Abstract

It is shown that two stochastic electromagnetic beams that propagate from the source plane z=0 into the half-space z>0 may have different degrees of polarization throughout the half-space, even though they have the same sets of Stokes parameters in the source plane. This fact is due to a possible difference in the coherence properties of the field in that plane, but other reasons are also possible. The result is illustrated by an example.

© 2006 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. F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A, Pure Appl. Opt. 3, 1 (2001).
    [CrossRef]
  4. O. Korotkova and E. Wolf, Opt. Commun. 246, 35 (2005).
    [CrossRef]
  5. M. Mujat, A. Dogariu, and E. Wolf, J. Opt. Soc. Am. A 21, 2414 (2004).
    [CrossRef]
  6. H. Roychowdhury and E. Wolf, Opt. Commun. 252, 268 (2005).
    [CrossRef]
  7. Y. Li, H. Lee, and E. Wolf, Opt. Commun. 265, 63 (2006).
    [CrossRef]
  8. F. Gori, M. Santarsiero, R. Borghi, and E. Wolf, Opt. Lett. 31, 688 (2006).
    [CrossRef] [PubMed]
  9. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999).
  10. O. Korotkova and E. Wolf, Opt. Lett. 30, 198 (2005).
    [CrossRef] [PubMed]
  11. L. Mandel and E. Wolf, Coherence and Quantum Optics (Cambridge U. Press, 1995), Sect. 4.7.

2006

2005

O. Korotkova and E. Wolf, Opt. Lett. 30, 198 (2005).
[CrossRef] [PubMed]

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

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

2004

2001

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A, Pure Appl. Opt. 3, 1 (2001).
[CrossRef]

2000

1994

Agrawal, G. P.

Borghi, R.

F. Gori, M. Santarsiero, R. Borghi, and E. Wolf, Opt. Lett. 31, 688 (2006).
[CrossRef] [PubMed]

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A, Pure Appl. Opt. 3, 1 (2001).
[CrossRef]

Born, M.

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

Dogariu, A.

Gori, F.

F. Gori, M. Santarsiero, R. Borghi, and E. Wolf, Opt. Lett. 31, 688 (2006).
[CrossRef] [PubMed]

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A, Pure Appl. Opt. 3, 1 (2001).
[CrossRef]

James, D. F. V.

Korotkova, O.

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

O. Korotkova and E. Wolf, Opt. Lett. 30, 198 (2005).
[CrossRef] [PubMed]

Lee, H.

Y. Li, H. Lee, and E. Wolf, Opt. Commun. 265, 63 (2006).
[CrossRef]

Li, Y.

Y. Li, H. Lee, and E. Wolf, Opt. Commun. 265, 63 (2006).
[CrossRef]

Mandel, L.

L. Mandel and E. Wolf, Coherence and Quantum Optics (Cambridge U. Press, 1995), Sect. 4.7.

Mondello, A.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A, Pure Appl. Opt. 3, 1 (2001).
[CrossRef]

Mujat, M.

Piquero, G.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A, Pure Appl. Opt. 3, 1 (2001).
[CrossRef]

Roychowdhury, H.

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

Santarsiero, M.

F. Gori, M. Santarsiero, R. Borghi, and E. Wolf, Opt. Lett. 31, 688 (2006).
[CrossRef] [PubMed]

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A, Pure Appl. Opt. 3, 1 (2001).
[CrossRef]

Simon, R.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A, Pure Appl. Opt. 3, 1 (2001).
[CrossRef]

Wolf, E.

Y. Li, H. Lee, and E. Wolf, Opt. Commun. 265, 63 (2006).
[CrossRef]

F. Gori, M. Santarsiero, R. Borghi, and E. Wolf, Opt. Lett. 31, 688 (2006).
[CrossRef] [PubMed]

O. Korotkova and E. Wolf, Opt. Lett. 30, 198 (2005).
[CrossRef] [PubMed]

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

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

M. Mujat, A. Dogariu, and E. Wolf, J. Opt. Soc. Am. A 21, 2414 (2004).
[CrossRef]

G. P. Agrawal and E. Wolf, J. Opt. Soc. Am. A 17, 2019 (2000).
[CrossRef]

L. Mandel and E. Wolf, Coherence and Quantum Optics (Cambridge U. Press, 1995), Sect. 4.7.

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

J. Opt. A, Pure Appl. Opt.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, J. Opt. A, Pure Appl. Opt. 3, 1 (2001).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

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

Y. Li, H. Lee, and E. Wolf, Opt. Commun. 265, 63 (2006).
[CrossRef]

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

Opt. Lett.

Other

L. Mandel and E. Wolf, Coherence and Quantum Optics (Cambridge U. Press, 1995), Sect. 4.7.

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

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Figures (1)

Fig. 1
Fig. 1

Degree of polarization, calculated from Eq. (18), of beams generated by two unpolarized sources along the axis as a function of the propagation distance z from the source plane. The parameters of the two sources have been chosen as: Beam 1, σ = 1 cm , λ = 0.633 μ m , δ x = 0.1 mm , δ y ( 1 ) = 0.2 mm . Beam 2, σ = 1 cm , λ = 0.633 μ m , δ x = 0.1 mm , δ y ( 2 ) = 1 mm .

