Abstract

The intensity angular correlation function in multiple scattering of electromagnetic waves from randomly rough one-dimensional interfaces that separate a vacuum from a perfect conductor is studied by numerically solving the scattering equations that are based on the extinction theorem boundary condition. The so-called memory effect, discussed elsewhere for dense random media, is encountered, and its angular width is found to be considerably larger than for volume scattering. Comparisons are also made with situations for which the Kirchhoff approximation holds. In addition, because of the small number of asperities of the surface samples dealt with in the computations, a new enhanced long-range correlation of width reciprocal to the mean free path is found as a result of constructive interference between waves whose wave vector is the sum or difference of initial and final wave vectors and wave vectors that are due to time-reversed paths. The origin of this correlation effect, in that it is due to multiple scattering, is analogous to that of the peak of enhanced backscattering for the mean scattered intensity and arises from the non-Gaussian second-order statistics of the scattered field.

© 1993 Optical Society of America

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    [CrossRef]
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  13. J. X. Zhu, D. J. Pine, D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
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  18. M. Kaveh, M. Rosenbluh, I. Edrei, I. Freund, “Weak localization of light scattered from disordered solids,” Phys. Rev. Lett. 57, 2049–2052 (1986).
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  19. K. A. O’Donnell, E. R. Méndez, “Experimental study of scattering from characterized random surfaces,” J. Opt. Soc. Am. A 4, 1194–1205 (1987).
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  20. A. A. Maradudin, E. R. Méndez, T. Michel, in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (North-Holland, Amsterdam, 1990), pp. 169–172.
  21. 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]
  22. 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]
  23. 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]
  24. 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]
  25. J. A. Sánchez-Gil, M. Nieto-Vesperinas, “Light scattering from random rough dielectric surfaces,” J. Opt. Soc. Am. A 8, 1270–1286 (1991).
    [CrossRef]
  26. M. Nieto-Vesperinas, J. A. Sánchez-Gil, A. A. Maradudin, “Multiple light scattering from metal and dielectric rough surfaces,” Waves Random Media 1, S157–S163, (1991).
    [CrossRef]
  27. E. G. Liszka, J. J. McCoy, “Scattering at a rough boundary–extensions of the Kirchhoff approximation,” J. Acoust. Soc. Am. 71, 1093–1100 (1982).
    [CrossRef]
  28. A. Ishimaru, J. S. Chen, “Scattering from very rough surfaces based on the modified second-order Kirchhoff approximation with angular and propagation shadowing,” J. Acoust. Soc. Am. 88, 1877–1883 (1990).
    [CrossRef]
  29. N. Bruce, J. C. Dainty, “Multiple scattering from random rough surfaces using the Kirchhoff approximation,” J. Mod. Opt. 38, 579–590 (1991).
    [CrossRef]
  30. E. I. Thorsos, D. R. Jackson, “Studies of scattering theory using numerical methods,” Waves Random Media 1, S165–S190 (1991).
    [CrossRef]
  31. J. A. Sánchez-Gil, M. Nieto-Vesperinas, “Resonance effects in multiple light scattering from statistically rough metallic surfaces,” Phys. Rev. B 45, 8623–8633 (1992).
    [CrossRef]
  32. M. P. Van Albada, A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
    [CrossRef] [PubMed]
  33. E. Akkermans, P. E. Wolf, R. Maynard, “Coherent back-scattering of light by disordered media: analysis of the peak lineshape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
    [CrossRef] [PubMed]
  34. 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 (1987).
    [CrossRef]
  35. S. Etemad, R. Thompson, M. J. Andrejco, “Weak localization of photons: universal fluctuations and ensemble averaging,” Phys. Rev. Lett. 57, 575–578 (1986).
    [CrossRef] [PubMed]
  36. 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]
  37. B. E. A. Saleh, Photoelectron Statistics (Springer-Verlag, Berlin, 1978), Chap. 4.
    [CrossRef]
  38. E. Jakeman, “Speckle statistics with a small number of scatterers,” Opt. Eng. 23, 453–461 (1984).
    [CrossRef]
  39. M. Nieto-Vesperinas, J. M. Soto-Crespo, “Monto Carlo calculations of speckle contrast from perfectly conductive random rough surfaces,” Opt. Commun. 75, 215–218 (1990).
    [CrossRef]

