaces,” Phys. Rev. B 22, 4234–4240 (1980).
    [CrossRef]
  23. D. P. Winebrenner, I. Ishimaru, “Application of the phase perturbation technique to randomly rough surfaces,” J. Opt. Soc. Am. A 2, 2285–2294 (1985).
    [CrossRef]
  24. M. Nieto-Vesperinas, J. C. Dainty, eds., Scattering in Volumes and Surfaces (North Holland, Amsterdam, 1990).
  25. M. Nieto-Vesperinas, J. M. Soto-Crespo, “Light-diffracted intensities from very deep gratings,” Phys. Rev. B 38, 7250–7259 (1988).
    [CrossRef]
  26. M. Nieto-Vesperinas, J. M. Soto-Crespo, “Connection between blazes from gratings and enhancements from random rough surfaces,” Phys. Rev. B 39, 8193–8197 (1988).
    [CrossRef]
  27. A. R. McGurn, A. A. Maradudin, “An analogue of enhanced backscattering in the transmission of light through a thin film with a randomly rough surface,” Opt. Commun. 72, 279–285 (1989).
    [CrossRef]
  28. M. Nieto-Vesperinas, J. A. Sánchez-Gil, A. J. Sant, J. C. Dainty, “Light transmission from a randomly rough dielectric diffuser: theoretical and experimental results,” Opt. Lett. 15, 1261–1263 (1990).
    [CrossRef] [PubMed]
  29. 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 Volumes and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (North-Holland, Amsterdam, 1990), pp. 157–174.
  30. J. A. Sánchez-Gil, M. Nieto-Vesperinas, “Light scattering from random rough dielectric surfaces,” J. Opt. Soc. Am. A 8, 1270–1286 (1991).
    [CrossRef]
  31. D. N. Pattanayak, E. Wolf, “General form and a new interpretation of the Ewald-Oseen extinction theorem,” Opt. Commun. 6, 217–220 (1972).
    [CrossRef]
  32. V. D. Freylikher, Institute of Radiophysics, Kharkhov, USSR (personal communication, 1990).
  33. A. Banos, Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon, Oxford, 1966), Chap. 2.

1991 (1)

1990 (4)

1989 (4)

1988 (2)

M. Nieto-Vesperinas, J. M. Soto-Crespo, “Light-diffracted intensities from very deep gratings,” Phys. Rev. B 38, 7250–7259 (1988).
[CrossRef]

M. Nieto-Vesperinas, J. M. Soto-Crespo, “Connection between blazes from gratings and enhancements from random rough surfaces,” Phys. Rev. B 39, 8193–8197 (1988).
[CrossRef]

1987 (3)

1985 (2)

1982 (1)

1981 (1)

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

1980 (1)

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

1979 (1)

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

1977 (2)

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

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

1975 (1)

V. Celli, A. Marvin, F. Toigo, “Light scattering from rough surfaces,” Phys. Rev. B 11, 1779–1786 (1975).
[CrossRef]

1972 (1)

D. N. Pattanayak, E. Wolf, “General form and a new interpretation of the Ewald-Oseen extinction theorem,” Opt. Commun. 6, 217–220 (1972).
[CrossRef]

1967 (1)

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

1951 (1)

S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces,” Commun. Pure Appl. Math. 4, 4808–4816 (1951).
[CrossRef]

Agarwal, G. S.

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

Banos, A.

A. Banos, Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon, Oxford, 1966), Chap. 2.

Bass, F. G.

F. G. Bass, I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, Oxford1979).

Beckmann, P.

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

P. Beckmann, “Scattering of light by rough surfaces,” in Progress in Optics VI, E. Wolf, ed. (North Holland, Amsterdam, 1961), pp. 51–69.

Celli, V.

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

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

V. Celli, A. Marvin, F. Toigo, “Light scattering from rough surfaces,” Phys. Rev. B 11, 1779–1786 (1975).
[CrossRef]

Dainty, J. C.

Freylikher, V. D.

V. D. Freylikher, Institute of Radiophysics, Kharkhov, USSR (personal communication, 1990).

Friberg, A. T.

