Abstract

We measured the angular distribution of light scattering from dielectric random surfaces and confirmed the existence of the quasi-anomalous scattering and Brewster’s scattering angle, which were predicted theoretically in our previous work. The quasi-anomalous scattering produces peaks at the critical angle of total reflection. Brewster’s scattering angle is the angle of a zero in the p-polarized scattering distribution. In the case of vertical incidence there is a dip at the critical angle in the p-polarized scattering distribution, because Brewster’s scattering angle overlaps the critical angle, while the peak due to the quasi-anomalous scattering exists in s-polarized scattering.

© 1999 Optical Society of America

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References

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  1. Y. Q. Jin, M. Lax, “Backscattering enhancement from a randomly rough surface,” Phys. Rev. B 42, 9819–9829 (1990).
    [CrossRef]
  2. M. E. Knotts, K. A. O’Donnell, “Backscattering enhancement from a conducting surface with isotropic roughness,” Opt. Commun. 99, 1–6 (1993).
    [CrossRef]
  3. A. Ishimaru, J. S. Chen, P. Phu, K. Yoshitomi, “Numerical, analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement,” Waves Random Media 1, 91–107 (1991).
    [CrossRef]
  4. A. R. McGurn, A. A. Maradudin, “Localization effects in the elastic scattering of light form a randomly rough surface,” J. Opt. Soc. Am. B 4, 910–926 (1985).
    [CrossRef]
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    [CrossRef]
  6. H. Ogura, Z. L. Wang, “Surface-plasmon mode on a random rough metal surface: enhanced backscattering and localization,” Phys. Rev. B 53, 10358–10371 (1996).
    [CrossRef]
  7. H. Ogura, T. Kawanishi, N. Takahashi, Z. L. Wang, “Scattering of electromagnetic waves from a slightly random surface—reciprocal theorem, cross-polarization and backscattering enhancement,” Waves Random Media 5, 461–495 (1995).
    [CrossRef]
  8. T. Kawanishi, H. Ogura, Z. L. Wang, “Scattering of electromagnetic waves from a planar waveguide structure with a slightly 2D random surface,” Waves Random Media 7, 35–64 (1997).
    [CrossRef]
  9. V. Freilikher, M. Pustilnik, I. Yurkevich, “Wave scattering from a bounded medium with disorder,” Phys. Rev. A 193, 467–470 (1994).
  10. Z. L. Wang, H. Ogura, N. Takahashi, “Enhanced scattering from a planar waveguide structure with a slightly rough boundary,” Phys. Rev. B 52, 6027–6041 (1995).
    [CrossRef]
  11. T. Kawanishi, H. Ogura, Z. L. Wang, “Scattering of electromagnetic wave from a slightly random dielectric surface—Yoneda peak and Brewster angle in incoherent scattering,” Waves Random Media 7, 351–384 (1997).
    [CrossRef]
  12. O. J. Guentert, “Study of the anomalous surface reflection of x rays,” J. Appl. Phys. 36, 1361–1366 (1965).
    [CrossRef]
  13. S. K. Sinha, E. B. Sirota, S. Garoff, H. B. Stanley, “X-ray and neutron scattering from rough surfaces,” Phys. Rev. B 38, 2997–2311 (1988).
    [CrossRef]
  14. T. A. Leskova, A. A. Maradudin, “X-ray scattering from a randomly rough surface,” Waves Random Media 7, 395–434 (1997).
    [CrossRef]
  15. C. Amra, S. Maure, “Electromagnetic power provided by sources within multilayer optics: free-space and modal patterns,” J. Opt. Soc. Am. A 14, 3102–3113 (1997).
    [CrossRef]
  16. C. Amra, S. Maure, “Mutual coherence and conical pattern of sources optimally excited within multilayer optics,” J. Opt. Soc. Am. A 14, 3114–3124 (1997).
    [CrossRef]
  17. C. Amra, C. Grezes-Besset, L. Bruel, “Comparison of surface and bulk scattering in optical multilayers,” Appl. Opt. 32, 5492–5503 (1993).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

1997 (5)

T. Kawanishi, H. Ogura, Z. L. Wang, “Scattering of electromagnetic waves from a planar waveguide structure with a slightly 2D random surface,” Waves Random Media 7, 35–64 (1997).
[CrossRef]

T. Kawanishi, H. Ogura, Z. L. Wang, “Scattering of electromagnetic wave from a slightly random dielectric surface—Yoneda peak and Brewster angle in incoherent scattering,” Waves Random Media 7, 351–384 (1997).
[CrossRef]

T. A. Leskova, A. A. Maradudin, “X-ray scattering from a randomly rough surface,” Waves Random Media 7, 395–434 (1997).
[CrossRef]