1992 (1)

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

1991 (6)

N. Bruce, J. C. Dainty, “Multiple scattering from random rough surfaces using the Kirchhoff approximation,” J. Mod. Opt. 38, 579–590 (1991).
[CrossRef]

E. I. Thorsos, D. R. Jackson, “Studies of scattering theory using numerical methods,” Waves Random Media 1, S165–S190 (1991).
[CrossRef]

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. A. Maradudin, “Multiple light scattering from metal and dielectric rough surfaces,” Waves Random Media 1, S157–S163, (1991).
[CrossRef]

J. X. Zhu, D. J. Pine, D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
[CrossRef] [PubMed]

D. Eliyahu, R. Berkovits, M. Kaveh, “Long-range angular correlations of waves in a tube geometry,” Phys. Rev. B 43, 13501–13505 (1991);M. Kaveh, “New phenomena in the propagation of optical waves through random media,” Waves Random Media 3, S121–S128 (1991).
[CrossRef]

1990 (6)

R. Berkovits, M. Kaveh, “Time-reversed memory effects,” Phys. Rev. B 41, 2635–2638 (1990).
[CrossRef]

M. P. van Albada, J. F. de Boer, A. Lagendijk, “Observation of long-range intensity correlation in the transport of coherent light through a random medium,” Phys. Rev. Lett. 64, 2787–2790 (1990).
[CrossRef] [PubMed]

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. Ishimaru, J. S. Chen, “Scattering from very rough surfaces based on the modified second-order Kirchhoff approximation with angular and propagation shadowing,” J. Acoust. Soc. Am. 88, 1877–1883 (1990).
[CrossRef]

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]

M. Nieto-Vesperinas, J. M. Soto-Crespo, “Monto Carlo calculations of speckle contrast from perfectly conductive random rough surfaces,” Opt. Commun. 75, 215–218 (1990).
[CrossRef]

1989 (4)

R. Berkovits, M. Kaveh, S. Feng, “Memory effect of waves in disordered systems: a real-space approach,” Phys. Rev. B 40, 737–740 (1989).
[CrossRef]

I. Edrei, M. Kaveh, “Wavelength intensity correlation functions for transmitted waves through a slab: numerical results,” Phys. Rev. B 40, 9419–9422 (1989).
[CrossRef]

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]

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]

1988 (4)

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. (Paris) 49, 77–98 (1988).
[CrossRef]

D. N. Qu, J. C. Dainty, “Polarization dependence of dynamic light scattering by dense disordered media,” Opt. Lett. 13, 1066–1068 (1988).
[CrossRef] [PubMed]

S. Feng, C. Kane, P. A. Lee, A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

I. Freund, M. Rosenbluh, S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[CrossRef] [PubMed]

1987 (3)

1986 (4)

S. Etemad, R. Thompson, M. J. Andrejco, “Weak localization of photons: universal fluctuations and ensemble averaging,” Phys. Rev. Lett. 57, 575–578 (1986).
[CrossRef] [PubMed]

E. Akkermans, P. E. Wolf, R. Maynard, “Coherent back-scattering of light by disordered media: analysis of the peak lineshape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef] [PubMed]

M. Kaveh, M. Rosenbluh, I. Edrei, I. Freund, “Weak localization of light scattered from disordered solids,” Phys. Rev. Lett. 57, 2049–2052 (1986).
[CrossRef] [PubMed]

B. Shapiro, “Large intensity fluctuations for wave propagation in random media,” Phys. Rev. Lett. 57, 2168–2171 (1986).
[CrossRef] [PubMed]

1985 (1)

M. P. Van Albada, A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[CrossRef] [PubMed]

1984 (1)

E. Jakeman, “Speckle statistics with a small number of scatterers,” Opt. Eng. 23, 453–461 (1984).
[CrossRef]

1982 (1)

E. G. Liszka, J. J. McCoy, “Scattering at a rough boundary–extensions of the Kirchhoff approximation,” J. Acoust. Soc. Am. 71, 1093–1100 (1982).
[CrossRef]

1975 (1)

Akkermans, E.

