Abstract

We generalize scattering theory to stochastic electromagnetic light waves. It is shown that when a stochastic electromagnetic light wave is scattered from a medium, the properties of the scattered field can be characterized by a 3×3 cross-spectral density matrix. An example of scattering of a spatially coherent electromagnetic light wave from a deterministic medium is discussed. Some interesting phenomena emerge, including the changes of the spectral degree of coherence and of the spectral degree of polarization of the scattered field.

© 2010 Optical Society of America

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References

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  1. E. Wolf, J. T. Foley, and F. Gori, J. Opt. Soc. Am. A 6, 1142 (1989).
    [CrossRef]
  2. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge U. Press, 2007).
  3. O. Korotkova and E. Wolf, Phys. Rev. E 75, 056609 (2007).
    [CrossRef]
  4. G. Gbur and E. Wolf, Opt. Commun. 168, 39 (1999).
    [CrossRef]
  5. D. Zhao, O. Korotkova, and E. Wolf, Opt. Lett. 32, 3483(2007).
    [CrossRef] [PubMed]
  6. D. G. Fischer and E. Wolf, J. Opt. Soc. Am. A 11, 1128(1994).
    [CrossRef]
  7. M. Lahiri, E. Wolf, D. G. Fisher, and T. Shirai, Phys. Rev. Lett. 102, 123901 (2009).
    [CrossRef] [PubMed]
  8. E. Wolf, Phys. Rev. Lett. 103, 075501 (2009).
    [CrossRef] [PubMed]
  9. F. Parrin, J. Chem. Phys. 10, 415 (1942).
    [CrossRef]
  10. Y. Xin, Y. Chen, Q. Zhao, and M. Zhou, Opt. Commun. 278, 247 (2007).
    [CrossRef]
  11. M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge U. Press, 1999).
  12. L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2000).
    [CrossRef]
  13. O. Korotkova and E. Wolf, J. Opt. Soc. Am. A 21, 2382(2004).
    [CrossRef]
  14. J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, Opt. Commun. 248, 333 (2005).
    [CrossRef]

2009 (2)

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

E. Wolf, Phys. Rev. Lett. 103, 075501 (2009).
[CrossRef] [PubMed]

2007 (3)

Y. Xin, Y. Chen, Q. Zhao, and M. Zhou, Opt. Commun. 278, 247 (2007).
[CrossRef]

O. Korotkova and E. Wolf, Phys. Rev. E 75, 056609 (2007).
[CrossRef]

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

2005 (1)

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, Opt. Commun. 248, 333 (2005).
[CrossRef]

2004 (1)

1999 (1)

G. Gbur and E. Wolf, Opt. Commun. 168, 39 (1999).
[CrossRef]

1994 (1)

1989 (1)

1942 (1)

F. Parrin, J. Chem. Phys. 10, 415 (1942).
[CrossRef]

Born, M.

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

Chen, Y.

Y. Xin, Y. Chen, Q. Zhao, and M. Zhou, Opt. Commun. 278, 247 (2007).
[CrossRef]

Ding, K. H.

L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2000).
[CrossRef]

Dogariu, A.

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, Opt. Commun. 248, 333 (2005).
[CrossRef]

Ellis, J.

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, Opt. Commun. 248, 333 (2005).
[CrossRef]

Fischer, D. G.

Fisher, D. G.

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

Foley, J. T.

Gbur, G.

G. Gbur and E. Wolf, Opt. Commun. 168, 39 (1999).
[CrossRef]

Gori, F.

Kong, J. A.

L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2000).
[CrossRef]

Korotkova, O.

Lahiri, M.

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

Parrin, F.

F. Parrin, J. Chem. Phys. 10, 415 (1942).
[CrossRef]

Ponomarenko, S.

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, Opt. Commun. 248, 333 (2005).
[CrossRef]

Shirai, T.

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

Tsang, L.

L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2000).
[CrossRef]

Wolf, E.

E. Wolf, Phys. Rev. Lett. 103, 075501 (2009).
[CrossRef] [PubMed]

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

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

O. Korotkova and E. Wolf, Phys. Rev. E 75, 056609 (2007).
[CrossRef]

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, Opt. Commun. 248, 333 (2005).
[CrossRef]

O. Korotkova and E. Wolf, J. Opt. Soc. Am. A 21, 2382(2004).
[CrossRef]

G. Gbur and E. Wolf, Opt. Commun. 168, 39 (1999).
[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]

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

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

Xin, Y.

Y. Xin, Y. Chen, Q. Zhao, and M. Zhou, Opt. Commun. 278, 247 (2007).
[CrossRef]

Zhao, D.

Zhao, Q.

Y. Xin, Y. Chen, Q. Zhao, and M. Zhou, Opt. Commun. 278, 247 (2007).
[CrossRef]

Zhou, M.

