Abstract

We present a new approximate theory of scattering by randomly rough surfaces. The selvedge region is considered to be a layer with fluctuating index. A mean-field theory is used to derive the diffuse intensity. Comparisons with Monte Carlo simulations based on surface integral equations show that the technique can be used for rms heights as large as λ/2 and for any type of slope for a dielectric constant of 2.25. However, the accuracy decreases with increasing dielectric constant.

© 1998 Optical Society of America

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References

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  1. A. G. Voronovich, Wave Scattering from Rough Surfaces (Springer-Verlag, Berlin, 1994).
  2. M. Nieto–Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991).
  3. J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Hilger, London, 1991).
  4. S. Dietrich, A. Haase, “Scattering of x-rays and neutrons at interfaces,” Phys. Rep. 260, 1–138 (1995).
    [CrossRef]
  5. J.-J. Greffet, “Backscattering of s-polarized light from a cloud of small particles above a dielectric substrate,” Waves Random Media 1, S65–S74 (1991).
    [CrossRef]
  6. J. E. Sipe, “New Green function formalism for surface optics,” J. Opt. Soc. Am. B 4, 481–489 (1987).
    [CrossRef]
  7. 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]
  8. A. Sentenac, G. Toso, M. Saillard, “Study of coherent and incoherent scattering from one-dimensional rough surfaces with a mean-field theory,” J. Opt. Soc. Am. A (to be published).

1995 (1)

S. Dietrich, A. Haase, “Scattering of x-rays and neutrons at interfaces,” Phys. Rep. 260, 1–138 (1995).
[CrossRef]

1991 (1)

J.-J. Greffet, “Backscattering of s-polarized light from a cloud of small particles above a dielectric substrate,” Waves Random Media 1, S65–S74 (1991).
[CrossRef]

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]

1987 (1)

Dietrich, S.

S. Dietrich, A. Haase, “Scattering of x-rays and neutrons at interfaces,” Phys. Rep. 260, 1–138 (1995).
[CrossRef]

Greffet, J.-J.

J.-J. Greffet, “Backscattering of s-polarized light from a cloud of small particles above a dielectric substrate,” Waves Random Media 1, S65–S74 (1991).
[CrossRef]

Haase, A.

S. Dietrich, A. Haase, “Scattering of x-rays and neutrons at interfaces,” Phys. Rep. 260, 1–138 (1995).
[CrossRef]

Maradudin, A. A.

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]

McGurn, A. R.

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]

Méndez, E. R.

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.

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]

Nieto–Vesperinas, M.

M. Nieto–Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991).

Ogilvy, J. A.

J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Hilger, London, 1991).

Saillard, M.

A. Sentenac, G. Toso, M. Saillard, “Study of coherent and incoherent scattering from one-dimensional rough surfaces with a mean-field theory,” J. Opt. Soc. Am. A (to be published).

Sentenac, A.

A. Sentenac, G. Toso, M. Saillard, “Study of coherent and incoherent scattering from one-dimensional rough surfaces with a mean-field theory,” J. Opt. Soc. Am. A (to be published).

Sipe, J. E.

Toso, G.

A. Sentenac, G. Toso, M. Saillard, “Study of coherent and incoherent scattering from one-dimensional rough surfaces with a mean-field theory,” J. Opt. Soc. Am. A (to be published).

Voronovich, A. G.

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

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]

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

Phys. Rep. (1)

S. Dietrich, A. Haase, “Scattering of x-rays and neutrons at interfaces,” Phys. Rep. 260, 1–138 (1995).
[CrossRef]

Waves Random Media (1)

J.-J. Greffet, “Backscattering of s-polarized light from a cloud of small particles above a dielectric substrate,” Waves Random Media 1, S65–S74 (1991).
[CrossRef]

Other (4)

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

M. Nieto–Vesperinas, Scattering and Diffraction in Physical Optics (Wiley, New York, 1991).

J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces (Hilger, London, 1991).

A. Sentenac, G. Toso, M. Saillard, “Study of coherent and incoherent scattering from one-dimensional rough surfaces with a mean-field theory,” J. Opt. Soc. Am. A (to be published).

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Figures (6)

Fig. 1
Fig. 1

Schematic view of the system.

Fig. 2
Fig. 2

Diffuse reflected intensity, θi=62°, n=1.5, and a=λ. The markers indicate the numerical simulation.

Fig. 3
Fig. 3

Diffuse reflected intensity, θi=0°, δ=0.2λ, and n=1.5.

Fig. 4
Fig. 4

Diffuse reflected intensity, θi=62°, δ=0.2λ, and a=λ.

Fig. 5
Fig. 5

Diffuse reflected intensity, θi=0°, δ=0.2λ, a=0.2λ, and n=1.5.

Fig. 6
Fig. 6

Diffuse reflected intensity, θi=0°, δ=0.5λ, a=0.3λ, and n=1.5.

Equations (14)

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ΔE(x, z)+ref(z)k02E(x, z)=S(x, z)-[(x, z)-ref(z)]k02E(x, z)
ΔG(x-x, z, z)+ref(z)k02G(x-x, z, z)=δ(x-x)δ(z-z)
E=GS-GL1E=E0-GL1E
Gf(x, z)=G(x-x, z, z)f(x, z)dxdz.
EE0-GL1E0.
EE*E0E0*+GL1E0G*L1*E0*.
p1(h)=1δ2πexp-h22δ2.
p2(h, h, r)=12πδ21-C2(r)×exp-h2+h2-2hhC(r)2δ2[1-C2(r)],
Pa(z)=-zp1(h)dh;Pb(z)=z+p1(h)dh.
(z)=Pa(z)a+Pb(z)b.
(z)=12a+b+(a-b)erfz2δ.
Paa(r, z, z)=-z-zp2(r, h, h)dhdh,
L(r, z, z)=[Paa(r, z, z)-Pa(z)Pa(z)]aa+[Pbb(r, z, z)-Pb(z)Pb(z)]bb+[Pab(r, z, z)-Pa(z)Pb(z)]ab+[Pba(r, z, z)-Pb(z)Pa(z)]ba.
L(r, z, z)=A22πδ-z exp-h22δ2×erfz-C(r)hδ2-2C2(r)-erfz2δdh,

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