Abstract

We employ Monte Carlo techniques based on the reduced Rayleigh equations to study an enhanced specular peak that appears in the light scattered from weakly rough metal surfaces. This peak is not associated with the specular reflection but instead appears, with finite angular width, at the specular angle of the mean diffusely scattered intensity. As is the case with backscattering enhancement, the specular peak arises from the interference of contributions of multiple-scattering processes related to surface plasmon polariton excitation. We demonstrate that the specular peak is seen clearly for surface roughness that has a conventional Gaussian power spectrum. Further, we show that the peak appears more distinctly for roughness whose power spectrum has a new rectangular form, which is proposed here with the intent of better isolation of the scattering processes essential to the specular peak. Finally, for a pair of rough surfaces that have appropriately correlated surface roughness, it is found that the cross correlation of scattered amplitudes presents a well-isolated specular peak, which directly demonstrates the constructive interference that produces the effect.

© 2003 Optical Society of America

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References

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  1. J. A. DeSanto, G. S. Brown, “Analytical techniques for multiple scattering from rough surfaces,” in Progress in Optics, Vol. XXIII, E. Wolf, ed. (Elsevier, Amsterdam, 1986), pp. 1–62.
  2. A. G. Voronovich, Wave Scattering from Rough Surfaces (Springer-Verlag, Berlin, 1994).
  3. A. A. Maradudin, E. R. Méndez, “Scattering by surfaces and phase screens,” in Scattering, R. Pike, P. Sabatier, eds. (Academic, London, 2002), pp. 864–893.
  4. A. R. McGurn, A. A. Maradudin, V. Celli, “Localization effects in the scattering of light from a randomly rough grating,” Phys. Rev. B 31, 4866–4871 (1985).
    [CrossRef]
  5. E. R. Méndez, K. A. O’Donnell, “Observation of enhanced backscattering and strong depolarization in scattering from Gaussian random surfaces,” Opt. Commun. 61, 91–95 (1987).
    [CrossRef]
  6. 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]
  7. M. E. Knotts, T. R. Michel, K. A. O’Donnell, “Comparisons of theory and experiment in light scattering from a randomly rough surface,” J. Opt. Soc. Am. A 9, 1822–1831 (1992).
    [CrossRef]
  8. 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]
  9. A. A. Maradudin, E. R. Méndez, “Enhanced backscattering of light from weakly rough, random metal surfaces,” Appl. Opt. 32, 3335–3343 (1993).
    [CrossRef] [PubMed]
  10. C. S. West, K. A. O’Donnell, “Observations of backscattering enhancement from polaritons on a rough metal surface,” J. Opt. Soc. Am. A 12, 390–397 (1995).
    [CrossRef]
  11. C. S. West, K. A. O’Donnell, “Scattering by plasmon polaritons on a metal surface with a detuned roughness spectrum,” Opt. Lett. 21, 1–3 (1996).
    [CrossRef] [PubMed]
  12. K. A. O’Donnell, C. S. West, E. R. Méndez, “Backscattering enhancement from polariton–polariton coupling on a rough metal surface,” Phys. Rev. B 57, 13209–13219 (1998).
    [CrossRef]
  13. A. R. McGurn, A. A. Maradudin, “Localization effects in the elastic scattering of light from a randomly rough surface,” J. Opt. Soc. Am. B 4, 910–926 (1987).
    [CrossRef]
  14. A. R. McGurn, A. A. Maradudin, “Perturbation theory results for the diffuse scattering of light from two-dimensional randomly rough metal surfaces,” Waves Random Media 6, 251–267 (1996).
    [CrossRef]
  15. K. A. O’Donnell, “High-order perturbation theory for light scattering from a rough metal surface,” J. Opt. Soc. Am. A 18, 1507–1518 (2001).
    [CrossRef]
  16. M. Nieto-Vesperinas, J. M. Soto-Crespo, “Connection between blazes from gratings and enhancements from random rough surfaces,” Phys. Rev. B 39, 8193–8197 (1989).
    [CrossRef]
  17. E. R. Méndez, M. A. Ponce, V. Ruiz-Cortés, Z. Ghu, “Coherent effects in the scattering of light from random surfaces with symmetry,” Opt. Lett. 16, 123–125 (1991).
    [CrossRef]
  18. See, for example, J. W. Goodman, Statistical Optics (Wiley, New York, 1985).
  19. A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (N.Y.) 203, 255–307 (1990).
    [CrossRef]
  20. G. C. Brown, V. Celli, M. Coopersmith, M. Haller, “Unitary and reciprocal expansions in the theory of light scattering from a grating,” Surf. Sci. 129, 507–515 (1983).
    [CrossRef]
  21. T. R. Michel, “Resonant light scattering from weakly rough random surfaces and imperfect gratings,” J. Opt. Soc. Am. A 11, 1874–1885 (1994).
    [CrossRef]
  22. D. S. Saxon, “Tensor scattering matrix for the electromagnetic field,” Phys. Rev. 100, 1771–1775 (1955).
    [CrossRef]
  23. P. W. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]
  24. A. A. Maradudin, A. R. McGurn, E. R. Méndez, “Surface plasmon polariton mechanism for enhanced backscattering of light from one-dimensional randomly rough metal surfaces,” J. Opt. Soc. Am. A 12, 2500–2506 (1995).
    [CrossRef]
  25. P. Tran, V. Celli, “Monte Carlo calculation of backscattering enhancement for a randomly rough grating,” J. Opt. Soc. Am. A 5, 1635–1637 (1989).
    [CrossRef]

