Abstract

The far-zone spectral isotropy of an electromagnetic light wave on scattering has been discussed. It is shown that a sufficient condition for the far-zone spectral isotropy of an electromagnetic light wave on scattering can be expressed by the following two requirements: the two-point correlation function of the dielectric susceptibility of the scattering medium obeys the so-called scaling law, and the normalized spectrum of the incident light wave has the same distribution along the two perpendicular directions.

© 2011 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge University, 1999).
  2. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).
  3. T. Visser, D. Fischer, and E. Wolf, J. Opt. Soc. Am. A 23, 1631 (2006).
    [CrossRef]
  4. S. Sahin and O. Korotkova, Phys. Rev. A 78, 063815 (2008).
    [CrossRef]
  5. G. Gbur and E. Wolf, Opt. Commun. 168, 39 (1999).
    [CrossRef]
  6. D. Zhao, O. Korotkova, and E. Wolf, Opt. Lett. 32, 3483(2007).
    [CrossRef] [PubMed]
  7. M. Lahiri, E. Wolf, D. G. Fischer, and T. Shirai, Phys. Rev. Lett. 102, 123901 (2009).
    [CrossRef] [PubMed]
  8. E. Wolf, J. T. Foley, and F. Gori, J. Opt. Soc. Am. A 6, 1142(1989).
    [CrossRef]
  9. A. Dogariu and E. Wolf, Opt. Lett. 23, 1340 (1998).
    [CrossRef]
  10. T. Shirai and T. Asakura, J. Opt. Soc. Am. A 12, 1354 (1995).
    [CrossRef]
  11. E. Wolf, J. Opt. Soc. Am. A 14, 2820 (1997).
    [CrossRef]
  12. Z. Tong and O. Korotkova, Phys. Rev. A 82, 033836 (2010).
    [CrossRef]
  13. L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2000).
    [CrossRef]
  14. Y. Xin, Y. Chen, Q. Zhao, and M. Zhou, Opt. Commun. 278, 247 (2007).
    [CrossRef]
  15. T. Wang and D. Zhao, Opt. Lett. 35, 2412 (2010).
    [CrossRef] [PubMed]

2010 (2)

Z. Tong and O. Korotkova, Phys. Rev. A 82, 033836 (2010).
[CrossRef]

T. Wang and D. Zhao, Opt. Lett. 35, 2412 (2010).
[CrossRef] [PubMed]

2009 (1)

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

2008 (1)

S. Sahin and O. Korotkova, Phys. Rev. A 78, 063815 (2008).
[CrossRef]

2007 (2)

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

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

2006 (1)

1999 (1)

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

1998 (1)

1997 (1)

1995 (1)

1989 (1)

Asakura, T.

Born, M.

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

Fischer, D.

Fischer, D. G.

M. Lahiri, E. Wolf, D. G. Fischer, 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.

Z. Tong and O. Korotkova, Phys. Rev. A 82, 033836 (2010).
[CrossRef]

S. Sahin and O. Korotkova, Phys. Rev. A 78, 063815 (2008).
[CrossRef]

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

Lahiri, M.

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

Sahin, S.

S. Sahin and O. Korotkova, Phys. Rev. A 78, 063815 (2008).
[CrossRef]

Shirai, T.

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

T. Shirai and T. Asakura, J. Opt. Soc. Am. A 12, 1354 (1995).
[CrossRef]

Tong, Z.

Z. Tong and O. Korotkova, Phys. Rev. A 82, 033836 (2010).
[CrossRef]

Tsang, L.

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

Visser, T.

Wang, T.

Wolf, E.

M. Lahiri, E. Wolf, D. G. Fischer, 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]

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

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

A. Dogariu and E. Wolf, Opt. Lett. 23, 1340 (1998).
[CrossRef]

E. Wolf, J. Opt. Soc. Am. A 14, 2820 (1997).
[CrossRef]

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

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. Opt. Soc. Am. A (4)

Opt. Commun. (2)

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. (3)

Phys. Rev. A (2)

S. Sahin and O. Korotkova, Phys. Rev. A 78, 063815 (2008).
[CrossRef]

Z. Tong and O. Korotkova, Phys. Rev. A 82, 033836 (2010).
[CrossRef]

Phys. Rev. Lett. (1)

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

Other (3)

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

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

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

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Figures (1)

Fig. 1
Fig. 1

Illustration of the notation.