Equations (24)

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P ( r , ω ) = s 1 2 ( r , ω ) + s 2 2 ( r , ω ) + s 3 2 ( r , ω ) s 0 ( r , ω ) .
S 0 ( r 1 , r 2 , ω ) = E x * ( r 1 , ω ) E x ( r 2 , ω ) + E y * ( r 1 , ω ) E y ( r 2 , ω ) ,
S 1 ( r 1 , r 2 , ω ) = E x * ( r 1 , ω ) E x ( r 2 , ω ) E y * ( r 1 , ω ) E y ( r 2 , ω ) ,
S 2 ( r 1 , r 2 , ω ) = E x * ( r 1 , ω ) E y ( r 2 , ω ) + E y * ( r 1 , ω ) E x ( r 2 , ω ) ,
S 3 ( r 1 , r 2 , ω ) = i E y * ( r 1 , ω ) E x ( r 2 , ω ) E x * ( r 1 , ω ) E y ( r 2 , ω ) .
s α ( r , ω ) = S α ( r , r , ω ) ( α = 0 , 1 , 2 , 3 ) .
S α ( r 1 , r 2 , ω ) = z = 0 S α ( 0 ) ( ρ 1 , ρ 2 , ω ) G * ( r 1 ρ 1 , z ; ω ) G ( r 2 ρ 2 , z ; ω ) d 2 ρ 1 d 2 ρ 2 ,
η ( r 1 , r 2 , ω ) = S 0 ( r 1 , r 2 , ω ) S 0 ( r 1 , r 1 , ω ) S 0 ( r 2 , r 2 , ω ) .
s α ( 2 ) ( ρ , ω ) = s α ( 1 ) ( ρ , ω ) ( α = 0 , 1 , 2 , 3 ) ,
S α ( 2 ) ( ρ 1 , ρ 2 , ω ) S α ( 1 ) ( ρ 1 , ρ 2 , ω ) ( α = 0 , 1 , 2 , 3 ) .
P ( 2 ) ( ρ , ω ) = P ( 1 ) ( ρ , ω ) .
s α ( 2 ) ( r , ω ) s α ( 1 ) ( r , ω ) ( α = 0 , 1 , 2 , 3 ) ,
W i i ( m ) ( 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 ( m ) ] 2 } ( m = 1 , 2 , i = x , y ) .
δ x ( 1 ) = δ x ( 2 ) δ x δ y ( 1 ) δ y ( 2 ) .
s 0 ( m ) ( ρ , ω ) = 2 exp ρ 2 2 σ 2 , s 1 , 2 , 3 ( m ) ( ρ , ω ) = 0 ,
S 0 , 1 ( m ) ( ρ 1 , ρ 2 , ω ) = exp [ ρ 1 2 + ρ 2 2 4 σ 2 ] exp [ ( ρ 2 ρ 1 ) 2 2 δ x 2 ] ± exp [ ρ 1 2 + ρ 2 2 4 σ 2 ] exp { ( ρ 2 ρ 1 ) 2 2 [ δ y ( m ) ] 2 } ,
S 2 ( m ) ( ρ 1 , ρ 2 , ω ) = S 3 ( m ) ( ρ 1 , ρ 2 , ω ) = 0 , ( m = 1 , 2 ) .
η ( m ) ( ρ 1 , ρ 2 , ω ) = exp ( ρ 2 ρ 1 ) 2 2 δ x 2 + exp ( ρ 2 ρ 1 ) 2 2 ( δ y ( m ) ) 2 , ( m = 1 , 2 ) .
s 0 , 1 ( m ) ( 0 , z , ω ) = 1 Δ x 2 ( z ) ± 1 [ Δ y ( m ) ( z ) ] 2 ,
s 2 ( m ) ( 0 , z , ω ) = s 3 ( m ) ( 0 , z , ω ) = 0 ,
Δ x 2 ( z ) = 1 + z 2 k 2 σ 2 ( 1 4 σ 2 + 1 δ x 2 ) ,
[ Δ y ( m ) ( z ) ] 2 = 1 + z 2 k 2 σ 2 ( 1 4 σ 2 + 1 [ δ y ( m ) ] 2 ) ( m = 1 , 2 ) .
s 0 ( 2 ) ( 0 , z , ω ) s 0 ( 1 ) ( 0 , z , ω ) , s 1 ( 2 ) ( 0 , z , ω ) s 1 ( 1 ) ( 0 , z , ω ) ,
P ( m ) ( 0 , z , ω ) = 1 Δ x 2 ( z ) 1 [ Δ y ( m ) ( z ) ] 2 ( 1 Δ x 2 ( z ) + 1 [ Δ y ( m ) ( z ) ] 2 ) ( m = 1 , 2 ) .

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