Abstract

The degree of coherence of scalar light remains constant when the fields are modified by the same random linear transformation, which can be represented by the multiplication by a random complex number. This shows that the coherence properties of scalar light at order two are not modified with the increase of disorder of each field that results from these transformations. We analyze the generalization of this property to partially polarized light. We determine the class of fields that can possess this property for any couple of points in a space-frequency or space-time domain after modification with deterministic Jones transformations. We show that the second-order coherence properties of this class of light can be generated experimentally with two uncorrelated totally polarized sources that have the same scalar coherence properties.

© 2014 Optical Society of America

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References

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  1. J. W. Goodman, Statistical Optics (Wiley, 1985).
  2. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).
  3. E. Wolf, Phys. Lett. A 312, 263 (2003).
    [CrossRef]
  4. J. Tervo, T. Setälä, and A. T. Friberg, Opt. Express 11, 1137 (2003).
    [CrossRef]
  5. F. Gori, M. Santarsiero, R. Simon, G. Piquero, R. Borghi, and G. Guattari, J. Opt. Soc. Am. A 20, 78 (2003).
    [CrossRef]
  6. S. A. Ponomarenko, H. Roychowdhury, and E. Wolf, Phys. Lett. A 345, 10 (2005).
    [CrossRef]
  7. Ph. Réfrégier and F. Goudail, Opt. Express 13, 6051 (2005).
    [CrossRef]
  8. A. Luis, J. Opt. Soc. Am A 24, 1063 (2007).
  9. R. Martinez-Herrero and P. M. Mejias, Opt. Lett. 32, 1504 (2007).
    [CrossRef]
  10. R. Martinez-Herrero, P. M. Mejias, and G. Piquero, in Characterization of Partially Polarized Light Fields (Springer-Verlag, 2009), pp. 93–124.
  11. Ph. Réfrégier, Opt. Lett. 33, 636 (2008).
    [CrossRef]
  12. Ph. Réfrégier and A. Luis, J. Opt. Soc. Am. A 25, 2749 (2008).
    [CrossRef]
  13. K. Kim, L. Mandel, and E. Wolf, J. Opt. Soc. Am. A 4, 433 (1987).
    [CrossRef]
  14. C. Brosseau and R. Barakat, Opt. Commun. 84, 127132 (1991).
  15. T. Shirai and E. Wolf, J. Opt. Soc. Am. A 21, 1907 (2004).
    [CrossRef]
  16. A. Roueff and Ph. Réfrégier, J. Opt. Soc. Am. A 25, 838 (2008).
    [CrossRef]
  17. Ph. Réfrégier, J. Tervo, and A. Roueff, Opt. Commun. 282, 1069 (2009).
  18. R. Martinez-Herrero and P. M. Mejias, Opt. Lett. 32, 1471 (2007).
    [CrossRef]
  19. F. Gori, M. Santarsiero, and R. Borghi, Opt. Lett. 32, 588 (2007).
    [CrossRef]

2009

Ph. Réfrégier, J. Tervo, and A. Roueff, Opt. Commun. 282, 1069 (2009).

2008

2007

2005

S. A. Ponomarenko, H. Roychowdhury, and E. Wolf, Phys. Lett. A 345, 10 (2005).
[CrossRef]

Ph. Réfrégier and F. Goudail, Opt. Express 13, 6051 (2005).
[CrossRef]

2004

2003

1991

C. Brosseau and R. Barakat, Opt. Commun. 84, 127132 (1991).

1987

Barakat, R.

C. Brosseau and R. Barakat, Opt. Commun. 84, 127132 (1991).

Borghi, R.

Brosseau, C.

C. Brosseau and R. Barakat, Opt. Commun. 84, 127132 (1991).

Friberg, A. T.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, 1985).

Gori, F.

Goudail, F.

Guattari, G.

Kim, K.

Luis, A.

Mandel, L.

K. Kim, L. Mandel, and E. Wolf, J. Opt. Soc. Am. A 4, 433 (1987).
[CrossRef]

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

Martinez-Herrero, R.

R. Martinez-Herrero and P. M. Mejias, Opt. Lett. 32, 1504 (2007).
[CrossRef]

R. Martinez-Herrero and P. M. Mejias, Opt. Lett. 32, 1471 (2007).
[CrossRef]

R. Martinez-Herrero, P. M. Mejias, and G. Piquero, in Characterization of Partially Polarized Light Fields (Springer-Verlag, 2009), pp. 93–124.

Mejias, P. M.

