Abstract

We consider polarization changes of partially coherent pulses propagating through birefringent dispersive fibers in the linear regime. We show that the evolution of the degree of polarization across such pulses is determined not only by the coherence properties of the pulse in the source plane, but also by the spatial walk-off introduced by the group-velocity mismatch between the two polarization components. The interplay between these two factors determines the asymptotic value of the degree of polarization of an initially unpolarized statistical pulse. We compare our results with previously discussed coherence-induced polarization changes of partially coherent beams propagating in free space.

© 2007 Optical Society of America

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  1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995).
  2. J. Pérez-Téllez, F. Mendieta-Jiménez, and A. Arvizu-Mondragón, "Degree of polarization and heterodyne spectrum in coherent detection of partially polarized wavefield," J. Mod. Opt. 52, 2511-2522 (2005).
    [CrossRef]
  3. E. Wolf, "Unified theory of coherence and polarization of random electromagnetic beams," Phys. Lett. A 312, 263-267 (2003).
    [CrossRef]
  4. Q. D. Liu, L. Shi, P. P. Ho, and R. R. Alfano, "Nonlinear vector rotation and depolarization of femtosecond laser pulses propagating in non-birefringent single-mode optical fibers," Opt. Commun. 138, 45-48 (1997).
    [CrossRef]
  5. Q. Lin and Govind P. Agrawal, "Intrapulse depolarization in optical fibers: a classical analog of spin decoherence," Opt. Lett. 30, 821-823 (2005).
    [CrossRef] [PubMed]
  6. G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).
  7. A. K. Jaiswal, G. P. Agrawal, and C. L. Mehta, "Coherence functions in the far-field diffraction plane," Nuovo Cimento B 15, 295-307 (1973).
    [CrossRef]
  8. D. James, "Change of polarization of light beams on propagation in free space," J. Opt. Soc. Am. A 11, 1641-1643 (1993).
    [CrossRef]
  9. G. P. Agrawal and E. Wolf, "Propagation-induced polarization changes in partially coherent optical beams," J. Opt. Soc. Am. A 17, 2019-2023 (2000).
    [CrossRef]
  10. E. Wolf, "Correlation-induced changes in the degree of polarization, the degree of coherence, and the spectrum of random electromagnetic beams on propagation," Opt. Lett. 28, 1078-1080 (2003).
    [CrossRef] [PubMed]
  11. F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, "Partially polarized Gaussian Schell-model beams," J. Opt. A, Pure Appl. Opt. 3, 1-9 (2001).
    [CrossRef]
  12. J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, "Correlation matrix of a completely polarized, statistically stationary electromagnetic field," Opt. Lett. 29, 1536-1538 (2004).
    [CrossRef] [PubMed]
  13. J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, "Degree of polarization of statistically stationary electromagnetic fields," Opt. Commun. 248, 333-337 (2005).
    [CrossRef]
  14. H. Roychowdhury, S. Ponomarenko, and E. Wolf, "Change in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmostphere," J. Mod. Opt. 52, 1611-1618 (2005).
    [CrossRef]
  15. H. Roychowdhury, G. P. Agrawal, and E. Wolf, "Changes in the spectrum, in the spectral degree of polarization, and in the spectral degree of coherence of a partially coherent beam propagating through a gradient-index fiber," J. Opt. Soc. Am. A 23, 940-948 (2006).
    [CrossRef]
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    [CrossRef]
  19. Q. Lin, L. Wang, and S. Zhu, "Partially coherent light pulse and its propagation," Opt. Commun. 219, 67-70 (2003).
    [CrossRef]
  20. P. Paakkonen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, "Partially coherent Gaussian pulses," Opt. Commun. 204, 53-58 (2002).
    [CrossRef]
  21. S. A. Ponomarenko, G. P. Agrawal, and E. Wolf, "Energy spectrum of a nonstationary ensemble of pulses," Opt. Lett. 29, 394-396 (2004).
    [CrossRef] [PubMed]
  22. H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, "Spectrally partially coherent pulses in dispersive media," Opt. Commun. 255, 12-20 (2005).
    [CrossRef]
  23. H. Lajunen, A. T. Friberg, and P. Ostlund, "Quasi-stationary plane-wave optical pulses and the van Cittert-Zernike theorem in time," J. Opt. Soc. Am. A 23, 2530-2537 (2006).
    [CrossRef]
  24. J. Cho, J. W. Lee, J. S. Im, C. Sone, Y. Park, D. Kim, H. Jeon, E. Yoon, D. S. Leem, and T. Y. Seong, "Recent developments in patterned structure light-emitting diodes," Proc. SPIE 5941, 11-18 (2005).
  25. S. Robinson and I. Ashdown, "Polychromatic optical feedback: Control, stability, and dimming," Proc. SPIE 6337, 633714(1-10) (2005).
  26. J. Lancis, V. Torres-Company, E. Silvestre, and P. Andés, "Space-time analogy for partially coherent plane-wave pulses," Opt. Lett. 30, 2973-2975 (2005).
    [CrossRef] [PubMed]