C. Amra, S. Maure, “Electromagnetic power provided by sources within multilayer optics: free-space and modal patterns,” J. Opt. Soc. Am. A 14, 3102–3113 (1997).
[CrossRef]

C. Amra, S. Maure, “Mutual coherence and conical pattern of sources optimally excited within multilayer optics,” J. Opt. Soc. Am. A 14, 3114–3124 (1997).
[CrossRef]

1996 (1)

H. Ogura, Z. L. Wang, “Surface-plasmon mode on a random rough metal surface: enhanced backscattering and localization,” Phys. Rev. B 53, 10358–10371 (1996).
[CrossRef]

1995 (2)

H. Ogura, T. Kawanishi, N. Takahashi, Z. L. Wang, “Scattering of electromagnetic waves from a slightly random surface—reciprocal theorem, cross-polarization and backscattering enhancement,” Waves Random Media 5, 461–495 (1995).
[CrossRef]

Z. L. Wang, H. Ogura, N. Takahashi, “Enhanced scattering from a planar waveguide structure with a slightly rough boundary,” Phys. Rev. B 52, 6027–6041 (1995).
[CrossRef]

1994 (1)

V. Freilikher, M. Pustilnik, I. Yurkevich, “Wave scattering from a bounded medium with disorder,” Phys. Rev. A 193, 467–470 (1994).

1993 (2)

M. E. Knotts, K. A. O’Donnell, “Backscattering enhancement from a conducting surface with isotropic roughness,” Opt. Commun. 99, 1–6 (1993).
[CrossRef]

C. Amra, C. Grezes-Besset, L. Bruel, “Comparison of surface and bulk scattering in optical multilayers,” Appl. Opt. 32, 5492–5503 (1993).
[CrossRef] [PubMed]

1991 (1)

A. Ishimaru, J. S. Chen, P. Phu, K. Yoshitomi, “Numerical, analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement,” Waves Random Media 1, 91–107 (1991).
[CrossRef]

1990 (1)

Y. Q. Jin, M. Lax, “Backscattering enhancement from a randomly rough surface,” Phys. Rev. B 42, 9819–9829 (1990).
[CrossRef]

1988 (1)

S. K. Sinha, E. B. Sirota, S. Garoff, H. B. Stanley, “X-ray and neutron scattering from rough surfaces,” Phys. Rev. B 38, 2997–2311 (1988).
[CrossRef]

1985 (2)

1980 (1)

1965 (1)

O. J. Guentert, “Study of the anomalous surface reflection of x rays,” J. Appl. Phys. 36, 1361–1366 (1965).
[CrossRef]

Amra, C.

Bennett, J. M.

Bruel, L.

Celli, V.

Chen, J. S.

A. Ishimaru, J. S. Chen, P. Phu, K. Yoshitomi, “Numerical, analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement,” Waves Random Media 1, 91–107 (1991).
[CrossRef]

Elson, J. M.

Freilikher, V.

V. Freilikher, M. Pustilnik, I. Yurkevich, “Wave scattering from a bounded medium with disorder,” Phys. Rev. A 193, 467–470 (1994).

Garoff, S.

S. K. Sinha, E. B. Sirota, S. Garoff, H. B. Stanley, “X-ray and neutron scattering from rough surfaces,” Phys. Rev. B 38, 2997–2311 (1988).
[CrossRef]

Grezes-Besset, C.

Guentert, O. J.

O. J. Guentert, “Study of the anomalous surface reflection of x rays,” J. Appl. Phys. 36, 1361–1366 (1965).
[CrossRef]

Ishimaru, A.

A. Ishimaru, J. S. Chen, P. Phu, K. Yoshitomi, “Numerical, analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement,” Waves Random Media 1, 91–107 (1991).
[CrossRef]

Jin, Y. Q.

Y. Q. Jin, M. Lax, “Backscattering enhancement from a randomly rough surface,” Phys. Rev. B 42, 9819–9829 (1990).
[CrossRef]

Kawanishi, T.

T. Kawanishi, H. Ogura, Z. L. Wang, “Scattering of electromagnetic waves from a planar waveguide structure with a slightly 2D random surface,” Waves Random Media 7, 35–64 (1997).
[CrossRef]

T. Kawanishi, H. Ogura, Z. L. Wang, “Scattering of electromagnetic wave from a slightly random dielectric surface—Yoneda peak and Brewster angle in incoherent scattering,” Waves Random Media 7, 351–384 (1997).
[CrossRef]

H. Ogura, T. Kawanishi, N. Takahashi, Z. L. Wang, “Scattering of electromagnetic waves from a slightly random surface—reciprocal theorem, cross-polarization and backscattering enhancement,” Waves Random Media 5, 461–495 (1995).
[CrossRef]

Knotts, M. E.