Y. Xin, Y. Chen, Q. Zhao, and M. Zhou, Opt. Commun. 278, 247 (2007).
[CrossRef]

J. Chem. Phys. (1)

F. Parrin, J. Chem. Phys. 10, 415 (1942).
[CrossRef]

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

Opt. Commun. (3)

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, Opt. Commun. 248, 333 (2005).
[CrossRef]

G. Gbur and E. Wolf, Opt. Commun. 168, 39 (1999).
[CrossRef]

Y. Xin, Y. Chen, Q. Zhao, and M. Zhou, Opt. Commun. 278, 247 (2007).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. E (1)

O. Korotkova and E. Wolf, Phys. Rev. E 75, 056609 (2007).
[CrossRef]

Phys. Rev. Lett. (2)

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

E. Wolf, Phys. Rev. Lett. 103, 075501 (2009).
[CrossRef] [PubMed]

Other (3)

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

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

L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2000).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Illustrating the notation.

Fig. 2
Fig. 2

Spectral density of the scattered field.

Fig. 3
Fig. 3

Spectral degree of coherence of the scattered field as a function of ϕ = θ 2 when θ 1 = 0 .

Fig. 4
Fig. 4

Spectral degree of polarization of the scattered field.

Equations (22)

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W ( i ) ( r 1 , r 2 , s 0 ; ω ) [ W i j ( i ) ( r 1 , r 2 , s 0 ; ω ) ] = [ E i * ( r 1 , s 0 ; ω ) E j ( r 2 , s 0 ; ω ) ] ( i = x , y ; j = x , y ) ,
E ( s ) ( r s , ω ) = s × [ s × D F ( r , ω ) E ( i ) ( r , s 0 ; ω ) G ( r s , r , ω ) d 3 r ] ,
a ^ i = a ^ S = s × s 0 | s × s 0 | ,
b ^ i = s 0 × a i , b ^ s = s × a s .
E a s ( r s , ω ) = D F ( r , ω ) E a i ( r , s 0 ; ω ) G ( r s , r , ω ) d 3 r ,
E b s ( r s , ω ) = cos θ · D F ( r , ω ) E b i ( r , s 0 ; ω ) G ( r s , r , ω ) d 3 r .
E x s ( r s , ω ) = f x ( θ ) D F ( r , ω ) E x i ( r , s 0 ; ω ) G ( r s , r , ω ) d 3 r ,
E y s ( r s , ω ) = f y ( θ ) D F ( r , ω ) E y i ( r , s 0 ; ω ) G ( r s , r , ω ) d 3 r ,
E z s ( r s , ω ) = f z ( θ ) D F ( r , ω ) E y i ( r , s 0 ; ω ) G ( r s , r , ω ) d 3 r ,
f x ( θ ) = 1 , f y ( θ ) = cos 2 θ , f z ( θ ) = sin θ cos θ .
W s ( r s 1 , r s 2 ; ω ) [ W i j s ( r s 1 , r s 2 ; ω ) ] = [ E i s * ( r s 1 , ω ) E j s ( r s 2 , ω ) ] , ( i = x , y , z ; j = x , y , z ) .
S ( s ) ( r s ; ω ) = Tr W i j s ( r s , r s ; ω ) ,
μ ( s ) ( r s 1 , r s 2 ; ω ) = Tr W i j s ( r s 1 , r s 2 ; ω ) Tr W i j s ( r s 1 , r s 1 ; ω ) Tr W i j s ( r s 2 , r s 2 ; ω ) ,
P ( r s ; ω ) = λ 1 ( r s ; ω ) λ 2 ( r s ; ω ) λ 1 ( r s ; ω ) + λ 2 ( r s ; ω ) + λ 3 ( r s ; ω ) ,
E i ( r , s 0 ; ω ) = A i a i ( ω ) exp ( i k s 0 · r ) ( i = x , y ) ,
W i j ( i ) ( r 1 , r 2 , s 0 ; ω ) = A i A j B i j S ( ω ) exp [ i k s 0 · ( r 2 r 1 ) ] ,
F ( r , ω ) = B exp ( r 2 2 σ 2 ) .
S ( S ) ( r s ; ω ) = S ( ω ) C ( θ , θ ) r 2 C ˜ F ( K , K , ω ) ,
μ ( S ) ( r s 1 , r s 2 ; ω ) = C ( θ 1 , θ 2 ) C ( θ 1 , θ 1 ) C ( θ 2 , θ 2 ) ,
P 2 ( r s ; ω ) = A x 2 A y 2 cos 2 θ A x 2 + A y 2 cos 2 θ ,
C ( θ 1 , θ 2 ) = A x 2 + cos θ 1 cos θ 2 cos ( θ 1 θ 2 ) A y 2 ,
C ˜ F ( K 1 , K 2 , ω ) = B 2 ( 2 π ) 3 σ 6 exp [ 1 2 σ 2 ( K 1 2 + K 2 2 ) ] ,

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