Fuks, I. M.

F. G. Bass, I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, Oxford1979).

Garcia, N.

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

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

Hill, N. R.

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

Ishimaru, I.

Kim, M. J.

Kim, M.-J.

Maradudin, A. A.

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

A. R. McGurn, A. A. Maradudin, “An analogue of enhanced backscattering in the transmission of light through a thin film with a randomly rough surface,” Opt. Commun. 72, 279–285 (1989).
[CrossRef]

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]

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]

J. Shen, A. A. Maradudin, “Multiple scattering of waves from random rough surfaces,” Phys. Rev. B 22, 4234–4240 (1980).
[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 Volumes and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (North-Holland, Amsterdam, 1990), pp. 157–174.

Marvin, A.

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

V. Celli, A. Marvin, F. Toigo, “Light scattering from rough surfaces,” Phys. Rev. B 11, 1779–1786 (1975).
[CrossRef]

Marvin, A. M.

Maystre, D.

McGurn, A. R.

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

A. R. McGurn, A. A. Maradudin, “An analogue of enhanced backscattering in the transmission of light through a thin film with a randomly rough surface,” Opt. Commun. 72, 279–285 (1989).
[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, T. Michel, A. R. McGurn, E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 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 metallic grating,” Opt. Lett. 14, 151–153 (1989).
[CrossRef] [PubMed]

K. A. O’Donnell, E. R. Méndez, “Experimental study of scattering from characterized random surfaces,” J. Opt. Soc. Am. A 4, 1194–1205 (1987).
[CrossRef]

E. R. Méndez, K. A. O’Donnell, “Observation of depolarization and backscattering enhancement in light scattering from Gaussian random surfaces,” Opt. Commun. 61, 91–95 (1987).
[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 Volumes and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (North-Holland, Amsterdam, 1990), pp. 157–174.

Michel, T.

A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. 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 metallic grating,” Opt. Lett. 14, 151–153 (1989).
[CrossRef] [PubMed]

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 Volumes and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (North-Holland, Amsterdam, 1990), pp. 157–174.

Nieto-Vesperinas, M.

J. A. Sánchez-Gil, M. Nieto-Vesperinas, “Light scattering from random rough dielectric surfaces,” J. Opt. Soc. Am. A 8, 1270–1286 (1991).
[CrossRef]

M. Nieto-Vesperinas, J. A. Sánchez-Gil, A. J. Sant, J. C. Dainty, “Light transmission from a randomly rough dielectric diffuser: theoretical and experimental results,” Opt. Lett. 15, 1261–1263 (1990).
[CrossRef] [PubMed]

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]

M. Nieto-Vesperinas, J. M. Soto-Crespo, “Light-diffracted intensities from very deep gratings,” Phys. Rev. B 38, 7250–7259 (1988).
[CrossRef]

M. Nieto-Vesperinas, J. M. Soto-Crespo, “Connection between blazes from gratings and enhancements from random rough surfaces,” Phys. Rev. B 39, 8193–8197 (1988).
[CrossRef]

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]

M. Nieto-Vesperinas, “Depolarization of electromagnetic waves scattered from slightly rough random surfaces: a study by means of the extinction theorem,”J. Opt. Soc. Am. 72, 539–547 (1982).
[CrossRef]

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

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

O’Donnell, K. A.

E. R. Méndez, K. A. O’Donnell, “Observation of depolarization and backscattering enhancement in light scattering from Gaussian random surfaces,” Opt. Commun. 61, 91–95 (1987).
[CrossRef]

K. A. O’Donnell, E. R. Méndez, “Experimental study of scattering from characterized random surfaces,” J. Opt. Soc. Am. A 4, 1194–1205 (1987).
[CrossRef]

Pattanayak, D. N.

D. N. Pattanayak, E. Wolf, “General form and a new interpretation of the Ewald-Oseen extinction theorem,” Opt. Commun. 6, 217–220 (1972).
[CrossRef]

Rice, S. O.

