Abstract

Measurements of a reduced Mueller matrix in backscattering from highly diffusive, dielectric samples are reported as a function of the angle of incidence. It was found that the off-diagonal terms depend greatly on the angle of incidence, increasing to a maximum near grazing incidence. We show that, despite a significant scattering originating in the bulk of such diffusive media, the nontrivial behavior of the off-diagonal Muller matrix is primarily due to surface scattering phenomena. The experimental data can be simply explained by assuming a random orientation of small particles and considering only double scattering in the plane of the surface.

© 2002 Optical Society of America

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References

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  20. I. V. Novikov, A. A. Maradudin, “The Stokes matrix in conical scattering from a one-dimensional perfectly conducting randomly rough surface,” Radio Sci. 34, 599–614 (1999).

2000 (1)

G. Popescu, C. Mujat, A. Dogariu, “Evidence of scattering anisotropy effects on boundary conditions of the diffusion equation,” Phys. Rev. E 61, 4523–4529 (2000).
[CrossRef]

1999 (3)

1998 (2)

1997 (1)

1996 (1)

1995 (1)

F. M. Ismagilov, “Polarization effects in backscattering by a particle near the interface,” Waves Random Media 5, 27–32 (1995).
[CrossRef]

1993 (4)

1992 (2)

1986 (1)

Asakura, T.

M. Dogariu, T. Asakura, “Polarization-dependent backscattering patterns from weakly scattering media,” J. Opt. (Paris) 24, 271–278 (1993).
[CrossRef]

Bickel, W.

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Boreman, G.

Brennan, M. J.

Brosseau, C.

C. Brosseau, Fundamentals of Polarized Light—a Statistical Optics Approach (Wiley, New York, 1998).

Carrieri, A. H.

Dogariu, A.

Dogariu, M.

M. Dogariu, T. Asakura, “Polarization-dependent backscattering patterns from weakly scattering media,” J. Opt. (Paris) 24, 271–278 (1993).
[CrossRef]

Eliyahu, D.

Freund, I.

Herzinger, C. M.

Hsu, J.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Oxford U. Press, New York, 1997).

Ismagilov, F. M.

F. M. Ismagilov, “Polarization effects in backscattering by a particle near the interface,” Waves Random Media 5, 27–32 (1995).
[CrossRef]

Jakeman, E.

Jensen, J. O.

Jordan, D. L.

Kattawar, G. W.

Knotts, M. E.

Kouzoubov, A.

Kutsche, C.

Lewis, G. D.

Likamwa, P.

Maradudin, A. A.

I. V. Novikov, A. A. Maradudin, “The Stokes matrix in conical scattering from a one-dimensional perfectly conducting randomly rough surface,” Radio Sci. 34, 599–614 (1999).

Michel, T. R.

Moreno, F.

Moudgil, B.

Mujat, C.

G. Popescu, C. Mujat, A. Dogariu, “Evidence of scattering anisotropy effects on boundary conditions of the diffusion equation,” Phys. Rev. E 61, 4523–4529 (2000).
[CrossRef]

Novikov, I. V.

I. V. Novikov, A. A. Maradudin, “The Stokes matrix in conical scattering from a one-dimensional perfectly conducting randomly rough surface,” Radio Sci. 34, 599–614 (1999).

O’Donnell, K. A.

Popescu, G.

G. Popescu, C. Mujat, A. Dogariu, “Evidence of scattering anisotropy effects on boundary conditions of the diffusion equation,” Phys. Rev. E 61, 4523–4529 (2000).
[CrossRef]

Rakovic, M. J.

Roberts, P. J.

Rosenbluh, M.

Schmitt, C. J.

Thomas, J. C.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), pp. 19–81.

Videen, G.

Williams, M. W.

Wolfe, W.

