Abstract

We consider a class of stochastic electromagnetic beams, and we show both analytically and by numerical examples that coherence properties of the electromagnetic field in the source plane affect the polarization properties of the radiated beam.

© 2008 Optical Society of America

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References

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  1. D. F. V. James, J. Opt. Soc. Am. A 11, 1641 (1994).
    [CrossRef]
  2. G. P. Agrawal and E. Wolf, J. Opt. Soc. Am. A 17, 2019 (2000).
    [CrossRef]
  3. T. Shirai and E. Wolf, J. Opt. Soc. Am. A 21, 1907 (2004).
    [CrossRef]
  4. O. Korotkova and E. Wolf, Opt. Commun. 246, 35 (2005).
    [CrossRef]
  5. E. Wolf, Phys. Lett. A 312, 263 (2003).
    [CrossRef]
  6. E. Wolf, Opt. Lett. 28, 1078 (2003).
    [CrossRef] [PubMed]
  7. H. Roychowdhury and E. Wolf, Opt. Commun. 226, 57 (2003).
    [CrossRef]
  8. E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge U. Press, 2007).
  9. H. Roychowdhury and E. Wolf, Opt. Commun. 252, 268 (2005).
    [CrossRef]
  10. F. Gori, M. Santarsiero, R. Borghi, and E. Wolf, Opt. Lett. 31, 688 (2006).
    [CrossRef] [PubMed]
  11. O. Korotokova, B. G. Hoover, V. L. Gomiz, and E. Wolf, J. Opt. Soc. Am. A 22, 2547 (2005).
    [CrossRef]
  12. H. Wang, X. Wang, A. Zeng, and K. Yang, Opt. Lett. 32, 2215 (2007).
    [CrossRef] [PubMed]
  13. E. Wolf, Phys. Rev. Lett. 56, 1370 (1986).
    [CrossRef] [PubMed]
  14. For research in this area until 1996, see E. Wolf and D. F. V. James, Rep. Prog. Phys. 59, 771 (1996).
    [CrossRef]
  15. The essence of coherence theory in the space-frequency domain is clear from its formulation for stochastic scalar fields (see , Chap. 4). The theory was generalized to stochastic electromagnetic fields by J. Tervo, T. Setälä and A. Friberg, J. Opt. Soc. Am. A 21, 2205 (2004), and by M. A. Alonso, E. Wolf, Opt. Commun. 281, 2393 (2008).
    [CrossRef]
  16. D. Zhao and E. Wolf, Opt. Commun. 281, 3067 (2008)

2008 (1)

D. Zhao and E. Wolf, Opt. Commun. 281, 3067 (2008)

2007 (1)

2006 (1)

2005 (3)

O. Korotokova, B. G. Hoover, V. L. Gomiz, and E. Wolf, J. Opt. Soc. Am. A 22, 2547 (2005).
[CrossRef]

O. Korotkova and E. Wolf, Opt. Commun. 246, 35 (2005).
[CrossRef]

H. Roychowdhury and E. Wolf, Opt. Commun. 252, 268 (2005).
[CrossRef]

2004 (2)

2003 (3)

E. Wolf, Phys. Lett. A 312, 263 (2003).
[CrossRef]

E. Wolf, Opt. Lett. 28, 1078 (2003).
[CrossRef] [PubMed]

H. Roychowdhury and E. Wolf, Opt. Commun. 226, 57 (2003).
[CrossRef]

2000 (1)

1996 (1)

For research in this area until 1996, see E. Wolf and D. F. V. James, Rep. Prog. Phys. 59, 771 (1996).
[CrossRef]

1994 (1)

1986 (1)

E. Wolf, Phys. Rev. Lett. 56, 1370 (1986).
[CrossRef] [PubMed]

Agrawal, G. P.

Alonso, M. A.

Borghi, R.

Friberg, A.

Gomiz, V. L.

Gori, F.

Hoover, B. G.

James, D. F. V.

For research in this area until 1996, see E. Wolf and D. F. V. James, Rep. Prog. Phys. 59, 771 (1996).
[CrossRef]

D. F. V. James, J. Opt. Soc. Am. A 11, 1641 (1994).
[CrossRef]

Korotkova, O.

O. Korotkova and E. Wolf, Opt. Commun. 246, 35 (2005).
[CrossRef]

Korotokova, O.

Roychowdhury, H.

H. Roychowdhury and E. Wolf, Opt. Commun. 252, 268 (2005).
[CrossRef]

H. Roychowdhury and E. Wolf, Opt. Commun. 226, 57 (2003).
[CrossRef]

Santarsiero, M.

Setälä, T.

Shirai, T.

Tervo, J.

Wang, H.

Wang, X.

Wolf, E.

Yang, K.

Zeng, A.

Zhao, D.