S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces,” Commun. Pure Appl. Math. 4, 4808–4816 (1951).
[CrossRef]

Saillard, M.

Sánchez-Gil, J. A.

Sant, A. J.

Shen, J.

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

Soto-Crespo, J. M.

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]

M. Nieto-Vesperinas, J. M. Soto-Crespo, “Connection between blazes from gratings and enhancements from random rough surfaces,” Phys. Rev. B 39, 8193–8197 (1988).
[CrossRef]

M. Nieto-Vesperinas, J. M. Soto-Crespo, “Light-diffracted intensities from very deep gratings,” Phys. Rev. B 38, 7250–7259 (1988).
[CrossRef]

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]

Spizzichino, A.

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

Toigo, F.

V. Celli, A. Marvin, F. Toigo, “Light scattering from rough surfaces,” Phys. Rev. B 11, 1779–1786 (1975).
[CrossRef]

Toigo, R.

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

Valenzuela, G. R.

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

Winebrenner, D. P.

Wolf, E.

D. N. Pattanayak, E. Wolf, “General form and a new interpretation of the Ewald-Oseen extinction theorem,” Opt. Commun. 6, 217–220 (1972).
[CrossRef]

Ann. Phys. (1)

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

Commun. Pure Appl. Math. (1)

S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces,” Commun. Pure Appl. Math. 4, 4808–4816 (1951).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

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

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (7)

Opt. Acta (1)

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

Opt. Commun. (4)

D. N. Pattanayak, E. Wolf, “General form and a new interpretation of the Ewald-Oseen extinction theorem,” Opt. Commun. 6, 217–220 (1972).
[CrossRef]

A. R. McGurn, A. A. Maradudin, “An analogue of enhanced backscattering in the transmission of light through a thin film with a randomly rough surface,” Opt. Commun. 72, 279–285 (1989).
[CrossRef]

E. R. Méndez, K. A. O’Donnell, “Observation of depolarization and backscattering enhancement in light scattering from Gaussian random surfaces,” Opt. Commun. 61, 91–95 (1987).
[CrossRef]

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

Opt. Lett. (4)

Phys. Rev. B (6)

M. Nieto-Vesperinas, J. M. Soto-Crespo, “Light-diffracted intensities from very deep gratings,” Phys. Rev. B 38, 7250–7259 (1988).
[CrossRef]

M. Nieto-Vesperinas, J. M. Soto-Crespo, “Connection between blazes from gratings and enhancements from random rough surfaces,” Phys. Rev. B 39, 8193–8197 (1988).
[CrossRef]

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

V. Celli, A. Marvin, F. Toigo, “Light scattering from rough surfaces,” Phys. Rev. B 11, 1779–1786 (1975).
[CrossRef]

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

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

Other (7)

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

P. Beckmann, “Scattering of light by rough surfaces,” in Progress in Optics VI, E. Wolf, ed. (North Holland, Amsterdam, 1961), pp. 51–69.

F. G. Bass, I. M. Fuks, Wave Scattering from Statistically Rough Surfaces (Pergamon, Oxford1979).

M. Nieto-Vesperinas, J. C. Dainty, eds., Scattering in Volumes and Surfaces (North Holland, Amsterdam, 1990).

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 Volumes and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (North-Holland, Amsterdam, 1990), pp. 157–174.

V. D. Freylikher, Institute of Radiophysics, Kharkhov, USSR (personal communication, 1990).

A. Banos, Dipole Radiation in the Presence of a Conducting Half-Space (Pergamon, Oxford, 1966), Chap. 2.

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Figures (16)

Fig. 1
Fig. 1

Illustration of the scattering geometry.

Fig. 2
Fig. 2

Average reflectance from 300 samples versus θ0. The reflectance from a plane is also included.

Fig. 3
Fig. 3

Angular distribution of mean reflected intensity from a dielectric surface at θ0 = 0°, 10°, 20°, and 40°. Average over 300 samples. The specular direction is shown by the marks at the upper right. The backscattering direction is marked by vertical lines. The average reflectance and transmittance are shown.

