Abstract

We present a method for numerically generating a one-dimensional random surface, defined by the equation x3=ζx1, that suppresses single-scattering processes in the scattering of light from the surface within a specified range of scattering angles. Rigorous numerical calculations of the scattering of light from surfaces generated by this approach show that the single-scattering contribution to the mean scattered intensity is indeed suppressed within that range of angles.

© 1999 Optical Society of America

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References

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  1. A. R. McGurn, A. A. Maradudin, and V. Celli, Phys. Rev. B 31, 4866 (1985); A. A. Maradudin and E. R. Méndez, Appl. Opt. 32, 3335 (1993).
    [Crossref] [PubMed]
  2. A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Méndez, Ann. Phys. (N.Y.) 203, 255 (1990); A. Sentenac and A. A. Maradudin, Waves Random Media 3, 343 (1993).
    [Crossref]
  3. C. S. West and K. A. O’Donnell, J. Opt. Soc. Am. A 12, 390 (1995).
    [Crossref]
  4. E. R. Méndez, G. Martínez-Niconoff, A. A. Maradudin, and T. A. Leskova, Proc. SPIE 3426, 2 (1998).
    [Crossref]
  5. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran, 2nd ed. (Cambridge U. Press, Cambridge, 1992), pp. 281–282.
  6. A. A. Maradudin, E. R. Méndez, and T. Michel, in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas and J. C. Dainty, eds. (North-Holland, Amsterdam, 1990), p. 157.

1998 (1)

E. R. Méndez, G. Martínez-Niconoff, A. A. Maradudin, and T. A. Leskova, Proc. SPIE 3426, 2 (1998).
[Crossref]

1995 (1)

1990 (1)

A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Méndez, Ann. Phys. (N.Y.) 203, 255 (1990); A. Sentenac and A. A. Maradudin, Waves Random Media 3, 343 (1993).
[Crossref]

1985 (1)

A. R. McGurn, A. A. Maradudin, and V. Celli, Phys. Rev. B 31, 4866 (1985); A. A. Maradudin and E. R. Méndez, Appl. Opt. 32, 3335 (1993).
[Crossref] [PubMed]

Celli, V.

A. R. McGurn, A. A. Maradudin, and V. Celli, Phys. Rev. B 31, 4866 (1985); A. A. Maradudin and E. R. Méndez, Appl. Opt. 32, 3335 (1993).
[Crossref] [PubMed]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran, 2nd ed. (Cambridge U. Press, Cambridge, 1992), pp. 281–282.

Leskova, T. A.

E. R. Méndez, G. Martínez-Niconoff, A. A. Maradudin, and T. A. Leskova, Proc. SPIE 3426, 2 (1998).
[Crossref]

Maradudin, A. A.

E. R. Méndez, G. Martínez-Niconoff, A. A. Maradudin, and T. A. Leskova, Proc. SPIE 3426, 2 (1998).
[Crossref]

A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Méndez, Ann. Phys. (N.Y.) 203, 255 (1990); A. Sentenac and A. A. Maradudin, Waves Random Media 3, 343 (1993).
[Crossref]

A. R. McGurn, A. A. Maradudin, and V. Celli, Phys. Rev. B 31, 4866 (1985); A. A. Maradudin and E. R. Méndez, Appl. Opt. 32, 3335 (1993).
[Crossref] [PubMed]

A. A. Maradudin, E. R. Méndez, and T. Michel, in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas and J. C. Dainty, eds. (North-Holland, Amsterdam, 1990), p. 157.

Martínez-Niconoff, G.

E. R. Méndez, G. Martínez-Niconoff, A. A. Maradudin, and T. A. Leskova, Proc. SPIE 3426, 2 (1998).
[Crossref]

McGurn, A. R.

A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Méndez, Ann. Phys. (N.Y.) 203, 255 (1990); A. Sentenac and A. A. Maradudin, Waves Random Media 3, 343 (1993).
[Crossref]

A. R. McGurn, A. A. Maradudin, and V. Celli, Phys. Rev. B 31, 4866 (1985); A. A. Maradudin and E. R. Méndez, Appl. Opt. 32, 3335 (1993).
[Crossref] [PubMed]

Méndez, E. R.

