Abstract

The scattering of a partially coherent plane-wave pulse on a Gaussian-correlated, quasi-homogeneous random medium is investigated. The analytical expressions for the temporal coherence length and the pulse duration of the scattered field are derived. We demonstrate that the scattering-induced changes in the temporal coherence length and the pulse duration may be used to determine the correlation function of the scattering potential of the medium.

© 2011 Optical Society of America

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References

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  21. H. Lajunen, P. Vahimaa, and J. Tervo, J. Opt. Soc. Am. A 22, 1536 (2005).
    [CrossRef]
  22. A. T. Friberg, H. Lajunen, and V. Torres-Company, Opt. Express 15, 5160 (2007).
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  23. H. Lajunen, V. Torres-Company, J. Lancis, E. Silvestre, and P. Andrès, Opt. Express 18, 14979 (2010).
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  24. C. Ding, L. Pan, and B. Lü, New J. Phys. 11, 083001 (2009).
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  27. E. Wolf and J. T. Foley, Phys. Rev. A 40, 579 (1989).
    [CrossRef] [PubMed]
  28. J. T. Foley and E. Wolf, Phys. Rev. A 40, 588 (1989).
    [CrossRef] [PubMed]
  29. D. G. Fischer and B. Cairns, J. Mod. Opt. 42, 655 (1995).
    [CrossRef]

2010 (4)

2009 (3)

C. Ding, L. Pan, and B. Lü, New J. Phys. 11, 083001 (2009).
[CrossRef]

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

S. Sahin and O. Korotkova, Opt. Lett. 34, 1762 (2009).
[CrossRef] [PubMed]

2008 (2)

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

V. Torres-Company, H. Lajunen, J. Lancis, and A. T. Friberg, Phys. Rev. A 77, 043811 (2008).
[CrossRef]

2007 (4)

2006 (1)

2005 (3)

2004 (1)

2003 (2)

2002 (1)

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, Opt. Commun. 204, 53 (2002).
[CrossRef]

1995 (2)

A. T. Friberg and E. Wolf, Opt. Lett. 20, 623 (1995).
[CrossRef] [PubMed]

D. G. Fischer and B. Cairns, J. Mod. Opt. 42, 655 (1995).
[CrossRef]

1994 (1)

1989 (3)

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

E. Wolf and J. T. Foley, Phys. Rev. A 40, 579 (1989).
[CrossRef] [PubMed]

J. T. Foley and E. Wolf, Phys. Rev. A 40, 588 (1989).
[CrossRef] [PubMed]

Andrés, P.

Andrès, P.

Born, M.

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

Cairns, B.

D. G. Fischer and B. Cairns, J. Mod. Opt. 42, 655 (1995).
[CrossRef]

Ding, C.

C. Ding, L. Pan, and B. Lü, New J. Phys. 11, 083001 (2009).
[CrossRef]

Du, X.

Fischer, D. G.

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

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

D. G. Fischer and B. Cairns, J. Mod. Opt. 42, 655 (1995).
[CrossRef]

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

Foley, J. T.

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

E. Wolf and J. T. Foley, Phys. Rev. A 40, 579 (1989).
[CrossRef] [PubMed]

J. T. Foley and E. Wolf, Phys. Rev. A 40, 588 (1989).
[CrossRef] [PubMed]

Friberg, A. T.

Gao, W.

Gori, F.

Korotkova, O.

Lahiri, M.

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

Lajunen, H.

Lancis, J.

Lin, Q.

Q. Lin, L. Wang, and S. Zhu, Opt. Commun. 219, 65 (2003).
[CrossRef]

Lü, B.

C. Ding, L. Pan, and B. Lü, New J. Phys. 11, 083001 (2009).
[CrossRef]

Mínguez-Vega, G.

Pääkkönen, P.

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, Opt. Commun. 204, 53 (2002).
[CrossRef]

Pan, L.

C. Ding, L. Pan, and B. Lü, New J. Phys. 11, 083001 (2009).
[CrossRef]

Sahin, S.

S. Sahin and O. Korotkova, Opt. Lett. 34, 1762 (2009).
[CrossRef] [PubMed]

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]

Silvestre, E.

Tervo, J.

Torres-Company, V.

Turunen, J.

H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, Opt. Commun. 255, 12 (2005).
[CrossRef]

H. Lajunen, J. Tervo, J. Turunen, P. Vahimaa, and F. Wyrowski, Opt. Express 11, 1894 (2003).
[CrossRef] [PubMed]

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, Opt. Commun. 204, 53 (2002).
[CrossRef]

Vahimaa, P.

Visser, T. D.

Wang, L.

Q. Lin, L. Wang, and S. Zhu, Opt. Commun. 219, 65 (2003).
[CrossRef]

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]

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

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

A. T. Friberg and E. Wolf, Opt. Lett. 20, 623 (1995).
[CrossRef] [PubMed]

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]

E. Wolf and J. T. Foley, Phys. Rev. A 40, 579 (1989).
[CrossRef] [PubMed]

J. T. Foley and E. Wolf, Phys. Rev. A 40, 588 (1989).
[CrossRef] [PubMed]

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

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

Wyrowski, F.

H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, Opt. Commun. 255, 12 (2005).
[CrossRef]

H. Lajunen, J. Tervo, J. Turunen, P. Vahimaa, and F. Wyrowski, Opt. Express 11, 1894 (2003).
[CrossRef] [PubMed]

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, Opt. Commun. 204, 53 (2002).
[CrossRef]

Zhao, D.

Zhu, S.