M. E. Knotts, K. A. O’Donnell, “Backscattering enhancement from a conducting surface with isotropic roughness,” Opt. Commun. 99, 1–6 (1993).
[CrossRef]

Lax, M.

Y. Q. Jin, M. Lax, “Backscattering enhancement from a randomly rough surface,” Phys. Rev. B 42, 9819–9829 (1990).
[CrossRef]

Leskova, T. A.

T. A. Leskova, A. A. Maradudin, “X-ray scattering from a randomly rough surface,” Waves Random Media 7, 395–434 (1997).
[CrossRef]

Maradudin, A. A.

Marvin, A. M.

Maure, S.

McGrun, A. R.

McGurn, A. R.

O’Donnell, K. A.

M. E. Knotts, K. A. O’Donnell, “Backscattering enhancement from a conducting surface with isotropic roughness,” Opt. Commun. 99, 1–6 (1993).
[CrossRef]

Ogura, H.

T. Kawanishi, H. Ogura, Z. L. Wang, “Scattering of electromagnetic wave from a slightly random dielectric surface—Yoneda peak and Brewster angle in incoherent scattering,” Waves Random Media 7, 351–384 (1997).
[CrossRef]

T. Kawanishi, H. Ogura, Z. L. Wang, “Scattering of electromagnetic waves from a planar waveguide structure with a slightly 2D random surface,” Waves Random Media 7, 35–64 (1997).
[CrossRef]

H. Ogura, Z. L. Wang, “Surface-plasmon mode on a random rough metal surface: enhanced backscattering and localization,” Phys. Rev. B 53, 10358–10371 (1996).
[CrossRef]

H. Ogura, T. Kawanishi, N. Takahashi, Z. L. Wang, “Scattering of electromagnetic waves from a slightly random surface—reciprocal theorem, cross-polarization and backscattering enhancement,” Waves Random Media 5, 461–495 (1995).
[CrossRef]

Z. L. Wang, H. Ogura, N. Takahashi, “Enhanced scattering from a planar waveguide structure with a slightly rough boundary,” Phys. Rev. B 52, 6027–6041 (1995).
[CrossRef]

Phu, P.

A. Ishimaru, J. S. Chen, P. Phu, K. Yoshitomi, “Numerical, analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement,” Waves Random Media 1, 91–107 (1991).
[CrossRef]

Pustilnik, M.

V. Freilikher, M. Pustilnik, I. Yurkevich, “Wave scattering from a bounded medium with disorder,” Phys. Rev. A 193, 467–470 (1994).

Rahn, J. P.

Sinha, S. K.

S. K. Sinha, E. B. Sirota, S. Garoff, H. B. Stanley, “X-ray and neutron scattering from rough surfaces,” Phys. Rev. B 38, 2997–2311 (1988).
[CrossRef]

Sirota, E. B.

S. K. Sinha, E. B. Sirota, S. Garoff, H. B. Stanley, “X-ray and neutron scattering from rough surfaces,” Phys. Rev. B 38, 2997–2311 (1988).
[CrossRef]

Stanley, H. B.

S. K. Sinha, E. B. Sirota, S. Garoff, H. B. Stanley, “X-ray and neutron scattering from rough surfaces,” Phys. Rev. B 38, 2997–2311 (1988).
[CrossRef]

Takahashi, N.

Z. L. Wang, H. Ogura, N. Takahashi, “Enhanced scattering from a planar waveguide structure with a slightly rough boundary,” Phys. Rev. B 52, 6027–6041 (1995).
[CrossRef]

H. Ogura, T. Kawanishi, N. Takahashi, Z. L. Wang, “Scattering of electromagnetic waves from a slightly random surface—reciprocal theorem, cross-polarization and backscattering enhancement,” Waves Random Media 5, 461–495 (1995).
[CrossRef]

Wang, Z. L.

T. Kawanishi, H. Ogura, Z. L. Wang, “Scattering of electromagnetic wave from a slightly random dielectric surface—Yoneda peak and Brewster angle in incoherent scattering,” Waves Random Media 7, 351–384 (1997).
[CrossRef]

T. Kawanishi, H. Ogura, Z. L. Wang, “Scattering of electromagnetic waves from a planar waveguide structure with a slightly 2D random surface,” Waves Random Media 7, 35–64 (1997).
[CrossRef]

H. Ogura, Z. L. Wang, “Surface-plasmon mode on a random rough metal surface: enhanced backscattering and localization,” Phys. Rev. B 53, 10358–10371 (1996).
[CrossRef]

H. Ogura, T. Kawanishi, N. Takahashi, Z. L. Wang, “Scattering of electromagnetic waves from a slightly random surface—reciprocal theorem, cross-polarization and backscattering enhancement,” Waves Random Media 5, 461–495 (1995).
[CrossRef]

Z. L. Wang, H. Ogura, N. Takahashi, “Enhanced scattering from a planar waveguide structure with a slightly rough boundary,” Phys. Rev. B 52, 6027–6041 (1995).
[CrossRef]

Yoshitomi, K.