Fig. 4
Fig. 4

Same as Fig. 3 for −1 = 0.5 at θ0 = 0°.

Fig. 5
Fig. 5

Same as Fig. 3 for σ = 0.5λ, T = 3.16λ, and −1 = 0.25. The results at two angles of incidence are shown.

Fig. 6
Fig. 6

Angular distribution of mean transmitted intensity from a dielectric surface at θ0 = 20° and 40°. Dashed curves, s polarization; solid curves, p polarization. Average over 300 samples. The forward direction is shown by the mark at the upper right. The specular direction of refraction, namely, that from Snell’s law for a plane, is marked by vertical lines. The average reflectance and transmittance are included.

Fig. 7
Fig. 7

Same as Fig. 6 for −1 = 0.25.

Fig. 8
Fig. 8

Same as Fig. 6 for the diffuse component; σ = 0.5λ and T = 3.16λ. The results at two angles of incidence are shown.

Fig. 9
Fig. 9

Average reflectance from 200 samples versus θ0. The reflectance from a plane is also shown.

Fig. 10
Fig. 10

Same as Fig. 3 for the diffuse component for σ = T = 0.2λ and = 0.25; θ0 = 0°, 20°, and 40°. Average over 200 samples.

Fig. 11
Fig. 11

Same as Fig. 3 for the diffuse component for σ = T = 0.2λ, and −1 = 0.5; θ0 = 0°, 20°, and 50°. Average over 200 samples.

Fig. 12
Fig. 12

Same as Fig. 6 for the diffuse component from 200 samples for σ = T = 0.2λ; θ0 = 0°, 20°, 40°.

Fig. 13
Fig. 13

(a) Average TIRE from 200 samples versus θ0. (b) Average TITE versus θ0 for the same surfaces.

Fig. 14
Fig. 14

Square modulus of the angular spectrum of the transmitted field versus the parallel momentum in the nonradiative region for plane surfaces.

Fig. 15
Fig. 15

Same as Fig. 14 with the origin shifted from z = 0 to z = Dmin, Dmin being the minimum of the surface whose statistical parameters are σ = T = 0.2λ.

Fig. 16
Fig. 16

Average of the square modulus of the angular spectrum of the transmitted field over 200 samples versus the parallel momentum in the nonradiative region.

Equations (47)