D. Zhao and E. Wolf, Opt. Commun. 281, 3067 (2008)

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

Opt. Commun. (4)

D. Zhao and E. Wolf, Opt. Commun. 281, 3067 (2008)

O. Korotkova and E. Wolf, Opt. Commun. 246, 35 (2005).
[CrossRef]

H. Roychowdhury and E. Wolf, Opt. Commun. 226, 57 (2003).
[CrossRef]

H. Roychowdhury and E. Wolf, Opt. Commun. 252, 268 (2005).
[CrossRef]

Opt. Lett. (3)

Phys. Lett. A (1)

E. Wolf, Phys. Lett. A 312, 263 (2003).
[CrossRef]

Phys. Rev. Lett. (1)

E. Wolf, Phys. Rev. Lett. 56, 1370 (1986).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

For research in this area until 1996, see E. Wolf and D. F. V. James, Rep. Prog. Phys. 59, 771 (1996).
[CrossRef]

Other (1)

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

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Figures (1)

Fig. 1
Fig. 1

a, Variation of the magnitude of the spectral degree of coherence η ( 0 ) ( ρ 1 , ρ 1 , ω ) , with the separation distance Δ ρ = 2 ρ 1 for three Gaussian Schell-model sources, at a pair of points located symmetrically with respect to the axis of the beam. The parameters were chosen as follows: λ = 633 nm , σ = 10 cm , δ x x = 0.5 mm , A x 2 = 0.5 , A y 2 = 1 , for (A) δ y y = 0.3 mm , (B) δ y y = 0.5 mm , and (C) δ y y = 0.7 mm . b, Variation of the spectral degree of polarization along the axis of the three beams whose parameters are specified in the caption of Fig. 1a.

Equations (14)

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W ( 0 ) ( ρ 1 , ρ 2 , ω ) = ( W x x ( 0 ) ( ρ 1 , ρ 2 , ω ) W x y ( 0 ) ( ρ 1 , ρ 2 , ω ) W y x ( 0 ) ( ρ 1 , ρ 2 , ω ) W y y ( 0 ) ( ρ 1 , ρ 2 , ω ) ) ,
W i j ( 0 ) ( ρ 1 , ρ 2 , ω ) = S i ( 0 ) ( ρ 1 , ω ) S j ( 0 ) ( ρ 2 , ω ) μ i j ( 0 ) ( ρ 2 ρ 1 , ω ) ,
( i = x , y ; j = x , y ) .
S j ( 0 ) ( ρ , ω ) = A j 2 exp [ ρ 2 2 σ 2 ] , ( j = x , y ) ,
μ i j ( 0 ) ( ρ 2 ρ 1 , ω ) = B i j exp [ ( ρ 2 ρ 1 ) 2 2 δ i j 2 ] , ( i = x , y ; j = x , y ) .
W i j ( r 1 , r 2 , ω ) = D D W i j ( 0 ) ( ρ 1 , ρ 2 , ω ) K ( ρ 1 ρ 1 , ρ 2 ρ 2 , z , ω ) d 2 ρ 1 d 2 ρ 2 .
G ( ρ , ρ , z ) = i k 2 π z exp [ ik ( ρ ρ ) 2 z ] ,
P ( r , ω ) = 1 4 Det ( W ( r , r , ω ) ) Tr [ W ( r , r , ω ) ] 2 ,
η ( r 1 , r 2 , ω ) = Tr ( W ( r 1 , r 2 , ω ) ) Tr ( W ( r 1 , r 1 , ω ) ) Tr ( W ( r 2 , r 2 , ω ) ) .
W ( 0 ) ( ρ 1 , ρ 2 , ω ) = ( W x x ( 0 ) ( ρ 1 , ρ 2 , ω ) 0 0 W y y ( 0 ) ( ρ 1 , ρ 2 , ω ) ) ,
W i i ( 0 ) ( ρ 1 , ρ 2 , ω ) = A i 2 exp [ ρ 1 2 + ρ 2 2 4 σ 2 ] exp [ ( ρ 2 ρ 1 ) 2 2 δ i i 2 ] , ( i = x , y ) .
P ( ρ , z , ω ) = A x 2 Δ x x 2 ( z ) exp [ ρ 2 2 σ Δ x x 2 ( z ) ] A y 2 Δ y y 2 ( z ) exp [ ρ 2 2 σ Δ y y 2 ( z ) ] A x 2 Δ x x 2 ( z ) exp [ ρ 2 2 σ Δ x x 2 ( z ) ] + A y 2 Δ y y 2 ( z ) exp [ ρ 2 2 σ Δ y y 2 ( z ) ] ,
Δ i i 2 ( z ) = 1 + z 2 k 2 σ 2 ( 1 4 σ 2 + 1 δ i i 2 ) , ( i = x , y ) .
η ( 0 ) ( ρ 1 ρ 2 , ω ) = 1 ( A x 2 + A y 2 ) { A x 2 exp [ ( ρ 2 ρ 1 ) 2 2 δ x x 2 ] + A y 2 exp [ ( ρ 2 ρ 1 ) 2 2 δ y y 2 ] } .

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