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. (Paris) 49, 77–98 (1988).
[CrossRef]

E. Akkermans, P. E. Wolf, R. Maynard, “Coherent back-scattering of light by disordered media: analysis of the peak lineshape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef] [PubMed]

Andrejco, M. J.

S. Etemad, R. Thompson, M. J. Andrejco, “Weak localization of photons: universal fluctuations and ensemble averaging,” Phys. Rev. Lett. 57, 575–578 (1986).
[CrossRef] [PubMed]

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. 55–69.

Berkovits, R.

D. Eliyahu, R. Berkovits, M. Kaveh, “Long-range angular correlations of waves in a tube geometry,” Phys. Rev. B 43, 13501–13505 (1991);M. Kaveh, “New phenomena in the propagation of optical waves through random media,” Waves Random Media 3, S121–S128 (1991).
[CrossRef]

R. Berkovits, M. Kaveh, “Time-reversed memory effects,” Phys. Rev. B 41, 2635–2638 (1990).
[CrossRef]

R. Berkovits, M. Kaveh, S. Feng, “Memory effect of waves in disordered systems: a real-space approach,” Phys. Rev. B 40, 737–740 (1989).
[CrossRef]

Bruce, N.

N. Bruce, J. C. Dainty, “Multiple scattering from random rough surfaces using the Kirchhoff approximation,” J. Mod. Opt. 38, 579–590 (1991).
[CrossRef]

Chen, J. S.

A. Ishimaru, J. S. Chen, “Scattering from very rough surfaces based on the modified second-order Kirchhoff approximation with angular and propagation shadowing,” J. Acoust. Soc. Am. 88, 1877–1883 (1990).
[CrossRef]

Dainty, J. C.

de Boer, J. F.

M. P. van Albada, J. F. de Boer, A. Lagendijk, “Observation of long-range intensity correlation in the transport of coherent light through a random medium,” Phys. Rev. Lett. 64, 2787–2790 (1990).
[CrossRef] [PubMed]

Edrei, I.

I. Edrei, M. Kaveh, “Wavelength intensity correlation functions for transmitted waves through a slab: numerical results,” Phys. Rev. B 40, 9419–9422 (1989).
[CrossRef]

M. Kaveh, M. Rosenbluh, I. Edrei, I. Freund, “Weak localization of light scattered from disordered solids,” Phys. Rev. Lett. 57, 2049–2052 (1986).
[CrossRef] [PubMed]

Eliyahu, D.

D. Eliyahu, R. Berkovits, M. Kaveh, “Long-range angular correlations of waves in a tube geometry,” Phys. Rev. B 43, 13501–13505 (1991);M. Kaveh, “New phenomena in the propagation of optical waves through random media,” Waves Random Media 3, S121–S128 (1991).
[CrossRef]

Etemad, S.

S. Etemad, R. Thompson, M. J. Andrejco, “Weak localization of photons: universal fluctuations and ensemble averaging,” Phys. Rev. Lett. 57, 575–578 (1986).
[CrossRef] [PubMed]

Feng, S.

R. Berkovits, M. Kaveh, S. Feng, “Memory effect of waves in disordered systems: a real-space approach,” Phys. Rev. B 40, 737–740 (1989).
[CrossRef]

I. Freund, M. Rosenbluh, S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[CrossRef] [PubMed]

S. Feng, C. Kane, P. A. Lee, A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

Freund, I.

I. Freund, M. Rosenbluh, S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[CrossRef] [PubMed]

M. Kaveh, M. Rosenbluh, I. Edrei, I. Freund, “Weak localization of light scattered from disordered solids,” Phys. Rev. Lett. 57, 2049–2052 (1986).
[CrossRef] [PubMed]

Friberg, A. T.

Genack, A. Z.

A. Z. Genack, “Fluctuations, correlation and average transport of electromagnetic radiation in random media,” in Scattering and Localization of Classical Waves in Random Media, P. Sheng, ed. (World Scientific, Singapore, 1990), pp. 207–311.
[CrossRef]

Goodman, J. W.

J. W. Goodman, “The statistics of speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984).

Ishimaru, A.

