Abstract

The generalized Stokes parameters (GSP) are studied under the theory of phase space. It is noted that phase-space Stokes parameters can be a useful tool for Wigner distribution function measurements. Electromagnetic Wigner functions are introduced by use of the two-point statistics of GSP. The advantage in the GSP is that they can be measured in terms of the electric correlation matrix (which is a measurable quantity) or they can be measured independently. Hence, the GSP help in finding the polarization and coherence properties of electromagnetic beams. Within this framework, by using the GSP in phase space, the intensity feature of electromagnetic beams in phase space is given, as well.

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References

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S. Cho, J. C. Petruccelli, and M. A. Alonso, J. Mod. Opt. 56, 1843 (2009).
[CrossRef]

S. Sahin, O. Korotkova, G. Zhang, and J. Pu, J. Opt. A Pure Appl. Opt. 11, 085703 (2009).
[CrossRef]

B. Kanseri, S. Rath, and H. C. Kandpal, Opt. Lett. 34, 719(2009).
[CrossRef] [PubMed]

2008 (3)

2007 (1)

A. C. Fannjiang, J. Phys. A 40, 13667 (2007).
[CrossRef]

2005 (4)

2004 (1)

2003 (1)

1995 (1)

1993 (1)

D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, Phys. Rev. Lett. 70, 1244 (1993).
[CrossRef] [PubMed]

1979 (2)

M. J. Bastiaans, J. Opt. Soc. Am. 69, 1710 (1979).
[CrossRef]

M. J. Bastiaans, J. Mod. Opt. 26, 1265 (1979).

Alonso, M. A.

S. Cho, J. C. Petruccelli, and M. A. Alonso, J. Mod. Opt. 56, 1843 (2009).
[CrossRef]

Banaszek, K.

Bastiaans, M. J.

M. J. Bastiaans, J. Mod. Opt. 26, 1265 (1979).

M. J. Bastiaans, J. Opt. Soc. Am. 69, 1710 (1979).
[CrossRef]

Beck, M.

D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, Phys. Rev. Lett. 70, 1244 (1993).
[CrossRef] [PubMed]

Betancur, R.

Brosseau, C.

C. Brosseau, Appl. Opt. 34, 4788 (1995).
[CrossRef] [PubMed]

C. Brosseau, Polarized Light: A Statistical Optics Approach (Wiley, 1998).

Castaneda, R.

Cho, S.

S. Cho, J. C. Petruccelli, and M. A. Alonso, J. Mod. Opt. 56, 1843 (2009).
[CrossRef]

Curtright, T. L.

C. K. Zachos, D. B. Fairlie, and T. L. Curtright, Quantum Mechanics in Phase Space: An Overview with Selected Papers (World Scientific, 2005).
[CrossRef]

Dorrer, C.

Duan, K.

Fairlie, D. B.

C. K. Zachos, D. B. Fairlie, and T. L. Curtright, Quantum Mechanics in Phase Space: An Overview with Selected Papers (World Scientific, 2005).
[CrossRef]

Fannjiang, A. C.

A. C. Fannjiang, J. Phys. A 40, 13667 (2007).
[CrossRef]

Faridani, A.

D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, Phys. Rev. Lett. 70, 1244 (1993).
[CrossRef] [PubMed]

James, D. F. V.

S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, J. Opt. A Pure Appl. Opt. 10, 055001 (2008).
[CrossRef]

Kandpal, H. C.

Kanseri, B.

Korotkova, O.

S. Sahin, O. Korotkova, G. Zhang, and J. Pu, J. Opt. A Pure Appl. Opt. 11, 085703 (2009).
[CrossRef]

H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).
[CrossRef]

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

Lu, B.

Luis, A.

A. Luis, Opt. Commun. 251, 243 (2005).
[CrossRef]

Mandel, L.

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

Mukamel, E.

Petruccelli, J. C.

S. Cho, J. C. Petruccelli, and M. A. Alonso, J. Mod. Opt. 56, 1843 (2009).
[CrossRef]

Pu, J.

S. Sahin, O. Korotkova, G. Zhang, and J. Pu, J. Opt. A Pure Appl. Opt. 11, 085703 (2009).
[CrossRef]

Rath, S.

Raymer, M. G.

D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, Phys. Rev. Lett. 70, 1244 (1993).
[CrossRef] [PubMed]

Restrepo, J. F.

Roychowdhury, H.

H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).
[CrossRef]

Sahin, S.

S. Sahin, O. Korotkova, G. Zhang, and J. Pu, J. Opt. A Pure Appl. Opt. 11, 085703 (2009).
[CrossRef]

Shirai, T.

S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, J. Opt. A Pure Appl. Opt. 10, 055001 (2008).
[CrossRef]

Smithey, D. T.

D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, Phys. Rev. Lett. 70, 1244 (1993).
[CrossRef] [PubMed]

Volkov, S. N.

S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, J. Opt. A Pure Appl. Opt. 10, 055001 (2008).
[CrossRef]

Walmsley, I. A.

Wolf, E.

S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, J. Opt. A Pure Appl. Opt. 10, 055001 (2008).
[CrossRef]

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

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

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

Zachos, C. K.

C. K. Zachos, D. B. Fairlie, and T. L. Curtright, Quantum Mechanics in Phase Space: An Overview with Selected Papers (World Scientific, 2005).
[CrossRef]

Zhang, G.