2006 (2)

2005 (8)

J. Cho, J. W. Lee, J. S. Im, C. Sone, Y. Park, D. Kim, H. Jeon, E. Yoon, D. S. Leem, and T. Y. Seong, "Recent developments in patterned structure light-emitting diodes," Proc. SPIE 5941, 11-18 (2005).

S. Robinson and I. Ashdown, "Polychromatic optical feedback: Control, stability, and dimming," Proc. SPIE 6337, 633714(1-10) (2005).

J. Lancis, V. Torres-Company, E. Silvestre, and P. Andés, "Space-time analogy for partially coherent plane-wave pulses," Opt. Lett. 30, 2973-2975 (2005).
[CrossRef] [PubMed]

H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, "Spectrally partially coherent pulses in dispersive media," Opt. Commun. 255, 12-20 (2005).
[CrossRef]

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, "Degree of polarization of statistically stationary electromagnetic fields," Opt. Commun. 248, 333-337 (2005).
[CrossRef]

H. Roychowdhury, S. Ponomarenko, and E. Wolf, "Change in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmostphere," J. Mod. Opt. 52, 1611-1618 (2005).
[CrossRef]

J. Pérez-Téllez, F. Mendieta-Jiménez, and A. Arvizu-Mondragón, "Degree of polarization and heterodyne spectrum in coherent detection of partially polarized wavefield," J. Mod. Opt. 52, 2511-2522 (2005).
[CrossRef]

Q. Lin and Govind P. Agrawal, "Intrapulse depolarization in optical fibers: a classical analog of spin decoherence," Opt. Lett. 30, 821-823 (2005).
[CrossRef] [PubMed]

2004 (2)

2003 (3)

Q. Lin, L. Wang, and S. Zhu, "Partially coherent light pulse and its propagation," Opt. Commun. 219, 67-70 (2003).
[CrossRef]

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

E. Wolf, "Correlation-induced changes in the degree of polarization, the degree of coherence, and the spectrum of random electromagnetic beams on propagation," Opt. Lett. 28, 1078-1080 (2003).
[CrossRef] [PubMed]

2002 (1)

P. Paakkonen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, "Partially coherent Gaussian pulses," Opt. Commun. 204, 53-58 (2002).
[CrossRef]

2001 (1)

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, "Partially polarized Gaussian Schell-model beams," J. Opt. A, Pure Appl. Opt. 3, 1-9 (2001).
[CrossRef]

2000 (1)

1998 (1)

1997 (2)

Q. D. Liu, L. Shi, P. P. Ho, and R. R. Alfano, "Nonlinear vector rotation and depolarization of femtosecond laser pulses propagating in non-birefringent single-mode optical fibers," Opt. Commun. 138, 45-48 (1997).
[CrossRef]

M. Bertolotti, L. Sereda, and A. Ferrari, "Application of the spectral representation of stochastic processes to the study of nonstationary light radiation: A tutorial," Pure Appl. Opt. 6153-171 (1997).
[CrossRef]

1995 (1)

1993 (1)

1973 (1)

A. K. Jaiswal, G. P. Agrawal, and C. L. Mehta, "Coherence functions in the far-field diffraction plane," Nuovo Cimento B 15, 295-307 (1973).
[CrossRef]

Agrawal, G. P.

