Abstract

The scattering of the polychromatic plane light wave incident upon rotational quasi-homogeneous anisotropic media is investigated. It is different from the light wave scattered by quasi-homogeneous isotropic medium in that the spectral shift can be produced by the rotation of the anisotropic medium. We derive the analytical formula for the spectrum of the scattered field and show some numerical examples.

© 2011 Optical Society of America

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References

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  1. W. H. Carter and E. Wolf, Opt. Commun. 67, 85 (1988).
    [CrossRef]
  2. D. G. Fischer and E. Wolf, J. Opt. Soc. Am. A 11, 1128 (1994).
    [CrossRef]
  3. T. D. Visser, D. G. Fischer, and E. Wolf, J. Opt. Soc. Am. A 23, 1631 (2006).
    [CrossRef]
  4. M. Lahiri, E. Wolf, D. G. Fischer, and T. Shirai, Phy. Rev. Lett. 102, 123901 (2009).
    [CrossRef]
  5. X. Du and D. Zhao, Opt. Lett. 35, 384 (2010).
    [CrossRef]
  6. E. Wolf, J. T. Foley, and F. Gori, J. Opt. Soc. Am. A 6, 1142 (1989).
    [CrossRef]
  7. D. Zhao, O. Korotkova, and E. Wolf, Opt. Lett. 32, 3483 (2007).
    [CrossRef]
  8. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).
  9. M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge University, 1999).

2010 (1)

2009 (1)

M. Lahiri, E. Wolf, D. G. Fischer, and T. Shirai, Phy. Rev. Lett. 102, 123901 (2009).
[CrossRef]

2007 (1)

2006 (1)

1994 (1)

1989 (1)

1988 (1)

W. H. Carter and E. Wolf, Opt. Commun. 67, 85 (1988).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge University, 1999).

Carter, W. H.

W. H. Carter and E. Wolf, Opt. Commun. 67, 85 (1988).
[CrossRef]

Du, X.

Fischer, D. G.

Foley, J. T.

Gori, F.

Korotkova, O.

Lahiri, M.

M. Lahiri, E. Wolf, D. G. Fischer, and T. Shirai, Phy. Rev. Lett. 102, 123901 (2009).
[CrossRef]

Shirai, T.

M. Lahiri, E. Wolf, D. G. Fischer, and T. Shirai, Phy. Rev. Lett. 102, 123901 (2009).
[CrossRef]

Visser, T. D.

Wolf, E.

M. Lahiri, E. Wolf, D. G. Fischer, and T. Shirai, Phy. Rev. Lett. 102, 123901 (2009).
[CrossRef]

D. Zhao, O. Korotkova, and E. Wolf, Opt. Lett. 32, 3483 (2007).
[CrossRef]

T. D. Visser, D. G. Fischer, and E. Wolf, J. Opt. Soc. Am. A 23, 1631 (2006).
[CrossRef]

D. G. Fischer and E. Wolf, J. Opt. Soc. Am. A 11, 1128 (1994).
[CrossRef]

E. Wolf, J. T. Foley, and F. Gori, J. Opt. Soc. Am. A 6, 1142 (1989).
[CrossRef]

W. H. Carter and E. Wolf, Opt. Commun. 67, 85 (1988).
[CrossRef]

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge University, 1999).

Zhao, D.

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

Opt. Commun. (1)

W. H. Carter and E. Wolf, Opt. Commun. 67, 85 (1988).
[CrossRef]

Opt. Lett. (2)

Phy. Rev. Lett. (1)

M. Lahiri, E. Wolf, D. G. Fischer, and T. Shirai, Phy. Rev. Lett. 102, 123901 (2009).
[CrossRef]

Other (2)

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge University, 1999).

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Figures (4)

Fig. 1.
Fig. 1.

Illustrating the notation relating to the scattering from a rotational quasi-homogeneous anisotropic medium.

Fig. 2.
Fig. 2.

Normalized spectrum of the scattered field in the far zone. The angle of rotation θ=π/6. The effective radius σIx=30λ0, σIy=10λ0, σIz=20λ0 in line (a), but σIx=10λ0, σIy=20λ0, σIz=30λ0 in lines (b), (c), and (d). The correlation length σμx=λ0, σμy=2λ0, σμz=3λ0, in lines (a) and (b), but σμx=1.5λ0, σμy=3λ0, σμz=4.5λ0 in line (c), and σμx=2λ0, σμy=4λ0, σμz=6λ0 in line (d).

Fig. 3.
Fig. 3.

Normalized spectrum of the scattered field in the far zone. The effective radius σIx=10λ0, σIy=20λ0, σIz=30λ0, and the correlation length σμx=λ0, σμy=2λ0, σμz=3λ0. The angle of rotation: (a) θ=0, (b) θ=π/6, and (c) θ=π/3.

Fig. 4.
Fig. 4.

Spectral shifts produced by rotation of the scatterer versus the angle of rotation. The effective radius σIx=10λ0, σIy=20λ0, σIz=30λ0, the correlation length: (a) σμx=λ0, σμy=2λ0, σμz=3λ0; (b) σμx=1.5λ0, σμy=3λ0, σμz=4.5λ0; and (c) σμx=2λ0, σμy=4λ0, σμz=6λ0.

Equations (23)

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W(i)(r1,r2,ω)=U(i)*(r1,ω)U(i)(r2,ω),
U(i)(r,ω)=a(ω)exp(iks0·r),
W(i)(r1,r2,ω)=S(i)(ω)exp[iks0·(r2r1)],
S(i)(ω)=A0exp[(ωω0)22Γ02],
W(s)(r1,r2,ω)=DDW(i)(r1,r2,ω)CF(r1,r2,ω)×G*(|r1r1|,ω)G(|r2r2|,ω)d3r1d3r2,
CF(r1,r2,ω)=F*(r1,ω)F(r2,ω)m
W(s)(rs1,rs2,ω)=1r2S(i)(ω)C˜F[k(s1s0),k(s2s0),ω],
C˜F(K1,K2,ω)=DDCF(r1,r2,ω)×exp[i(K1·r1+K2·r2)]d3r1d3r2
CF(r1,r2,ω)=C0exp(|R+|22σI2)exp(|R|22σμ2),
CF(r¯12,ω)=C0exp(r¯12TM¯r¯12),
M¯=[M+MMM+],
M±=[18σIx2±12σμx200018σIy2±12σμy200018σIz2±12σμz2].
{x=xcosαx+ycosβx+zcosγxy=xcosαy+ycosβy+zcosγyz=xcosαz+ycosβz+zcosγz,
CF(r¯12,ω)=C0exp(r¯12TR¯TM¯R¯r¯12),
R¯=[R00R],
R=[cosαxcosβxcosγxcosαycosβycosγycosαzcosβzcosγz],
C˜F(K¯12,ω)=CF(r¯12,ω)exp(ir¯12TK12)d6r¯12,
W(s)(rs¯12,ω)=π3C0r2S(i)(ω)[det(R¯TM¯R¯)]1/2×exp(14K¯12TR¯1M¯1R¯1TK¯12),
K¯12=kI¯(s¯12s¯00),
I¯=[I00I],
S(s)(rs,ω)W(s)(rs,rs,ω).
S(s)(rs¯,ω)=π3A0C0r2exp[(ωω0)22Γ02][det(R¯TM¯R¯)]1/2×exp(14K¯TR¯1M¯1R¯1TK¯),
R=[1000cosθsinθ0sinθcosθ],

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