R. Martinez-Herrero and P. M. Mejias, Opt. Lett. 32, 1504 (2007).
[CrossRef]

R. Martinez-Herrero and P. M. Mejias, Opt. Lett. 32, 1471 (2007).
[CrossRef]

R. Martinez-Herrero, P. M. Mejias, and G. Piquero, in Characterization of Partially Polarized Light Fields (Springer-Verlag, 2009), pp. 93–124.

Piquero, G.

F. Gori, M. Santarsiero, R. Simon, G. Piquero, R. Borghi, and G. Guattari, J. Opt. Soc. Am. A 20, 78 (2003).
[CrossRef]

R. Martinez-Herrero, P. M. Mejias, and G. Piquero, in Characterization of Partially Polarized Light Fields (Springer-Verlag, 2009), pp. 93–124.

Ponomarenko, S. A.

S. A. Ponomarenko, H. Roychowdhury, and E. Wolf, Phys. Lett. A 345, 10 (2005).
[CrossRef]

Réfrégier, Ph.

Roueff, A.

Ph. Réfrégier, J. Tervo, and A. Roueff, Opt. Commun. 282, 1069 (2009).

A. Roueff and Ph. Réfrégier, J. Opt. Soc. Am. A 25, 838 (2008).
[CrossRef]

Roychowdhury, H.

S. A. Ponomarenko, H. Roychowdhury, and E. Wolf, Phys. Lett. A 345, 10 (2005).
[CrossRef]

Santarsiero, M.

Setälä, T.

Shirai, T.

Simon, R.

Tervo, J.

Ph. Réfrégier, J. Tervo, and A. Roueff, Opt. Commun. 282, 1069 (2009).

J. Tervo, T. Setälä, and A. T. Friberg, Opt. Express 11, 1137 (2003).
[CrossRef]

Wolf, E.

S. A. Ponomarenko, H. Roychowdhury, and E. Wolf, Phys. Lett. A 345, 10 (2005).
[CrossRef]

T. Shirai and E. Wolf, J. Opt. Soc. Am. A 21, 1907 (2004).
[CrossRef]

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

K. Kim, L. Mandel, and E. Wolf, J. Opt. Soc. Am. A 4, 433 (1987).
[CrossRef]

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

J. Opt. Soc. Am A

A. Luis, J. Opt. Soc. Am A 24, 1063 (2007).

J. Opt. Soc. Am. A

Opt. Commun.

C. Brosseau and R. Barakat, Opt. Commun. 84, 127132 (1991).

Ph. Réfrégier, J. Tervo, and A. Roueff, Opt. Commun. 282, 1069 (2009).

Opt. Express

Opt. Lett.

Phys. Lett. A

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

S. A. Ponomarenko, H. Roychowdhury, and E. Wolf, Phys. Lett. A 345, 10 (2005).
[CrossRef]

Other

J. W. Goodman, Statistical Optics (Wiley, 1985).

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

R. Martinez-Herrero, P. M. Mejias, and G. Piquero, in Characterization of Partially Polarized Light Fields (Springer-Verlag, 2009), pp. 93–124.

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Figures (1)

Fig. 1.
Fig. 1.

Schematic representation of a possible setup for generation of isotropic bicomponent light.

Equations (21)

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ΩE(x1,x2)=E(x1)E(x2)E,
ΓE(xj)=E(xj)E(xj)E.
A(xj)=JE(xj),
μW,E(x1,x2)=tr[ΩE(x1,x2)]tr[ΓE(x1)]tr[ΓE(x2)],
tr[JΩE(x1,x2)JJ]tr[JΓE(x1)JJ]tr[JΓE(x2)JJ]
ΓE(xi)=g(xi)ΓEfori=1,2
ΩE(x1,x2)=μW,E(x1,x2)g(x1)g(x2)ΓE,
ME(x1,x2)=ΓE1/2(x1)ΩE(x1,x2)ΓE1/2(x2).
ME(x1,x2)=U1(x1,x2)D(x1,x2)U2(x1,x2),
D(x1,x2)=(μS(x1,x2)00μI(x1,x2)),
ME(x1,x2)=μW,E(x1,x2)Id,
ΩE(x1,x2)=f(x1,x2)F(x1)F(x2)
μW,A=tr[GΩE]tr[GΓ1]tr[GΓ2]
(abcd)(a,b,c,d)T,
μW,A=vuvV1vV2,
r(vα)=ρβ[β+α(1β)][1α(1β)],
R=tr[JΓE1/2MEΓE1/2J]tr[JΓEJ]=tr[MEU]tr[U],
U=(abb*d)andME=(αγβδ),
F=αa+γb*+βb+δd.
F=αa+δd+γbR+βbRiγbI+iβbI.
aR=0α(a+d)=F,dR=0δ(a+d)=F,bRR=0(a+d)(β+γ)=0,bIR=0i(a+d)(βγ)=0.

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