Abstract

Given the values of the degree of polarization of the fields at the pinholes in a Young interferometer, the maximum attainable visibility under unitary transformations is determined when the illuminating beam is mean-square light. Analytical expressions are also obtained for both the field vector (in the mean-square sense) and the cross-spectral density matrix associated with this kind of beams. A comparative summary is also provided of the main characteristics of well-known types of random electromagnetic fields frequently handled in the literature.

© 2009 Optical Society of America

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References

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  1. E. Wolf, "Unified theory of coherence and polarization of random electromagnetic beams," Phys. Lett. A 312, 263-267 (2003).
    [CrossRef]
  2. J. Tervo, T. Setälä and A. T. Friberg, "Degree of coherence of electromagnetic fields," Opt. Express 11, 1137-1142 (2003).
    [CrossRef] [PubMed]
  3. M. Mujat and A. Dogariu, "Polarimetric and spectral changes in random electromagnetic fields," Opt. Lett. 28, 2153-2155 (2003).
    [CrossRef] [PubMed]
  4. T. Setälä, J. Tervo, and A. T. Friberg, "Complete coherence in the space-frequency domain," Opt. Lett. 29, 328-330 (2004).
    [CrossRef] [PubMed]
  5. H. Roychowdhury and E. Wolf, "Young’s interference experiment with light of any state of coherence and polarization," Opt. Commun. 252, 268-274 (2005).
    [CrossRef]
  6. Ph. Réfrégier and F. Goudail, "Invariant degrees of coherence of partially polarized light," Opt. Express 13, 6051-6060 (2005).
    [CrossRef] [PubMed]
  7. F. Gori, M. Santarsiero, R. Borghi, and E. Wolf, "Effect of coherence on the degree of polarization in a young interference pattern," Opt. Lett. 31, 688-690 (2006).
    [CrossRef] [PubMed]
  8. Ph. Réfrégier and A. Roueff, "Coherence polarization filtering and relation with intrinsic degrees of coehrence," Opt. Lett. 31, 1175-1177 (2006).
    [CrossRef] [PubMed]
  9. Ph. Réfrégier and A. Roueff, "Linear relations of partially polarized and coherent electromagnetic fields," Opt. Lett. 31, 2827-2829 (2006).
    [CrossRef] [PubMed]
  10. F. Gori, M. Santarsiero, and R. Borghi, "Vector mode analysis of a Young interferometer," Opt. Lett. 31, 858-860 (2006).
    [CrossRef] [PubMed]
  11. Y. Li, H. Lee, and E. Wolf, "Spectra, coherence and polarization in Young’s interference pattern formed by stochastic electromagnetic beams," Opt. Commun. 265, 63-72 (2006).
    [CrossRef]
  12. F. Gori, M. Santarsiero, and R. Borghi, "Maximizing Young’s fringe visibility through reversible optical transformations," Opt. Lett. 32,588-590 (2007).
    [CrossRef] [PubMed]
  13. Ph. Réfrégier and A. Roueff, "Intrinsic Coherence: A New Concept in Polarization and Coherence Theory," Opt. Photon. News 18, 30-35 (2007).
    [CrossRef]
  14. Ph. Réfrégier and A. Roueff, "Visibility interference fringes optimization on a single beam in the case of partially polarized and partially coherent light," Opt. Lett. 32,1366-1368 (2007).
    [CrossRef] [PubMed]
  15. R. Martínez-Herrero and P. M. Mejías, "Maximum visibility under unitary transformations in two-pinhole interference for electromagnetic fields," Opt. Lett. 32,1471-1473 (2007).
    [CrossRef] [PubMed]
  16. R. Martínez-Herrero and P. M. Mejías, "Relation between degrees of coherence for electromagnetic fields," Opt. Lett. 32, 1504-1506 (2007).
    [CrossRef] [PubMed]
  17. R. Martínez-Herrero and P. M. Mejías, "Electromagnetic fields that remain totally polarized under propagation," Opt. Commun. 279, 20-22 (2007).
    [CrossRef]
  18. E. Wolf, "Polarization invariance in beam propagation," Opt. Lett. 32, 3400-3401 (2007).
    [CrossRef] [PubMed]
  19. M. Santarsiero, "Polarization invariance in a Young interferometer," J. Opt. Soc. Am. A 24, 3493-3499 (2007).
    [CrossRef]
  20. R. Martínez-Herrero and P. M. Mejías, "On the vectorial fields with position-independent stochastic behavior," Opt. Lett. 33, 195-197 (2008).
    [CrossRef] [PubMed]
  21. Ph. Réfrégier, "Mean-square coherent light," Opt. Lett. 33, 1551-1553 (2008).
    [CrossRef] [PubMed]
  22. R. Martínez-Herrero and P. M. Mejías, "Equivalence between optimum Young’s fringe visibility and position-independent stochastic behaviour of electromagnetic fields," J. Opt. Soc. Am. A 25, 1902-1905 (2008).
    [CrossRef]
  23. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, England, 1995).
  24. J. Perina, Coherence of Light (Van Nostrand Reinhold Co., London, 1971).