A. Ishimaru, J. S. Chen, “Scattering from very rough surfaces based on the modified second-order Kirchhoff approximation with angular and propagation shadowing,” J. Acoust. Soc. Am. 88, 1877–1883 (1990).
[CrossRef]

Jackson, D. R.

E. I. Thorsos, D. R. Jackson, “Studies of scattering theory using numerical methods,” Waves Random Media 1, S165–S190 (1991).
[CrossRef]

Jakeman, E.

E. Jakeman, “Speckle statistics with a small number of scatterers,” Opt. Eng. 23, 453–461 (1984).
[CrossRef]

Kane, C.

S. Feng, C. Kane, P. A. Lee, A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

Kaveh, M.

D. Eliyahu, R. Berkovits, M. Kaveh, “Long-range angular correlations of waves in a tube geometry,” Phys. Rev. B 43, 13501–13505 (1991);M. Kaveh, “New phenomena in the propagation of optical waves through random media,” Waves Random Media 3, S121–S128 (1991).
[CrossRef]

R. Berkovits, M. Kaveh, “Time-reversed memory effects,” Phys. Rev. B 41, 2635–2638 (1990).
[CrossRef]

R. Berkovits, M. Kaveh, S. Feng, “Memory effect of waves in disordered systems: a real-space approach,” Phys. Rev. B 40, 737–740 (1989).
[CrossRef]

I. Edrei, M. Kaveh, “Wavelength intensity correlation functions for transmitted waves through a slab: numerical results,” Phys. Rev. B 40, 9419–9422 (1989).
[CrossRef]

M. Kaveh, M. Rosenbluh, I. Edrei, I. Freund, “Weak localization of light scattered from disordered solids,” Phys. Rev. Lett. 57, 2049–2052 (1986).
[CrossRef] [PubMed]

Kim, M. J.

Lagendijk, A.

M. P. van Albada, J. F. de Boer, A. Lagendijk, “Observation of long-range intensity correlation in the transport of coherent light through a random medium,” Phys. Rev. Lett. 64, 2787–2790 (1990).
[CrossRef] [PubMed]

M. P. Van Albada, A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[CrossRef] [PubMed]

Lee, P. A.

S. Feng, C. Kane, P. A. Lee, A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

Léger, D.

Liszka, E. G.

E. G. Liszka, J. J. McCoy, “Scattering at a rough boundary–extensions of the Kirchhoff approximation,” J. Acoust. Soc. Am. 71, 1093–1100 (1982).
[CrossRef]

Maradudin, A. A.

M. Nieto-Vesperinas, J. A. Sánchez-Gil, A. A. Maradudin, “Multiple light scattering from metal and dielectric rough surfaces,” Waves Random Media 1, S157–S163, (1991).
[CrossRef]

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, in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (North-Holland, Amsterdam, 1990), pp. 169–172.

Maret, G.

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. (Paris) 49, 77–98 (1988).
[CrossRef]

Mathieu, E.

Maynard, R.

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. (Paris) 49, 77–98 (1988).
[CrossRef]

E. Akkermans, P. E. Wolf, R. Maynard, “Coherent back-scattering of light by disordered media: analysis of the peak lineshape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef] [PubMed]

McCoy, J. J.

E. G. Liszka, J. J. McCoy, “Scattering at a rough boundary–extensions of the Kirchhoff approximation,” J. Acoust. Soc. Am. 71, 1093–1100 (1982).
[CrossRef]

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]

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]

A. A. Maradudin, E. R. Méndez, T. Michel, in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (North-Holland, Amsterdam, 1990), pp. 169–172.

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, in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (North-Holland, Amsterdam, 1990), pp. 169–172.

Nieto-Vesperinas, M.

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

M. Nieto-Vesperinas, J. A. Sánchez-Gil, A. A. Maradudin, “Multiple light scattering from metal and dielectric rough surfaces,” Waves Random Media 1, S157–S163, (1991).
[CrossRef]

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. M. Soto-Crespo, “Monto Carlo calculations of speckle contrast from perfectly conductive random rough surfaces,” Opt. Commun. 75, 215–218 (1990).
[CrossRef]

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

O’Donnell, K. A.

Perrin, J. C.

Pine, D. J.