Appl. Opt. (6)

J. Opt. (Paris) (1)

M. Dogariu, T. Asakura, “Polarization-dependent backscattering patterns from weakly scattering media,” J. Opt. (Paris) 24, 271–278 (1993).
[CrossRef]

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

Opt. Lett. (2)

Phys. Rev. E (1)

G. Popescu, C. Mujat, A. Dogariu, “Evidence of scattering anisotropy effects on boundary conditions of the diffusion equation,” Phys. Rev. E 61, 4523–4529 (2000).
[CrossRef]

Radio Sci. (1)

I. V. Novikov, A. A. Maradudin, “The Stokes matrix in conical scattering from a one-dimensional perfectly conducting randomly rough surface,” Radio Sci. 34, 599–614 (1999).

Waves Random Media (1)

F. M. Ismagilov, “Polarization effects in backscattering by a particle near the interface,” Waves Random Media 5, 27–32 (1995).
[CrossRef]

Other (4)

A. Ishimaru, Wave Propagation and Scattering in Random Media (Oxford U. Press, New York, 1997).

C. Brosseau, Fundamentals of Polarized Light—a Statistical Optics Approach (Wiley, New York, 1998).

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), pp. 19–81.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

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Figures (3)

Fig. 1
Fig. 1

Experimental measurements of the reduced Muller matrix elements: (a) the diagonal elements and (b) the corresponding off-diagonal elements. See text for description of the samples.

Fig. 2
Fig. 2

Scattering geometry; the plane of the surface is the xy plane. As we consider only rotations about the y axis, the incident beam k is confined to the xz plane and makes an angle θ with the z axis. γ is the angle between the scattering plane (k,s) and the (x, z) plane.

Fig. 3
Fig. 3

Theoretical fits of the experimental data corresponding to different values of N. Sample A: N=0.120, r2=0.75; sample B: N=0.150, r2=0.92; sample C: N=0.374, r2=0.90.

Equations (28)

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J=IQUV=ExEx*+EyEy*ExEx*-EyEy*ExEy*+EyEx*i(ExEy*-EyEx*),
J=[M]J,
M11M12M13M14M21M22M23M24M31M32M33M34M41M42M43M44 IQUV=IQUV
[M]=k=n1[Mk],
[A±]=1±1±11,
J=[A±][M]J
IHH=M11+M12+M21+M22,
IHV=M11+M12-M21-M22,
IVH=M11-M12+M21-M22,
IVV=M11-M12-M21+M22,
M11=IHH+IHV+IVH+IVV,
M12=IHH+IHV-IVH-IVV,
M21=IHH-IHV+IVH-IVV,
M22=IHH-IHV-IVH+IVV.
I=SI(S) .
E(S)=E1(S)x+E2(S)y+E3(S)z,
M(S)(ψ, γ)=R(γ)M(ψ)R(-γ)R(γ)M(π-ψ)R(-γ),
R(γ)=10000cos(2γ)-sin(2γ)00sin(2γ)cos(2γ)00001,
J(S)=R(γ)M(ψ)M(π-ψ)R(-γ)J0.
Mtot=C02πM(S)(ψ, γ)W(γ)dϕ
cos(ψ)=cos(ϕ)sin(θ),
sin2(ψ)=1-cos2(ϕ)sin2(θ),
tan(ϕ)=tan(γ)cos(θ),
cos(2γ)=[1+cos2(θ)]cos2(ϕ)-11-cos2(ϕ)sin2(θ).
M(ψ)=8+2N-(2+3N)sin2(ψ)-(2+3N)sin2(ψ)00-(2+3N)sin2(ψ)(2+3N)(2-sin2(ψ))0000-(2+3N)cos(ψ)000010N cos(ψ),
N=(α1α2*+α2α3*+α3α1*+α2α1*+α3α2*+α1α3*)(α1α1*+α2α2*+α3α3*).
M12=C02π-2(2+3N)[(6+4N)sin2 ψ-(2+3N)sin4 ψ]cos 2γdϕ.
M12=M21=C(2+3N)sin2(θ)×4+N+(2+3N)[-3 cos2(θ)]4.

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