2001 (1)

1998 (1)

K. A. O’Donnell, C. S. West, E. R. Méndez, “Backscattering enhancement from polariton–polariton coupling on a rough metal surface,” Phys. Rev. B 57, 13209–13219 (1998).
[CrossRef]

1996 (2)

A. R. McGurn, A. A. Maradudin, “Perturbation theory results for the diffuse scattering of light from two-dimensional randomly rough metal surfaces,” Waves Random Media 6, 251–267 (1996).
[CrossRef]

C. S. West, K. A. O’Donnell, “Scattering by plasmon polaritons on a metal surface with a detuned roughness spectrum,” Opt. Lett. 21, 1–3 (1996).
[CrossRef] [PubMed]

1995 (2)

1994 (1)

1993 (1)

1992 (1)

1991 (1)

1990 (1)

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

1989 (2)

M. Nieto-Vesperinas, J. M. Soto-Crespo, “Connection between blazes from gratings and enhancements from random rough surfaces,” Phys. Rev. B 39, 8193–8197 (1989).
[CrossRef]

P. Tran, V. Celli, “Monte Carlo calculation of backscattering enhancement for a randomly rough grating,” J. Opt. Soc. Am. A 5, 1635–1637 (1989).
[CrossRef]

1987 (3)

1985 (2)

A. R. McGurn, A. A. Maradudin, V. Celli, “Localization effects in the scattering of light from a randomly rough grating,” Phys. Rev. B 31, 4866–4871 (1985).
[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]

1983 (1)

G. C. Brown, V. Celli, M. Coopersmith, M. Haller, “Unitary and reciprocal expansions in the theory of light scattering from a grating,” Surf. Sci. 129, 507–515 (1983).
[CrossRef]

1972 (1)

P. W. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

1955 (1)

D. S. Saxon, “Tensor scattering matrix for the electromagnetic field,” Phys. Rev. 100, 1771–1775 (1955).
[CrossRef]

Brown, G. C.

G. C. Brown, V. Celli, M. Coopersmith, M. Haller, “Unitary and reciprocal expansions in the theory of light scattering from a grating,” Surf. Sci. 129, 507–515 (1983).
[CrossRef]

Brown, G. S.

J. A. DeSanto, G. S. Brown, “Analytical techniques for multiple scattering from rough surfaces,” in Progress in Optics, Vol. XXIII, E. Wolf, ed. (Elsevier, Amsterdam, 1986), pp. 1–62.

Celli, V.

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

A. R. McGurn, A. A. Maradudin, V. Celli, “Localization effects in the scattering of light from a randomly rough grating,” Phys. Rev. B 31, 4866–4871 (1985).
[CrossRef]

G. C. Brown, V. Celli, M. Coopersmith, M. Haller, “Unitary and reciprocal expansions in the theory of light scattering from a grating,” Surf. Sci. 129, 507–515 (1983).
[CrossRef]

Christy, R. W.

P. W. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Coopersmith, M.

G. C. Brown, V. Celli, M. Coopersmith, M. Haller, “Unitary and reciprocal expansions in the theory of light scattering from a grating,” Surf. Sci. 129, 507–515 (1983).
[CrossRef]

DeSanto, J. A.

J. A. DeSanto, G. S. Brown, “Analytical techniques for multiple scattering from rough surfaces,” in Progress in Optics, Vol. XXIII, E. Wolf, ed. (Elsevier, Amsterdam, 1986), pp. 1–62.

Ghu, Z.

Goodman, J. W.

See, for example, J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

Haller, M.

G. C. Brown, V. Celli, M. Coopersmith, M. Haller, “Unitary and reciprocal expansions in the theory of light scattering from a grating,” Surf. Sci. 129, 507–515 (1983).
[CrossRef]

Johnson, P. W.

P. W. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Knotts, M. E.

Maradudin, A. A.

