Abstract

Stochastic electromagnetic fields characterized by optimized fringe visibility in a Young interferometric arrangement are shown to be those whose random character is position independent. The optimization procedure involves local unitary transformations, which can be implemented by using reversible anisotropic polarization devices placed at the two pinholes. It is also shown that the local degree of polarization in the optimized interferometer is constant across the superposition region and coincides with the degree of polarization at the two pinholes.

© 2008 Optical Society of America

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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, “Linear relations of partially polarized and coherent electromagnetic fields,” Opt. Lett. 31, 2827-2829 (2006).
    [CrossRef] [PubMed]
  9. F. Gori, M. Santarsiero, and R. Borghi, “Maximizing Young's fringe visibility through reversible optical transformations,” Opt. Lett. 32, 588-590 (2007).
    [CrossRef] [PubMed]
  10. Ph. Réfrégier and A. Roueff, “Intrinsic coherence: A new concept in polarization and coherence theory,” Opt. Photonics News 18, 30-35 (2007).
    [CrossRef]
  11. 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]
  12. 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]
  13. R. Martínez-Herrero and P. M. Mejías, “Relation between degrees of coherence for electromagnetic fields,” Opt. Lett. 32, 1504-1506 (2007).
    [CrossRef] [PubMed]
  14. R. Martínez-Herrero and P. M. Mejías, “Electromagnetic fields that remain totally polarized under propagation,” Opt. Commun. 279, 20-22 (2007).
    [CrossRef]
  15. E. Wolf, “Polarization invariance in beam propagation,” Opt. Lett. 32, 3400-3401 (2007).
    [CrossRef] [PubMed]
  16. R. Martínez-Herrero and P. M. Mejías, “On the vectorial fields with position-independent stochastic behavior,” Opt. Lett. 33, 195-197 (2008).
    [CrossRef] [PubMed]
  17. F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherent polarization matrix,” Pure Appl. Opt. 7, 941-951 (1998).
    [CrossRef]
  18. F. Gori, M. Santarsiero, and R. Borghi, “Vector mode analysis of a Young interferometer,” Opt. Lett. 31, 858-860 (2006).
    [CrossRef] [PubMed]
  19. 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]
  20. T. Setälä, J. Tervo, and A. T. Friberg, “Stokes parameters and polarization contrasts in Young's interference experiment,” Opt. Lett. 31, 2208-2210 (2006).
    [CrossRef] [PubMed]
  21. M. Santarsiero, “Polarization invariance in a Young interferometer,” J. Opt. Soc. Am. A 24, 3493-3499 (2007).
    [CrossRef]
  22. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  23. J. Perina, Coherence of Light (Van Nostrand Reinhold, 1971).
  24. The simple proof connecting Eqs. should be acknowledged to an anonymous referee.
  25. C. Brosseau, Fundamentals of Polarized Light (Wiley, 1998).
  26. P. M. Mejías, R. Martínez-Herrero, G. Piquero, and J. M. Movilla, “Parametric characterization of the spatial structure of non-uniformly polarized laser beams,” Prog. Quantum Electron. 26, 65-130 (2002).
    [CrossRef]

2008 (1)

2007 (8)

2006 (5)

2005 (2)

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

2004 (1)

2003 (3)

2002 (1)

P. M. Mejías, R. Martínez-Herrero, G. Piquero, and J. M. Movilla, “Parametric characterization of the spatial structure of non-uniformly polarized laser beams,” Prog. Quantum Electron. 26, 65-130 (2002).
[CrossRef]

1998 (2)

C. Brosseau, Fundamentals of Polarized Light (Wiley, 1998).

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherent polarization matrix,” Pure Appl. Opt. 7, 941-951 (1998).
[CrossRef]

1995 (1)

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

1971 (1)

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

Borghi, R.

Brosseau, C.

C. Brosseau, Fundamentals of Polarized Light (Wiley, 1998).

Dogariu, A.

Friberg, A. T.

Gori, F.

Goudail, F.

Guattari, G.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherent polarization matrix,” Pure Appl. Opt. 7, 941-951 (1998).
[CrossRef]

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]

Mandel, L.

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

Martínez-Herrero, R.

Mejías, P. M.

Movilla, J. M.

P. M. Mejías, R. Martínez-Herrero, G. Piquero, and J. M. Movilla, “Parametric characterization of the spatial structure of non-uniformly polarized laser beams,” Prog. Quantum Electron. 26, 65-130 (2002).
[CrossRef]

Mujat, M.

Perina, J.

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

Piquero, G.

P. M. Mejías, R. Martínez-Herrero, G. Piquero, and J. M. Movilla, “Parametric characterization of the spatial structure of non-uniformly polarized laser beams,” Prog. Quantum Electron. 26, 65-130 (2002).
[CrossRef]

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.