Q. Lin, L. Wang, and S. Zhu, Opt. Commun. 219, 65 (2003).
[CrossRef]

J. Mod. Opt. (1)

D. G. Fischer and B. Cairns, J. Mod. Opt. 42, 655 (1995).
[CrossRef]

J. Opt. Soc. Am. A (5)

New J. Phys. (1)

C. Ding, L. Pan, and B. Lü, New J. Phys. 11, 083001 (2009).
[CrossRef]

Opt. Commun. (3)

H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, Opt. Commun. 255, 12 (2005).
[CrossRef]

P. Pääkkönen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, Opt. Commun. 204, 53 (2002).
[CrossRef]

Q. Lin, L. Wang, and S. Zhu, Opt. Commun. 219, 65 (2003).
[CrossRef]

Opt. Express (3)

Opt. Lett. (8)

Phys. Rev. A (4)

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

V. Torres-Company, H. Lajunen, J. Lancis, and A. T. Friberg, Phys. Rev. A 77, 043811 (2008).
[CrossRef]

E. Wolf and J. T. Foley, Phys. Rev. A 40, 579 (1989).
[CrossRef] [PubMed]

J. T. Foley and E. Wolf, Phys. Rev. A 40, 588 (1989).
[CrossRef] [PubMed]

Phys. Rev. E (1)

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

Phys. Rev. Lett. (1)

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

Other (2)

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

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

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Figures (1)

Fig. 1
Fig. 1

Illustrating the notation relating to scattering of a partially coherent plane-wave pulse by a Gaussian-correlated, quasi-homogeneous random medium.

Equations (15)

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Γ ( t 1 , t 2 ) = Γ 0 exp [ t 1 2 + t 2 2 2 T 0 2 ( t 1 t 2 ) 2 2 T c 2 + i ω 0 ( t 1 t 2 ) ] ,
W ( ω 1 , ω 2 ) = W 0 exp [ ( ω 1 ω 0 ) 2 + ( ω 2 ω 0 ) 2 2 Ω 0 2 ( ω 1 ω 2 ) 2 2 Ω c 2 ] ,
W ( i ) ( r 1 , r 2 , ω 1 , ω 2 ) = W 0 exp [ ( ω 1 ω 0 ) 2 + ( ω 2 ω 0 ) 2 2 Ω 0 2 ( ω 1 ω 2 ) 2 2 Ω c 2 ] exp [ i ( k 2 s 0 · r 2 k 1 s 0 · r 1 ) ] ,
C F ( r 1 , r 2 , ω 0 ) = F * ( r 1 , ω 0 ) F ( r 2 , ω 0 ) m ,
W ( s ) ( r s 1 , r s 2 , ω 1 , ω 2 ) = W 0 exp [ ( ω 1 ω 0 ) 2 + ( ω 2 ω 0 ) 2 2 Ω 0 2 ( ω 1 ω 2 ) 2 2 Ω c 2 ] exp [ i r ( k 2 k 1 ) ] r 2 × D D C F ( r 1 , r 2 , ω 0 ) exp { i [ K 1 · r 1 + K 2 · r 2 ] } d 3 r 1 d 3 r 2 ,
C F ( r 1 , r 2 , ω 0 ) = C 0 exp [ | r 1 + r 2 | 2 8 σ R 2 ] exp [ | r 1 r 2 | 2 2 σ r 2 ] ,
W ( s ) ( r s 1 , r s 2 , ω 1 , ω 2 ) = W 0 exp [ ( ω 1 ω 0 ) 2 + ( ω 2 ω 0 ) 2 2 Ω 0 2 ( ω 1 ω 2 ) 2 2 Ω c 2 ] exp [ i r ( k 2 k 1 ) ] r 2 × ( 2 π σ R σ r ) 3 C 0 exp [ 1 2 σ R 2 | K 1 + K 2 | 2 ] exp [ 1 2 σ r 2 | K 2 K 1 2 | 2 ] .
Γ ( s ) ( r s 1 , r s 2 , t 1 , t 2 ) = W ( s ) ( r s 1 , r s 2 , ω 1 , ω 2 ) exp [ i ( ω 1 t 1 ω 2 t 2 ) ] d ω 1 d ω 2 .
| μ ( s ) ( r s , r s , t 1 , t 2 ) | = | Γ ( s ) ( r s , r s , t 1 , t 2 ) Γ ( s ) ( r s , r s , t 1 , t 1 ) Γ ( s ) ( r s , r s , t 2 , t 2 ) | ,
| μ ( s ) ( r s , r s , t 1 , t 2 ) | = exp [ ( t 1 t 2 ) 2 2 ( T c ( s ) ) 2 ] ,
I ( s ) ( r s , t ) = B exp [ t 2 ( T 0 ( s ) ) 2 ] ,
( T c ( s ) ) 2 = ( T 0 2 T c 2 T c 2 + 2 T 0 2 + 2 sin 2 θ 2 σ r 2 c 2 ) ( T 0 2 + 8 sin 2 θ 2 σ R 2 c 2 ) [ T 0 4 T c 2 + 2 T 0 2 + 4 sin 2 θ 2 ( σ R 2 c 2 σ r 2 4 c 2 ) ] ,
( T 0 ( s ) ) 2 = ( T 0 2 + 8 sin 2 θ 2 σ R 2 c 2 ) ,
σ r 2 = c 2 T 0 2 T c 2 + 2 T 0 2 [ T 0 2 ( T c ( s ) T 0 ( s ) ) 2 T c 2 ] + c 2 ( T c ( s ) ) 2 T 0 2 2 ( T c ( s ) T 0 ( s ) ) 2 sin 2 θ 2 [ 2 + ( T c ( s ) T 0 ( s ) ) 2 ] ,
σ R 2 = c 2 ( T 0 ( s ) ) 2 T 0 2 8 sin 2 θ 2 .

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