A. R. McGurn, A. A. Maradudin, “Perturbation theory results for the diffuse scattering of light from two-dimensional randomly rough metal surfaces,” Waves Random Media 6, 251–267 (1996).
[CrossRef]

A. A. Maradudin, A. R. McGurn, E. R. Méndez, “Surface plasmon polariton mechanism for enhanced backscattering of light from one-dimensional randomly rough metal surfaces,” J. Opt. Soc. Am. A 12, 2500–2506 (1995).
[CrossRef]

A. A. Maradudin, E. R. Méndez, “Enhanced backscattering of light from weakly rough, random metal surfaces,” Appl. Opt. 32, 3335–3343 (1993).
[CrossRef] [PubMed]

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

A. R. McGurn, A. A. Maradudin, “Localization effects in the elastic scattering of light from a randomly rough surface,” J. Opt. Soc. Am. B 4, 910–926 (1987).
[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]

A. R. McGurn, A. A. Maradudin, V. Celli, “Localization effects in the scattering of light from a randomly rough grating,” Phys. Rev. B 31, 4866–4871 (1985).
[CrossRef]

A. A. Maradudin, E. R. Méndez, “Scattering by surfaces and phase screens,” in Scattering, R. Pike, P. Sabatier, eds. (Academic, London, 2002), pp. 864–893.

Marvin, A. M.

McGurn, A. R.

A. R. McGurn, A. A. Maradudin, “Perturbation theory results for the diffuse scattering of light from two-dimensional randomly rough metal surfaces,” Waves Random Media 6, 251–267 (1996).
[CrossRef]

A. A. Maradudin, A. R. McGurn, E. R. Méndez, “Surface plasmon polariton mechanism for enhanced backscattering of light from one-dimensional randomly rough metal surfaces,” J. Opt. Soc. Am. A 12, 2500–2506 (1995).
[CrossRef]

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

A. R. McGurn, A. A. Maradudin, “Localization effects in the elastic scattering of light from a randomly rough surface,” J. Opt. Soc. Am. B 4, 910–926 (1987).
[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]

A. R. McGurn, A. A. Maradudin, V. Celli, “Localization effects in the scattering of light from a randomly rough grating,” Phys. Rev. B 31, 4866–4871 (1985).
[CrossRef]

Méndez, E. R.

K. A. O’Donnell, C. S. West, E. R. Méndez, “Backscattering enhancement from polariton–polariton coupling on a rough metal surface,” Phys. Rev. B 57, 13209–13219 (1998).
[CrossRef]

A. A. Maradudin, A. R. McGurn, E. R. Méndez, “Surface plasmon polariton mechanism for enhanced backscattering of light from one-dimensional randomly rough metal surfaces,” J. Opt. Soc. Am. A 12, 2500–2506 (1995).
[CrossRef]

A. A. Maradudin, E. R. Méndez, “Enhanced backscattering of light from weakly rough, random metal surfaces,” Appl. Opt. 32, 3335–3343 (1993).
[CrossRef] [PubMed]

E. R. Méndez, M. A. Ponce, V. Ruiz-Cortés, Z. Ghu, “Coherent effects in the scattering of light from random surfaces with symmetry,” Opt. Lett. 16, 123–125 (1991).
[CrossRef]

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

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

A. A. Maradudin, E. R. Méndez, “Scattering by surfaces and phase screens,” in Scattering, R. Pike, P. Sabatier, eds. (Academic, London, 2002), pp. 864–893.

Michel, T.

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

Michel, T. R.

Nieto-Vesperinas, M.

M. Nieto-Vesperinas, J. M. Soto-Crespo, “Connection between blazes from gratings and enhancements from random rough surfaces,” Phys. Rev. B 39, 8193–8197 (1989).
[CrossRef]

O’Donnell, K. A.

Ponce, M. A.

Ruiz-Cortés, V.

Saxon, D. S.

D. S. Saxon, “Tensor scattering matrix for the electromagnetic field,” Phys. Rev. 100, 1771–1775 (1955).
[CrossRef]

Soto-Crespo, J. M.

M. Nieto-Vesperinas, J. M. Soto-Crespo, “Connection between blazes from gratings and enhancements from random rough surfaces,” Phys. Rev. B 39, 8193–8197 (1989).
[CrossRef]

Tran, P.

Voronovich, A. G.

A. G. Voronovich, Wave Scattering from Rough Surfaces (Springer-Verlag, Berlin, 1994).

West, C. S.