Vicalvi, S.

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherent polarization matrix,” Pure Appl. Opt. 7, 941-951 (1998).
[CrossRef]

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]

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

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

Opt. Commun. (3)

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 (2)

Opt. Lett. (12)

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]

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]

T. Setälä, J. Tervo, and A. T. Friberg, “Stokes parameters and polarization contrasts in Young's interference experiment,” Opt. Lett. 31, 2208-2210 (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]

Opt. Photonics News (1)

Ph. Réfrégier and A. Roueff, “Intrinsic coherence: A new concept in polarization and coherence theory,” Opt. Photonics News 18, 30-35 (2007).
[CrossRef]

Phys. Lett. A (1)

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

Prog. Quantum Electron. (1)

P. M. Mejías, R. Martínez-Herrero, G. Piquero, and J. M. Movilla, “Parametric characterization of the spatial structure of non-uniformly polarized laser beams,” Prog. Quantum Electron. 26, 65-130 (2002).
[CrossRef]

Pure Appl. Opt. (1)

F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherent polarization matrix,” Pure Appl. Opt. 7, 941-951 (1998).
[CrossRef]

Other (4)

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

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

The simple proof connecting Eqs. should be acknowledged to an anonymous referee.

C. Brosseau, Fundamentals of Polarized Light (Wiley, 1998).

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Equations (28)

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W ̂ i j W ̂ ( r i , r j ) = E + ( r i ) E ( r j ) , i , j = 1 , 2 ,
E ( r ) = E 0 f ( r ) U ̂ ( r ) ,
V ( r ) = γ g ( r ) ,
W ̂ ( r 1 , r 2 ) = M ̂ + ( r 1 ) φ ̂ M ̂ ( r 2 ) ,
φ ̂ = E 0 + E 0 = ( α 2 α * β α β * β 2 ) ,
μ W 2 = tr W ̂ 12 2 tr W ̂ 11 tr W ̂ 22 ,
g 12 = ( μ W 2 ) max = tr ( W ̂ 12 W ̂ 21 ) + 2 Det W ̂ 12 tr W ̂ 11 tr W ̂ 22 ,
g 12 = 1 , for any r Ω .
μ W 2 = tr W ̂ 12 2 tr W ̂ 11 tr W ̂ 22 = 1 ,
W ̂ i j = U ̂ i + W ̂ i j U ̂ j , i , j = 1 , 2 .
tr W ̂ 12 2 = tr ( E 1 ) + E 2 2 = E 1 2 E 2 2 for any r 1 , r 2 Ω ,
E i = E i U ̂ i , I = 1 , 2 ,
E ( r 1 ) = ρ ( r 1 , r 2 ) E ( r 2 ) , r 1 , r 2 Ω .
ρ 12 ρ ( r 1 , r 2 ) = ρ ( r 1 , r 3 ) ρ ( r 3 , r 2 ) ρ 13 ρ 32 ,
ρ 12 = 1 = ρ 13 ρ 31 ,
ρ a b = ρ b a 1 .
ρ 12 = ρ 13 ρ 23 .
ρ 12 = g ( r 1 ) f ( r 2 ) ,
ρ 12 = g ( r 1 ) f ( r 2 ) = ρ 21 1 = f ( r 1 ) g ( r 2 ) , r 1 , r 2 Ω ,
E ( r 1 ) = f ( r 1 ) f ( r 2 ) E ( r 2 ) E ( r 1 ) f ( r 1 ) = E ( r 2 ) f ( r 2 ) = = E 0 ,
r 1 , r 2 Ω ,
E ( r ) = f ( r ) E 0 ( in the mean square sense ) , for any r Ω .
W ̂ ( r 1 , r 2 ) = f * ( r 1 ) f ( r 2 ) φ ̂ ,
W ̂ ( r 1 , r 2 ) = f * ( r 1 ) f ( r 2 ) U ̂ 1 + φ ̂ U ̂ 2 .
P S 2 ( R ) = 1 4 Det W ̂ S ( R , R ) [ tr W ̂ S ( R , R ) ] 2 ,
W ̂ S ( R , R ) = W ̂ ( r 1 , r 1 ) + W ̂ ( r 2 , r 2 ) + W ̂ ( r 1 , r 2 ) exp ( i δ ) + W ̂ ( r 2 , r 1 ) exp ( i δ ) ,
W ̂ S ( R , R ) = f ( r 1 ) + f ( r 2 ) exp ( i δ ) 2 φ ̂ ,
P S 2 ( R ) = 1 4 Det φ ̂ ( tr φ ̂ ) 2 ,

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