J. X. Zhu, D. J. Pine, D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
[CrossRef] [PubMed]

Qu, D. N.

Rosenbluh, M.

I. Freund, M. Rosenbluh, S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[CrossRef] [PubMed]

M. Kaveh, M. Rosenbluh, I. Edrei, I. Freund, “Weak localization of light scattered from disordered solids,” Phys. Rev. Lett. 57, 2049–2052 (1986).
[CrossRef] [PubMed]

Saleh, B. E. A.

B. E. A. Saleh, Photoelectron Statistics (Springer-Verlag, Berlin, 1978), Chap. 4.
[CrossRef]

Sánchez-Gil, J. A.

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

M. Nieto-Vesperinas, J. A. Sánchez-Gil, A. A. Maradudin, “Multiple light scattering from metal and dielectric rough surfaces,” Waves Random Media 1, S157–S163, (1991).
[CrossRef]

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

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Shapiro, B.

B. Shapiro, “Large intensity fluctuations for wave propagation in random media,” Phys. Rev. Lett. 57, 2168–2171 (1986).
[CrossRef] [PubMed]

Soto-Crespo, J. M.

Spizzichino, A.

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. 55–69.

Stone, A. D.

S. Feng, C. Kane, P. A. Lee, A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

Thompson, R.

S. Etemad, R. Thompson, M. J. Andrejco, “Weak localization of photons: universal fluctuations and ensemble averaging,” Phys. Rev. Lett. 57, 575–578 (1986).
[CrossRef] [PubMed]

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E. I. Thorsos, D. R. Jackson, “Studies of scattering theory using numerical methods,” Waves Random Media 1, S165–S190 (1991).
[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 (1987).
[CrossRef]

van Albada, M. P.

M. P. van Albada, J. F. de Boer, A. Lagendijk, “Observation of long-range intensity correlation in the transport of coherent light through a random medium,” Phys. Rev. Lett. 64, 2787–2790 (1990).
[CrossRef] [PubMed]

M. P. Van Albada, A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[CrossRef] [PubMed]

Weitz, D. A.

J. X. Zhu, D. J. Pine, D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
[CrossRef] [PubMed]

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E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. (Paris) 49, 77–98 (1988).
[CrossRef]

E. Akkermans, P. E. Wolf, R. Maynard, “Coherent back-scattering of light by disordered media: analysis of the peak lineshape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef] [PubMed]

Zhu, J. X.

J. X. Zhu, D. J. Pine, D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
[CrossRef] [PubMed]

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]

Appl. Opt. (1)

J. Acoust. Soc. Am. (3)

E. G. Liszka, J. J. McCoy, “Scattering at a rough boundary–extensions of the Kirchhoff approximation,” J. Acoust. Soc. Am. 71, 1093–1100 (1982).
[CrossRef]

A. Ishimaru, J. S. Chen, “Scattering from very rough surfaces based on the modified second-order Kirchhoff approximation with angular and propagation shadowing,” J. Acoust. Soc. Am. 88, 1877–1883 (1990).
[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 (1987).
[CrossRef]

J. Mod. Opt. (1)

N. Bruce, J. C. Dainty, “Multiple scattering from random rough surfaces using the Kirchhoff approximation,” J. Mod. Opt. 38, 579–590 (1991).
[CrossRef]

J. Opt. Soc. Am. A (4)

J. Phys. (Paris) (1)

E. Akkermans, P. E. Wolf, R. Maynard, G. Maret, “Theoretical study of the coherent backscattering of light by disordered media,” J. Phys. (Paris) 49, 77–98 (1988).
[CrossRef]

Opt. Commun. (1)

M. Nieto-Vesperinas, J. M. Soto-Crespo, “Monto Carlo calculations of speckle contrast from perfectly conductive random rough surfaces,” Opt. Commun. 75, 215–218 (1990).
[CrossRef]

Opt. Eng. (1)

E. Jakeman, “Speckle statistics with a small number of scatterers,” Opt. Eng. 23, 453–461 (1984).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (1)

J. X. Zhu, D. J. Pine, D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
[CrossRef] [PubMed]

Phys. Rev. B (5)