E. R. Méndez, G. Martínez-Niconoff, A. A. Maradudin, and T. A. Leskova, Proc. SPIE 3426, 2 (1998).
[Crossref]

A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Méndez, Ann. Phys. (N.Y.) 203, 255 (1990); A. Sentenac and A. A. Maradudin, Waves Random Media 3, 343 (1993).
[Crossref]

A. A. Maradudin, E. R. Méndez, and T. Michel, in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas and J. C. Dainty, eds. (North-Holland, Amsterdam, 1990), p. 157.

Michel, T.

A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Méndez, Ann. Phys. (N.Y.) 203, 255 (1990); A. Sentenac and A. A. Maradudin, Waves Random Media 3, 343 (1993).
[Crossref]

A. A. Maradudin, E. R. Méndez, and T. Michel, in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas and J. C. Dainty, eds. (North-Holland, Amsterdam, 1990), p. 157.

O’Donnell, K. A.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran, 2nd ed. (Cambridge U. Press, Cambridge, 1992), pp. 281–282.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran, 2nd ed. (Cambridge U. Press, Cambridge, 1992), pp. 281–282.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran, 2nd ed. (Cambridge U. Press, Cambridge, 1992), pp. 281–282.

West, C. S.

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

A. A. Maradudin, T. Michel, A. R. McGurn, and E. R. Méndez, Ann. Phys. (N.Y.) 203, 255 (1990); A. Sentenac and A. A. Maradudin, Waves Random Media 3, 343 (1993).
[Crossref]

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

Phys. Rev. B (1)

A. R. McGurn, A. A. Maradudin, and V. Celli, Phys. Rev. B 31, 4866 (1985); A. A. Maradudin and E. R. Méndez, Appl. Opt. 32, 3335 (1993).
[Crossref] [PubMed]

Proc. SPIE (1)

E. R. Méndez, G. Martínez-Niconoff, A. A. Maradudin, and T. A. Leskova, Proc. SPIE 3426, 2 (1998).
[Crossref]

Other (2)

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran, 2nd ed. (Cambridge U. Press, Cambridge, 1992), pp. 281–282.

A. A. Maradudin, E. R. Méndez, and T. Michel, in Scattering in Volumes and Surfaces, M. Nieto-Vesperinas and J. C. Dainty, eds. (North-Holland, Amsterdam, 1990), p. 157.

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Figures (3)

Fig. 1
Fig. 1

One-dimensional random surface-profile function ζx1 obtained from Eq. (1) by the use of the pdf given by Eq. (6), together with a function sx1 defined by Eq. (2), with b=3λ,m=3,h=0.2, and θm=40.1°.

Fig. 2
Fig. 2

R/θsincoh calculated by a computer-simulation approach for the random surface displayed in Fig. 1, when spolarized light of wavelength λ is incident normally upon it. Short-dashed curve, geometrical-optics limit of the Kirchhoff approximation; long-dashed curve, Kirchhoff approximation; solid curve, result with all multiple-scattering contributions included.

Fig. 3
Fig. 3

R/θsincoh calculated by a computer-simulation approach for the case in which spolarized light of wavelength λ=612.7 nm is incident normally upon a one-dimensional random silver surface. The arrows indicate the positions of the angles ±θm.

Equations (8)

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ζx1=l=-clsx1-l2b,
sx1=0x1<-m+1b-m+1bh-hx1-m+1b<x1<-mb-bh-mb<x1<mb-m+1bh+hx1mb<x1<m+1b0m+1b<x1,
Rθs=12h1+cosθ0+θs2cos θ0cos θ0+cos θs3×fsin θ0-sin θshcos θ0+cos θs+fsin θs-sin θ0hcos θ0+cos θs,
Rθs=1+tan2θ22×f-1htanθs2+f1htanθs24h,
Rθs=00<θs<θmcos θs21-sin θmθm<θs<π/2,
fγ=00<γ<γm2h1+h2γm21-hγm21-h2γ21+h2γ22γm<γ<1h,
c=1h1+h2γm21-hγm2cos θm+2 lncosπ/4cosθm/2,
c2=2h21+h2γm21-hγm2π2-θm+tanθm2×1+cos2θm2-32.

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