Agrawal, Govind P.

Alfano, R. R.

Q. D. Liu, L. Shi, P. P. Ho, and R. R. Alfano, "Nonlinear vector rotation and depolarization of femtosecond laser pulses propagating in non-birefringent single-mode optical fibers," Opt. Commun. 138, 45-48 (1997).
[CrossRef]

Andés, P.

Arvizu-Mondragón, A.

J. Pérez-Téllez, F. Mendieta-Jiménez, and A. Arvizu-Mondragón, "Degree of polarization and heterodyne spectrum in coherent detection of partially polarized wavefield," J. Mod. Opt. 52, 2511-2522 (2005).
[CrossRef]

Ashdown, I.

S. Robinson and I. Ashdown, "Polychromatic optical feedback: Control, stability, and dimming," Proc. SPIE 6337, 633714(1-10) (2005).

Bertolotti, M.

Borghi, R.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, "Partially polarized Gaussian Schell-model beams," J. Opt. A, Pure Appl. Opt. 3, 1-9 (2001).
[CrossRef]

Cho, J.

J. Cho, J. W. Lee, J. S. Im, C. Sone, Y. Park, D. Kim, H. Jeon, E. Yoon, D. S. Leem, and T. Y. Seong, "Recent developments in patterned structure light-emitting diodes," Proc. SPIE 5941, 11-18 (2005).

Dogariu, A.

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, "Degree of polarization of statistically stationary electromagnetic fields," Opt. Commun. 248, 333-337 (2005).
[CrossRef]

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, "Correlation matrix of a completely polarized, statistically stationary electromagnetic field," Opt. Lett. 29, 1536-1538 (2004).
[CrossRef] [PubMed]

Ellis, J.

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, "Degree of polarization of statistically stationary electromagnetic fields," Opt. Commun. 248, 333-337 (2005).
[CrossRef]

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, "Correlation matrix of a completely polarized, statistically stationary electromagnetic field," Opt. Lett. 29, 1536-1538 (2004).
[CrossRef] [PubMed]

Ferrari, A.

Friberg, A. T.

H. Lajunen, A. T. Friberg, and P. Ostlund, "Quasi-stationary plane-wave optical pulses and the van Cittert-Zernike theorem in time," J. Opt. Soc. Am. A 23, 2530-2537 (2006).
[CrossRef]

P. Paakkonen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, "Partially coherent Gaussian pulses," Opt. Commun. 204, 53-58 (2002).
[CrossRef]

Gori, F.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, "Partially polarized Gaussian Schell-model beams," J. Opt. A, Pure Appl. Opt. 3, 1-9 (2001).
[CrossRef]

Ho, P. P.

Q. D. Liu, L. Shi, P. P. Ho, and R. R. Alfano, "Nonlinear vector rotation and depolarization of femtosecond laser pulses propagating in non-birefringent single-mode optical fibers," Opt. Commun. 138, 45-48 (1997).
[CrossRef]

Im, J. S.

J. Cho, J. W. Lee, J. S. Im, C. Sone, Y. Park, D. Kim, H. Jeon, E. Yoon, D. S. Leem, and T. Y. Seong, "Recent developments in patterned structure light-emitting diodes," Proc. SPIE 5941, 11-18 (2005).

Jaiswal, A. K.

A. K. Jaiswal, G. P. Agrawal, and C. L. Mehta, "Coherence functions in the far-field diffraction plane," Nuovo Cimento B 15, 295-307 (1973).
[CrossRef]

James, D.

Jeon, H.

J. Cho, J. W. Lee, J. S. Im, C. Sone, Y. Park, D. Kim, H. Jeon, E. Yoon, D. S. Leem, and T. Y. Seong, "Recent developments in patterned structure light-emitting diodes," Proc. SPIE 5941, 11-18 (2005).

Kim, D.

J. Cho, J. W. Lee, J. S. Im, C. Sone, Y. Park, D. Kim, H. Jeon, E. Yoon, D. S. Leem, and T. Y. Seong, "Recent developments in patterned structure light-emitting diodes," Proc. SPIE 5941, 11-18 (2005).