A. Ishimaru, J. S. Chen, P. Phu, K. Yoshitomi, “Numerical, analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement,” Waves Random Media 1, 91–107 (1991).
[CrossRef]

Yurkevich, I.

V. Freilikher, M. Pustilnik, I. Yurkevich, “Wave scattering from a bounded medium with disorder,” Phys. Rev. A 193, 467–470 (1994).

Appl. Opt. (2)

J. Appl. Phys. (1)

O. J. Guentert, “Study of the anomalous surface reflection of x rays,” J. Appl. Phys. 36, 1361–1366 (1965).
[CrossRef]

J. Opt. Soc. Am. A (3)

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

Opt. Commun. (1)

M. E. Knotts, K. A. O’Donnell, “Backscattering enhancement from a conducting surface with isotropic roughness,” Opt. Commun. 99, 1–6 (1993).
[CrossRef]

Phys. Rev. A (1)

V. Freilikher, M. Pustilnik, I. Yurkevich, “Wave scattering from a bounded medium with disorder,” Phys. Rev. A 193, 467–470 (1994).

Phys. Rev. B (4)

Z. L. Wang, H. Ogura, N. Takahashi, “Enhanced scattering from a planar waveguide structure with a slightly rough boundary,” Phys. Rev. B 52, 6027–6041 (1995).
[CrossRef]

S. K. Sinha, E. B. Sirota, S. Garoff, H. B. Stanley, “X-ray and neutron scattering from rough surfaces,” Phys. Rev. B 38, 2997–2311 (1988).
[CrossRef]

Y. Q. Jin, M. Lax, “Backscattering enhancement from a randomly rough surface,” Phys. Rev. B 42, 9819–9829 (1990).
[CrossRef]

H. Ogura, Z. L. Wang, “Surface-plasmon mode on a random rough metal surface: enhanced backscattering and localization,” Phys. Rev. B 53, 10358–10371 (1996).
[CrossRef]

Waves Random Media (5)

H. Ogura, T. Kawanishi, N. Takahashi, Z. L. Wang, “Scattering of electromagnetic waves from a slightly random surface—reciprocal theorem, cross-polarization and backscattering enhancement,” Waves Random Media 5, 461–495 (1995).
[CrossRef]

T. Kawanishi, H. Ogura, Z. L. Wang, “Scattering of electromagnetic waves from a planar waveguide structure with a slightly 2D random surface,” Waves Random Media 7, 35–64 (1997).
[CrossRef]

A. Ishimaru, J. S. Chen, P. Phu, K. Yoshitomi, “Numerical, analytical, and experimental studies of scattering from very rough surfaces and backscattering enhancement,” Waves Random Media 1, 91–107 (1991).
[CrossRef]

T. A. Leskova, A. A. Maradudin, “X-ray scattering from a randomly rough surface,” Waves Random Media 7, 395–434 (1997).
[CrossRef]

T. Kawanishi, H. Ogura, Z. L. Wang, “Scattering of electromagnetic wave from a slightly random dielectric surface—Yoneda peak and Brewster angle in incoherent scattering,” Waves Random Media 7, 351–384 (1997).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Scattering structure from a dielectric rough interface.

Fig. 2
Fig. 2

Scattering from a random surface on (a) a plane of a prism or on (b) a rectangular parallelepiped glass plate. In the case of a prism shown in (a), the scattered wave of whichever angle is larger than the critical angle can be measured by a detector located in the air side, while it cannot be measured in the case of a rectangular parallelepiped glass plate, shown in (b).

Fig. 3
Fig. 3

Glass-side scattering profile. Incidence angle θ0=30° (glass side). There are peaks due to the quasi-anomalous scattering at θs=41° in both s-polarized and p-polarized components.

Fig. 4
Fig. 4

Air-side scattering profile. Incidence angle θ0=60° (air side). There is a dip due to Brewster’s scattering angle at θs50° in p-polarized components.

Fig. 5
Fig. 5

Glass-side scattering profile. Incidence angle θ0=0° (air side). In the s-polarized component the quasi-anomalous scattering peak exists. In the p-polarized component the peak vanishes owing to Brewster’s scattering angle, and there is a dip.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

sin θc=n(n<1)n-1(n>1),
θs=ΘB1sin-1n sintan-11n2 tan[sin-1(n-1 sin θ0)],
ϕs=0°,
θs=ΘB2sin-1n-1 sintan-11tan[sin-1(n-1 sin θ0)],
ϕs=180°.

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