S. Sahin, O. Korotkova, G. Zhang, and J. Pu, J. Opt. A Pure Appl. Opt. 11, 085703 (2009).
[CrossRef]

Zhang, Y.

Appl. Opt. (1)

J. Mod. Opt. (2)

S. Cho, J. C. Petruccelli, and M. A. Alonso, J. Mod. Opt. 56, 1843 (2009).
[CrossRef]

M. J. Bastiaans, J. Mod. Opt. 26, 1265 (1979).

J. Opt. A Pure Appl. Opt. (2)

S. N. Volkov, D. F. V. James, T. Shirai, and E. Wolf, J. Opt. A Pure Appl. Opt. 10, 055001 (2008).
[CrossRef]

S. Sahin, O. Korotkova, G. Zhang, and J. Pu, J. Opt. A Pure Appl. Opt. 11, 085703 (2009).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

J. Phys. A (1)

A. C. Fannjiang, J. Phys. A 40, 13667 (2007).
[CrossRef]

Opt. Commun. (2)

H. Roychowdhury and O. Korotkova, Opt. Commun. 249, 379 (2005).
[CrossRef]

A. Luis, Opt. Commun. 251, 243 (2005).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. Lett. (1)

D. T. Smithey, M. Beck, M. G. Raymer, and A. Faridani, Phys. Rev. Lett. 70, 1244 (1993).
[CrossRef] [PubMed]

Other (4)

C. K. Zachos, D. B. Fairlie, and T. L. Curtright, Quantum Mechanics in Phase Space: An Overview with Selected Papers (World Scientific, 2005).
[CrossRef]

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

C. Brosseau, Polarized Light: A Statistical Optics Approach (Wiley, 1998).

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

Three-dimensional plot of (a) Eq. (14) and (b) Eq. (11). Data used: σ = 5 cm , δ x x = δ y y = 1 mm , δ y x = δ x y = 1.2 mm , A x = A y = 1 , B x x = B y y = 1 , B = 0.8 , and θ = 0 .

Equations (18)

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W ( r 1 , r 2 , ω ) = ( W x x ( r 1 , r 2 , ω ) W x y ( r 1 , r 2 , ω ) W y x ( r 1 , r 2 , ω ) W y y ( r 1 , r 2 , ω ) ) ,
S 0 ( r 1 , r 2 , ω ) = W x x ( r 1 , r 2 , ω ) + W y y ( r 1 , r 2 , ω ) ,
S 1 ( r 1 , r 2 , ω ) = W x x ( r 1 , r 2 , ω ) W y y ( r 1 , r 2 , ω ) ,
S 2 ( r 1 , r 2 , ω ) = W x y ( r 1 , r 2 , ω ) + W y x ( r 1 , r 2 , ω ) ,
S 3 ( r 1 , r 2 , ω ) = i [ W y x ( r 1 , r 2 , ω ) W x y ( r 1 , r 2 , ω ) ] .
F i j ( r , k , ω 1 , ω 2 ) = W i j ( r + r / 2 , r r / 2 , ω 1 , ω 2 ) e i r · k d r ,
S l ( r , k , ω 1 , ω 2 ) = S l ( r + r / 2 , r r / 2 , ω 1 , ω 2 ) e i r · k d r , ( l = 0 , 1 , 2 , 3 ) .
S l ( r , k , ω ) = S l ( r + r / 2 , r r / 2 , ω ) e i r · k d r .
I p ( r , r , ω ) = S 0 ( r , k , ω ) d k ,
I d ( k , k , ω ) = S 0 ( r , k , ω ) d r .
S l ( r , k , z , ω ) = S l ( r λ z 2 π k , k , 0 , ω ) ,
S l ( r , k , z , ω ) = z 2 ρ 2 S l ( r λ ρ 2 π k , k , 0 , ω ) .
W i j ( r 1 , r 2 , z = 0 , ω ) = ( A i A j ) 1 / 2 B i j exp [ 1 4 σ 2 ( r 1 2 + r 2 2 ) ] × exp [ 1 2 δ i j 2 ( r 2 r 1 ) 2 ] .
S 0 ( r , k , 0 , ω ) = ( π Λ x x ) 1 / 2 A x B x x e ( r 2 2 σ 2 + k 2 4 Λ x x ) + ( π Λ y y ) 1 / 2 A y B y y e ( r 2 2 σ 2 + k 2 4 Λ y y ) ,
S 1 ( r , k , 0 , ω ) = ( π Λ x x ) 1 / 2 A x B x x e ( r 2 2 σ 2 + k 2 4 Λ x x ) ( π Λ y y ) 1 / 2 A y B y y e ( r 2 2 σ 2 + k 2 4 Λ y y ) ,
S 2 ( r , k , 0 , ω ) = ( π A x A y Λ x y ) 1 / 2 B x y e ( r 2 2 σ 2 + k 2 4 Λ x y ) + ( π A x A y Λ y x ) 1 / 2 B y x e ( r 2 2 σ 2 + k 2 4 Λ y x ) ,
S 3 ( r , k , 0 , ω ) = i [ ( π A x A y Λ y x ) 1 / 2 B y x e ( r 2 2 σ 2 + k 2 4 Λ y x ) ( π A x A y Λ x y ) 1 / 2 B x y e ( r 2 2 σ 2 + k 2 4 Λ x y ) ] ,
Λ i j = 1 8 σ 2 + 1 2 δ i j 2 .

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