2008

2007

2006

2005

H. Roychowdhury and E. Wolf, "Young’s interference experiment with light of any state of coherence and polarization," Opt. Commun. 252, 268-274 (2005).
[CrossRef]

Ph. Réfrégier and F. Goudail, "Invariant degrees of coherence of partially polarized light," Opt. Express 13, 6051-6060 (2005).
[CrossRef] [PubMed]

2004

2003

Borghi, R.

Dogariu, A.

Friberg, A. T.

Gori, F.

Goudail, F.

Lee, H.

Y. Li, H. Lee, and E. Wolf, "Spectra, coherence and polarization in Young’s interference pattern formed by stochastic electromagnetic beams," Opt. Commun. 265, 63-72 (2006).
[CrossRef]

Li, Y.

Y. Li, H. Lee, and E. Wolf, "Spectra, coherence and polarization in Young’s interference pattern formed by stochastic electromagnetic beams," Opt. Commun. 265, 63-72 (2006).
[CrossRef]

Martínez-Herrero, R.

Mejías, P. M.

Mujat, M.

Réfrégier, Ph.

Roueff, A.

Roychowdhury, H.

H. Roychowdhury and E. Wolf, "Young’s interference experiment with light of any state of coherence and polarization," Opt. Commun. 252, 268-274 (2005).
[CrossRef]

Santarsiero, M.

Setälä, T.

Tervo, J.

Wolf, E.

E. Wolf, "Polarization invariance in beam propagation," Opt. Lett. 32, 3400-3401 (2007).
[CrossRef] [PubMed]

Y. Li, H. Lee, and E. Wolf, "Spectra, coherence and polarization in Young’s interference pattern formed by stochastic electromagnetic beams," Opt. Commun. 265, 63-72 (2006).
[CrossRef]

F. Gori, M. Santarsiero, R. Borghi, and E. Wolf, "Effect of coherence on the degree of polarization in a young interference pattern," Opt. Lett. 31, 688-690 (2006).
[CrossRef] [PubMed]

H. Roychowdhury and E. Wolf, "Young’s interference experiment with light of any state of coherence and polarization," Opt. Commun. 252, 268-274 (2005).
[CrossRef]

E. Wolf, "Unified theory of coherence and polarization of random electromagnetic beams," Phys. Lett. A 312, 263-267 (2003).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

Y. Li, H. Lee, and E. Wolf, "Spectra, coherence and polarization in Young’s interference pattern formed by stochastic electromagnetic beams," Opt. Commun. 265, 63-72 (2006).
[CrossRef]

R. Martínez-Herrero and P. M. Mejías, "Electromagnetic fields that remain totally polarized under propagation," Opt. Commun. 279, 20-22 (2007).
[CrossRef]

H. Roychowdhury and E. Wolf, "Young’s interference experiment with light of any state of coherence and polarization," Opt. Commun. 252, 268-274 (2005).
[CrossRef]

Opt. Express

Opt. Lett.

F. Gori, M. Santarsiero, R. Borghi, and E. Wolf, "Effect of coherence on the degree of polarization in a young interference pattern," Opt. Lett. 31, 688-690 (2006).
[CrossRef] [PubMed]

F. Gori, M. Santarsiero, and R. Borghi, "Vector mode analysis of a Young interferometer," Opt. Lett. 31, 858-860 (2006).
[CrossRef] [PubMed]

Ph. Réfrégier and A. Roueff, "Coherence polarization filtering and relation with intrinsic degrees of coehrence," Opt. Lett. 31, 1175-1177 (2006).
[CrossRef] [PubMed]

Ph. Réfrégier and A. Roueff, "Linear relations of partially polarized and coherent electromagnetic fields," Opt. Lett. 31, 2827-2829 (2006).
[CrossRef] [PubMed]

F. Gori, M. Santarsiero, and R. Borghi, "Maximizing Young’s fringe visibility through reversible optical transformations," Opt. Lett. 32,588-590 (2007).
[CrossRef] [PubMed]

Ph. Réfrégier and A. Roueff, "Visibility interference fringes optimization on a single beam in the case of partially polarized and partially coherent light," Opt. Lett. 32,1366-1368 (2007).
[CrossRef] [PubMed]

R. Martínez-Herrero and P. M. Mejías, "Maximum visibility under unitary transformations in two-pinhole interference for electromagnetic fields," Opt. Lett. 32,1471-1473 (2007).
[CrossRef] [PubMed]

R. Martínez-Herrero and P. M. Mejías, "Relation between degrees of coherence for electromagnetic fields," Opt. Lett. 32, 1504-1506 (2007).
[CrossRef] [PubMed]