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

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

Appl. Opt. (1)

J. Opt. Soc. Am. A (8)

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

Opt. Commun. (1)

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

Opt. Lett. (2)

Phys. Rev. (1)

D. S. Saxon, “Tensor scattering matrix for the electromagnetic field,” Phys. Rev. 100, 1771–1775 (1955).
[CrossRef]

Phys. Rev. B (4)

P. W. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

A. R. McGurn, A. A. Maradudin, V. Celli, “Localization effects in the scattering of light from a randomly rough grating,” Phys. Rev. B 31, 4866–4871 (1985).
[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 (1989).
[CrossRef]

K. A. O’Donnell, C. S. West, E. R. Méndez, “Backscattering enhancement from polariton–polariton coupling on a rough metal surface,” Phys. Rev. B 57, 13209–13219 (1998).
[CrossRef]

Surf. Sci. (1)

G. C. Brown, V. Celli, M. Coopersmith, M. Haller, “Unitary and reciprocal expansions in the theory of light scattering from a grating,” Surf. Sci. 129, 507–515 (1983).
[CrossRef]

Waves Random Media (1)

A. R. McGurn, A. A. Maradudin, “Perturbation theory results for the diffuse scattering of light from two-dimensional randomly rough metal surfaces,” Waves Random Media 6, 251–267 (1996).
[CrossRef]

Other (4)

See, for example, J. W. Goodman, Statistical Optics (Wiley, New York, 1985).

J. A. DeSanto, G. S. Brown, “Analytical techniques for multiple scattering from rough surfaces,” in Progress in Optics, Vol. XXIII, E. Wolf, ed. (Elsevier, Amsterdam, 1986), pp. 1–62.

A. G. Voronovich, Wave Scattering from Rough Surfaces (Springer-Verlag, Berlin, 1994).

A. A. Maradudin, E. R. Méndez, “Scattering by surfaces and phase screens,” in Scattering, R. Pike, P. Sabatier, eds. (Academic, London, 2002), pp. 864–893.

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Figures (8)

Fig. 1
Fig. 1

(A) Scattering process involving surface waves that is essential to specular peak formation. (B) Proposed form of the surface power spectrum with rectangles centered at ±ksp and ±2ksp.

Fig. 2
Fig. 2

(A) For θi=9°, the mean diffuse intensity of a rough surface with =-7.5+0.24i, σ=3.5 nm, G2/G1=1.5, Δ1=(ω/c)sin(17°), and Δ2=0.1(ω/c). Enhancement peaks appear at both specular (θs=θi) and backscattering (θs=-θi) angles. (B) Result obtained with the spectral windows at ±2ksp removed; the specular enhancement vanishes.

Fig. 3
Fig. 3

For θi as indicated, the mean diffuse intensity with other parameters as in Fig. 2(A). Peaks persist both at specular (θs=θi) and backscattering (θs=-θi) angles, except for θi=20°, where the incident polariton coupling breaks down.

Fig. 4
Fig. 4

For σ as indicated, the mean diffuse intensity with other parameters as in Fig. 2(A) (solid curves; note differing vertical scales). The dashed curve in the upper plot is a comparison with the eighth-order perturbation theory of Ref. 15.

Fig. 5
Fig. 5

For θi=10°, the mean diffuse intensity of a rough metal surface having the Gaussian roughness spectrum G(k)=πaσ2 exp[-(ak/2)2], with σ=10 nm, a=40 nm, and =-7.5+0.24i.

Fig. 6
Fig. 6

Two scattering paths on a rough surface that have zero phase difference for outward coupling to the specular angle. Arrows below the surface denote polariton coupling.

Fig. 7
Fig. 7

Possible distributions of bumps along two otherwise flat metal surfaces. Open symbols represent bumps intended to allow inward–outward polariton coupling. Solid symbols denote bumps intended to produce counterpropagating polariton coupling.

Fig. 8
Fig. 8

Upper plot: For θi=9° and surface parameters analogous to Fig. 2(A), mean diffuse intensity I(θs) compared with the amplitude correlation function A*(θs)A(θs) for two surfaces that have different realizations of ζ1(x). Lower plot: amplitude correlation A*(θs)A(θs) for two surfaces that have different realizations of ζ2(x).

Equations (13)

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

-ksp=k+kr1,
+ksp=-ksp+kr2,
-ksp=+ksp+kr3.
q=-ksp+kr4,
R(q|k)=m=-2πδ(q-qm)Rm,
qm=k+2πmL=ωcsin θm,
I(θm)=Lλcos2 θmcos θ0|Rm|2.
[kpn-α(pn)α0(k)]Iˆ[α(pn)+α0(k)|pn-k]α(pn)+α0(k)=-m=-[pnqm+α(pn)α0(qm)]×Iˆ[α(pn)-α0(qm)|pn-qm]α(pn)-α0(qm)Rm,
Iˆ(γ|Q)=1L-L/2L/2dx exp(-iQx)exp[-iγζ(x)],
α0(k)=ω2c2-k21/2,α(q)= ω2c2-q21/2,
ϕA=kx1-qx4+β14,
ϕB=kx1-qx4+β14.
ΔϕBA=(q-k)(x1-x1).

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