D. Eliyahu, R. Berkovits, M. Kaveh, “Long-range angular correlations of waves in a tube geometry,” Phys. Rev. B 43, 13501–13505 (1991);M. Kaveh, “New phenomena in the propagation of optical waves through random media,” Waves Random Media 3, S121–S128 (1991).
[CrossRef]

R. Berkovits, M. Kaveh, S. Feng, “Memory effect of waves in disordered systems: a real-space approach,” Phys. Rev. B 40, 737–740 (1989).
[CrossRef]

R. Berkovits, M. Kaveh, “Time-reversed memory effects,” Phys. Rev. B 41, 2635–2638 (1990).
[CrossRef]

I. Edrei, M. Kaveh, “Wavelength intensity correlation functions for transmitted waves through a slab: numerical results,” Phys. Rev. B 40, 9419–9422 (1989).
[CrossRef]

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

Phys. Rev. Lett. (8)

M. P. Van Albada, A. Lagendijk, “Observation of weak localization of light in a random medium,” Phys. Rev. Lett. 55, 2692–2695 (1985).
[CrossRef] [PubMed]

E. Akkermans, P. E. Wolf, R. Maynard, “Coherent back-scattering of light by disordered media: analysis of the peak lineshape,” Phys. Rev. Lett. 56, 1471–1474 (1986).
[CrossRef] [PubMed]

S. Etemad, R. Thompson, M. J. Andrejco, “Weak localization of photons: universal fluctuations and ensemble averaging,” Phys. Rev. Lett. 57, 575–578 (1986).
[CrossRef] [PubMed]

M. P. van Albada, J. F. de Boer, A. Lagendijk, “Observation of long-range intensity correlation in the transport of coherent light through a random medium,” Phys. Rev. Lett. 64, 2787–2790 (1990).
[CrossRef] [PubMed]

B. Shapiro, “Large intensity fluctuations for wave propagation in random media,” Phys. Rev. Lett. 57, 2168–2171 (1986).
[CrossRef] [PubMed]

M. Kaveh, M. Rosenbluh, I. Edrei, I. Freund, “Weak localization of light scattered from disordered solids,” Phys. Rev. Lett. 57, 2049–2052 (1986).
[CrossRef] [PubMed]

S. Feng, C. Kane, P. A. Lee, A. D. Stone, “Correlations and fluctuations of coherent wave transmission through disordered media,” Phys. Rev. Lett. 61, 834–837 (1988).
[CrossRef] [PubMed]

I. Freund, M. Rosenbluh, S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61, 2328–2331 (1988).
[CrossRef] [PubMed]

Waves Random Media (2)

M. Nieto-Vesperinas, J. A. Sánchez-Gil, A. A. Maradudin, “Multiple light scattering from metal and dielectric rough surfaces,” Waves Random Media 1, S157–S163, (1991).
[CrossRef]

E. I. Thorsos, D. R. Jackson, “Studies of scattering theory using numerical methods,” Waves Random Media 1, S165–S190 (1991).
[CrossRef]

Other (7)

A. A. Maradudin, E. R. Méndez, T. Michel, in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas, J. C. Dainty, eds. (North-Holland, Amsterdam, 1990), pp. 169–172.

B. E. A. Saleh, Photoelectron Statistics (Springer-Verlag, Berlin, 1978), Chap. 4.
[CrossRef]

P. Sheng, ed., Scattering and Localization of Classical Waves in Random Media (World Scientific, Singapore, 1990).

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

A. Z. Genack, “Fluctuations, correlation and average transport of electromagnetic radiation in random media,” in Scattering and Localization of Classical Waves in Random Media, P. Sheng, ed. (World Scientific, Singapore, 1990), pp. 207–311.
[CrossRef]

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. 55–69.

J. W. Goodman, “The statistics of speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer-Verlag, Berlin, 1984).

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Figures (7)

Fig. 1
Fig. 1

Scattering geometry for the intensity angular correlation.

Fig. 2
Fig. 2

Multiple-scattering trajectories responsible for coherent interference.

Fig. 3
Fig. 3

Angular correlation function [Eq. (1)] versus θ0, with θ0′ = θ′ = 5° and θ = θ0 (memory effect), for a perfectly conductive surface with T = 3.16 λ and σ = 1.9 λ. Dashed curves, s polarization; solid curves, p polarization. With asterisks, SO; without asterisks, ET. Average over N = 4000 samples.