M. Mujat and A. Dogariu, "Polarimetric and spectral changes in random electromagnetic fields," Opt. Lett. 28, 2153-2155 (2003).
[CrossRef] [PubMed]

T. Setälä, J. Tervo, and A. T. Friberg, "Complete coherence in the space-frequency domain," Opt. Lett. 29, 328-330 (2004).
[CrossRef] [PubMed]

E. Wolf, "Polarization invariance in beam propagation," Opt. Lett. 32, 3400-3401 (2007).
[CrossRef] [PubMed]

R. Martínez-Herrero and P. M. Mejías, "On the vectorial fields with position-independent stochastic behavior," Opt. Lett. 33, 195-197 (2008).
[CrossRef] [PubMed]

Ph. Réfrégier, "Mean-square coherent light," Opt. Lett. 33, 1551-1553 (2008).
[CrossRef] [PubMed]

Opt. Photon. News

Ph. Réfrégier and A. Roueff, "Intrinsic Coherence: A New Concept in Polarization and Coherence Theory," Opt. Photon. News 18, 30-35 (2007).
[CrossRef]

Phys. Lett. A

E. Wolf, "Unified theory of coherence and polarization of random electromagnetic beams," Phys. Lett. A 312, 263-267 (2003).
[CrossRef]

Other

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

J. Perina, Coherence of Light (Van Nostrand Reinhold Co., London, 1971).

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Figures (1)

Fig. 1.
Fig. 1.

Illustrating the relation {T} ⊂ {V} ⊂ {R *} ⊂ {R}

Equations (35)

Equations on this page are rendered with MathJax. Learn more.

Wr1r2=f*(r1)f(r2),
ŴijŴrirj=E(ri)E(rj),i,j=1,2,
g12=gr1r2=Tr(Ŵ12Ŵ12)+2DetŴ12Tr(Ŵ11)Tr(Ŵ22),
g12=μSTF2+12(1P12)(1P22),
[gr1r2]max=12[1+P(r1)P(r2)+(1P2(r1))(1P2(r2))].
Ŵr1r2=λ1Ψ1(r1)Ψ1(r2)+λ2Ψ2(r1)Ψ2(r2),
Ŵr1r2=Ĥ(r1)Ĥ(r2),
Ĥ(r)=(λ1ψ11(r)λ1Ψ12(r)λ2Ψ21(r)λ2Ψ22(r)),
Ĥ(r)=V̂(r)D̂(r)Û(r),
D̂(r)=(α(r)00β(r)),
P(r)=α2(r)β2(r)α2(r)+β2(r).
Ŵr1r2=Û(r1)D̂(r1)V̂(r1)V̂(r2)D̂(r2)Û(r2).
Tr[Ŵr1r2Ŵr1r2]=Tr[D̂2(r1)Ŝr1r2D̂2(r2)Ŝr1r2],
Ŝr1r2=V̂(r1)V̂(r2),
Tr[Ŵr1r2Ŵr1r2]=
=cos2θ[α2(r1)α2(r2)+β2(r1)β2(r2)]+sin2θ[α2(r1)β2(r2)+β2(r1)α2(r2)],
S11=cosθr1r2=S22,
S12=sinθr1r2=S21,
1+P(r1)P(r2)=2α2(r1)α2(r2)+2β2(r1)β2(r2)TrŴr1r1TrŴr2r2,
1P(r1)P(r2)=2α2(r1)β2(r2)+2β2(r1)α2(r2)TrŴr1r1TrŴr2r2.
μSTF2=Tr(Ŵ12Ŵ12)Tr(Ŵ11)Tr(Ŵ22)=12[1+P(r1)P(r2)cos2θr1r2],
gr1r2=12[1+P(r1)P(r2)cos2θr1r2+(1P2(r1))(1P2(r2))].
[gr1r2]max=12[1+P(r1)P(r2)+(1P2(r1))(1P2(r2))],
Ŝr1r2=V̂(r1)V̂(r2)=(expi[φ(r2)φ(r2)]00expi[ϕ(r2)ϕ(r1)]).
V̂(r)=M̂(r)Q̂ ,
Ŵr1r2=Û(r1)D̂0(r1)D̂0(r2)Û(r2),
D̂0(r)=(α(r)expiφ(r)00β(r)expiϕ(r)).
E(r)=E0D̂0(r)Û(r),
E(r)=ε1Ψ˜1(r)+ε2Ψ˜2(r),
Ψ˜1(r)α(r)expiφ(r)(U11(r)U12(r)),
Ψ˜2(r)β(r)expiϕ(r)(U21(r)U22(r)),
E(r)=E0f(r)Û(r),
E(r)=ε1Ψ1(r)+ε2Ψ2(r),
E(r)=E0D̂0(r)Û(r)=ε1Ψ˜1(r)+ε2Ψ˜2(r),
{T}{V}{R*}{R}.

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