Equations (30)

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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 j ( r , s 0 ; ω ) = a j ( ω ) exp ( i k s 0 · r ) ( j = x , y ) ,
E ( s ) ( r s , ω ) = V F ( r , ω ) G ( r s , r , ω ) × { E ( r , s 0 ; ω ) [ s · E ( r , s 0 ; ω ) ] s } d 3 r ,
η ( r , ω ) = 1 4 π [ n 2 ( r , ω ) 1 ]
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 ) ,
E x ( s ) ( r s , ω ) = V F ( r , ω ) G ( r s , r , ω ) × { ( 1 s x 2 ) E x ( r , s 0 ; ω ) s x s y E y ( r , s 0 ; ω ) } d 3 r ,
E y ( s ) ( r s , ω ) = V F ( r , ω ) G ( r s , r , ω ) × { s x s y E x ( r , s 0 ; ω ) + ( 1 s y 2 ) E y ( r , s 0 ; ω ) } d 3 r ,
E z ( s ) ( r s , ω ) = V F ( r , ω ) G ( r s , r , ω ) × { s x s z E x ( r , s 0 ; ω ) } s y s z E y ( r , s 0 ; ω ) } d 3 r .
S ( s ) ( r s ; ω ) = Tr [ W i j ( s ) ( r s , r s ; ω ) ] .
S ( s ) ( r s ; ω ) = 1 r 2 Λ ( ω , s ) ( ω c ) 4 C ˜ η [ K , K , ω ] ,
Λ ( ω , s ) = S x ( ω ) ( 1 s x 2 ) + S y ( ω ) ( 1 s y 2 ) ,
C ˜ η [ K , K , ω ] = C η ( r 1 , r 2 , ω ) exp [ i K · ( r 2 r 1 ) ] d 3 r 1 d 3 r 2 ,
C η ( r 1 , r 2 , ω ) = η * ( r 1 , ω ) η ( r 2 , ω )
C η ( r 1 , r 2 , ω ) = { C η ( r 2 r 1 , ω ) , when r 1 V , r 2 V 0 , otherwise .
C ˜ η [ K , K , ω ] = V C η ( r , ω ) exp ( i K · r ) d 3 r .
S ( s ) ( r s ; ω ) = Λ ( ω , s ) r 2 V ( ω c ) 4 C η ( r , ω ) exp ( i K · r ) d 3 r .
s ( s ) ( r s ; ω ) = ω 4 Λ ( ω , s ) C ˜ η ( K , ω ) 0 ω 4 Λ ( ω , s ) C ˜ η ( K , ω ) d ω ,
C ˜ η ( K , ω ) = C η ( r , ω ) exp ( i K · r ) d 3 r .
C ˜ η [ K , ω ] = F ( ω ) H ˜ ( s s 0 ) ,
S y ( ω ) = γ · S x ( ω ) ,
s ( s ) ( r s ; ω ) = ω 4 S x ( ω ) F ( ω ) 0 ω 4 S x ( ω ) F ( ω ) d ω ,
C ˜ η [ K , ω ] = C ˜ η [ 0 , ω ] H ˜ ( 0 ) H ˜ ( K / k ) .
C η ( r , ω ) = C ˜ η [ 0 , ω ] ( 2 π ) 3 H ˜ ( 0 ) H ˜ ( K / k ) exp ( i K · r ) d 3 K .
C η ( r , ω ) = k 3 H ˜ ( 0 ) C ˜ η [ 0 , ω ] H ( k r ) ,
H ( r ) = 1 ( 2 π ) 3 H ˜ ( K ) exp ( i K · r ) d 3 K .
μ η ( r , ω ) = C η ( r , ω ) C η ( 0 , ω ) .
μ η ( r , ω ) = h ( k r ) ,
h ( k r ) = H ( k r ) H ( 0 ) .
μ η ( r , ω ) = h ( k r ) ,
S y ( ω ) = γ · S x ( ω ) ,

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