Fig. 4
Fig. 4

Same as Fig. 3, with θ0′ = θ′ = 25° for a surface with T = 3.16λ and σ = 0.5λ. Dashed curve, s polarization; solid curve, p polarization. With asterisks, KA; without asterisks, ET. Average over N = 4000 samples.

Fig. 5
Fig. 5

Angular correlation function [Eq. (1)] versus θ, with θ0′ = θ′ = 0°, for a perfectly conductive surface with T = 3.16λ and σ = 1.9λ. ET calculation with a Gaussian incident beam. (a) θ0 = 3°, (b) θ0 = 7°. Dashed curves, s polarization; solid curves, p polarization. Average over N = 4000 samples.

Fig. 6
Fig. 6

Angular correlation function [Eq. (1)] versus θ, with θ0′ = 5° and θ′ = 9°, for a perfectly conductive surface with T = 3.16λ and σ = 1.9λ. ET calculation with a Gaussian incident beam. (a) θ0 = 0°, (b) θ0 = 3°. Dashed curves, s polarization; solid curves, p polarization. Average over N = 4000 samples.

Fig. 7
Fig. 7

Angular correlation function [Eq. (1)] versus θ, with θ0′ = θ′ = 0° and θ0 = 3°, for a perfectly conductive surface with T = 3.16λ and σ = 1.9λ. Calculation with a Gaussian incident beam. Dashed curves, s polarization; solid curves,p polarization. (a) SO; (b) without asterisks, KA; with asterisks, IT. Average over N = 4000 samples.

Equations (15)

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C ( K i , K f ; K i , K f ) = δ I ( K i , K f ) δ I ( K i , K f ) I ( K i , K f ) I ( K i , K f ) ,
A ( K i , K f ) = 1 2 l , m { A l m exp [ i ( K i r l K f r m ) ] + A m l exp [ i ( K i r m K f r l ) ] } ,
I ( K i , K f ) = | A ( K i , K f ) | 2 = I 0 + l , m | A l m | 2 cos [ ( K i + K f ) ( r l r m ) ] + F ( K i , K f ) .
F ( K i , K f ) = 1 4 ( l , m ) ( l , m ) A l m A l m * exp [ i K i ( r l r l ) ] × exp [ i K f ( r m r m ) ] ,
A l m A l m * = | A l m | 2 δ l l δ m m .
δ I ( K i , K f ) δ I ( K i , K f ) = I ( K i , K f ) I ( K i , K f ) I ( K i , K f ) I ( K i , K f ) = 1 2 l , m ; j , k δ I l m δ I j k × { cos [ ( K i + K f ) ( r l r m ) + ( K i + K f ) ( r j r k ) ] + cos [ ( K i + K f ) ( r l r m ) ( K i + K f ) ( r j r k ) ] } + j , k F ( K i , K f ) I j k cos [ ( K i + K f ) ( r j r k ) ] + l , m I l m F ( K i , K f ) cos [ ( K i + K f ) ( r l r m ) ] + F ( K i , K f ) F ( K i , K f ) .
l , m δ I l m 2 ( cos { [ ( K i + K f ) + ( K i + K f ) ] ( r l r m ) } + cos { [ ( K i + K f ) ( K i + K f ) ] ( r l r m ) ] } ) .
K i + K f = ± ( K i + K f ) .
I ( K i , K f ) I ( K i , K f )
[ A ( K i , K f ) A * ( K i , K f ) ] [ A * ( K i , K f ) A ( K i , K f ) ] ,
δ I ( K i , K f ) δ I ( K i , K f ) = | A ( K i , K f ) A * ( K i K f ) | 2 ,
| l , m I l m exp [ i ( K i K r ) r l ] exp [ i ( K f K f ) r m ] | 2 + | l , m I l m exp [ i ( K i K f ) r l ] exp [ i ( K i + K f ) r m ] | 2 .
K i K i = K f K f ,
Δ k f = Δ k i ,
sin θ m sin θ 0 = sin θ sin θ 0 .

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