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K 0 = K = k 0 K t = k 0 ,
K 0 = K = k K t = - 1 k ,
λ 0 = λ .
K 0 k ( sin θ 0 , 0 , - cos θ 0 ) ,
K k ( sin θ , 0 , cos θ ) ,
K t - 1 k ( sin θ t , 0 , - cos θ t ) ,
K 2 = K 0 2 = k 2 = ω 2 c 2 = ( 2 π λ ) 2 ,
K t 2 = - 1 k 2 ,
E ( i ) ( r ) = j ^ E ( i ) exp ( i K 0 · r ) .
H ( i ) ( r ) = j ^ H ( i ) exp ( i K 0 · r ) .
E ( i ) [ x , D ( x ) ] + 1 4 π - d x × { E ( x ) [ G 0 z - D ( x ) G 0 x ] - G 0 F ( x ) } = E ( x ) ,
- 1 4 π - d x × { E ( x ) [ G z - D ( x ) G x ] - G F ( x ) } = 0.
G 0 ( r , r ) = π i H 0 ( 1 ) ( k r - r ) ,
G ( r , r ) = π i H 0 ( 1 ) ( - 1 k r - r ) ,
E ( x ) = E ( out ) [ x , D ( x ) ] = E ( in ) [ x , D ( x ) ] ,
F ( x ) = γ [ E ( out ) ( r ) n ] z = D ( + ) ( x ) = γ [ E ( in ) ( r ) n ] z = D ( - 1 ) ( x ) ,
γ = { 1 + [ D ( x ) ] 2 } 1 / 2 ,
D ( x ) = d D ( x ) d x .
E ( r ) ( r > , θ ) = exp [ i ( k r > - π / 4 ) ] 2 2 π k r > × - d x { k [ cos θ - D ( x ) sin θ ] × E ( x ) - i F ( x ) } exp ( - i K · r ) ,
E ( t ) ( r < , θ t ) = exp [ i ( - 1 k r < - π / 4 ) ] 2 [ 2 π - 1 k r < ] 1 / 2 × - d x { - 1 k [ cos θ t + D ( x ) sin θ t ] × E ( x ) + i F ( x ) } exp ( - i K t · r ) ,
1 I 0 I s ( r ) ( θ ) = r > I 0 E ( r ) ( r > , θ ) 2 ,
1 I 0 I s ( t ) ( θ t ) = - 1 r < I 0 E ( t ) ( r < , θ t ) 2 ,
R + T = 1 ,
R = 1 I 0 - π / 2 π / 2 I ( r ) ( θ ) d θ ,
T = 1 I 0 - π / 2 π / 2 I ( t ) ( θ t ) d θ t ,
H ( i ) [ x , D ( x ) ] + 1 4 π - d x × { H ( x ) [ G 0 z - D ( x ) G 0 x ] - G 0 L ( x ) } = H ( x ) ,
- 1 4 π - d x × { H ( x ) [ G x - D ( x ) G x ] - - 1 G L ( x ) } = 0.
H ( x ) = H ( out ) [ x , D ( x ) ] = H ( in ) [ x , D ( x ) ] ,
L ( x ) = γ [ H ( out ) ( r ) n ] z = D ( + ) ( x ) = γ - 1 [ H ( in ) ( r ) n ] z = D ( - 1 ) ( x ) .
H ( r ) ( r > , θ ) = exp [ i ( k r > - π / 4 ) ] 2 2 π k r > × - d x { k [ cos θ - D ( x ) sin θ ] × H ( x ) - i L ( x ) } exp ( - i K · r ) ,
H ( t ) ( r < , θ t ) = exp [ i ( - 1 k r < - π / 4 ) ] 2 ( 2 π - 1 k r < ) 1 / 2 × - d x { - 1 k [ cos θ t + D ( x ) sin θ t ] × H ( x ) + i - 1 L ( x ) } exp ( - i K t · r ) .
1 I 0 I p ( r ) ( θ ) = r > I 0 H ( r ) ( r > , θ ) 2 ,
1 I 0 I p ( t ) ( θ t ) = 1 - 1 r < I 0 H ( t ) ( r < , θ t ) 2 .
c ( τ ) = 1 σ 2 D ( x ) D ( x + τ ) = exp ( - τ 2 T 2 ) ,
E ( r ) = - 1 4 π - { E ( x ) [ G z - D ( x ) G x ] - G F ( x ) } d x ,
H ( r ) = - 1 4 π - { H ( x ) [ G z - D ( x ) G x ] - - 1 G L ( x ) } d x .
G ( r , r ) = - i d K k z exp { i [ K ( x - x ) + k z z - z ] } ,
k z = - 1 k 2 - K 2 ,             K 2 < - 1 k 2 ,
k z = i K 2 - - 1 k 2 ,             K 2 > - 1 k 2 .
E ( r ) = - A t ( s ) ( K ) exp [ i ( K x - k z z ) ] d K ,
A t ( s ) ( K ) = - i 4 π k z - d x exp { - i [ K x - k z D ( x ) ] } × { i [ K D ( x ) + k z ] E ( x ) - F ( x ) } .
H ( r ) = - A t ( p ) ( K ) exp [ i ( K x - k z z ) ] d K ,
A t ( p ) ( K ) = - i 4 π k z - d x exp { - i [ K x - k z D ( x ) ] } × { i [ K D ( x ) + k z ] H ( x ) - - 1 L ( x ) } .
A t ( s ) ( K ) = δ ( K - K t ) 2 k z 0 k z 0 + k z ,
A t ( p ) ( K ) = δ ( K - K t ) 2 - 1 k z 0 - 1 k z 0 + k z .
K / ( - 1 / 2 k ) = 1 - 1 sin θ 0 = 1.29 ,
K / ( - 1 / 2 k ) = 1 - 1 sin θ 0 = 1.08.

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