Lajunen, H.

H. Lajunen, A. T. Friberg, and P. Ostlund, "Quasi-stationary plane-wave optical pulses and the van Cittert-Zernike theorem in time," J. Opt. Soc. Am. A 23, 2530-2537 (2006).
[CrossRef]

H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, "Spectrally partially coherent pulses in dispersive media," Opt. Commun. 255, 12-20 (2005).
[CrossRef]

Lancis, J.

Lee, J. W.

J. Cho, J. W. Lee, J. S. Im, C. Sone, Y. Park, D. Kim, H. Jeon, E. Yoon, D. S. Leem, and T. Y. Seong, "Recent developments in patterned structure light-emitting diodes," Proc. SPIE 5941, 11-18 (2005).

Leem, D. S.

J. Cho, J. W. Lee, J. S. Im, C. Sone, Y. Park, D. Kim, H. Jeon, E. Yoon, D. S. Leem, and T. Y. Seong, "Recent developments in patterned structure light-emitting diodes," Proc. SPIE 5941, 11-18 (2005).

Lin, Q.

Liu, Q. D.

Q. D. Liu, L. Shi, P. P. Ho, and R. R. Alfano, "Nonlinear vector rotation and depolarization of femtosecond laser pulses propagating in non-birefringent single-mode optical fibers," Opt. Commun. 138, 45-48 (1997).
[CrossRef]

Mandel, L.

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

Mehta, C. L.

A. K. Jaiswal, G. P. Agrawal, and C. L. Mehta, "Coherence functions in the far-field diffraction plane," Nuovo Cimento B 15, 295-307 (1973).
[CrossRef]

Mendieta-Jiménez, F.

J. Pérez-Téllez, F. Mendieta-Jiménez, and A. Arvizu-Mondragón, "Degree of polarization and heterodyne spectrum in coherent detection of partially polarized wavefield," J. Mod. Opt. 52, 2511-2522 (2005).
[CrossRef]

Mondello, A.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, "Partially polarized Gaussian Schell-model beams," J. Opt. A, Pure Appl. Opt. 3, 1-9 (2001).
[CrossRef]

Ostlund, P.

Paakkonen, P.

P. Paakkonen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, "Partially coherent Gaussian pulses," Opt. Commun. 204, 53-58 (2002).
[CrossRef]

Park, Y.

J. Cho, J. W. Lee, J. S. Im, C. Sone, Y. Park, D. Kim, H. Jeon, E. Yoon, D. S. Leem, and T. Y. Seong, "Recent developments in patterned structure light-emitting diodes," Proc. SPIE 5941, 11-18 (2005).

Pérez-Téllez, J.

J. Pérez-Téllez, F. Mendieta-Jiménez, and A. Arvizu-Mondragón, "Degree of polarization and heterodyne spectrum in coherent detection of partially polarized wavefield," J. Mod. Opt. 52, 2511-2522 (2005).
[CrossRef]

Piquero, G.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, "Partially polarized Gaussian Schell-model beams," J. Opt. A, Pure Appl. Opt. 3, 1-9 (2001).
[CrossRef]

Ponomarenko, S.

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, "Degree of polarization of statistically stationary electromagnetic fields," Opt. Commun. 248, 333-337 (2005).
[CrossRef]

H. Roychowdhury, S. Ponomarenko, and E. Wolf, "Change in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmostphere," J. Mod. Opt. 52, 1611-1618 (2005).
[CrossRef]

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, "Correlation matrix of a completely polarized, statistically stationary electromagnetic field," Opt. Lett. 29, 1536-1538 (2004).
[CrossRef] [PubMed]

Ponomarenko, S. A.

Robinson, S.

S. Robinson and I. Ashdown, "Polychromatic optical feedback: Control, stability, and dimming," Proc. SPIE 6337, 633714(1-10) (2005).

Roychowdhury, H.

H. Roychowdhury, G. P. Agrawal, and E. Wolf, "Changes in the spectrum, in the spectral degree of polarization, and in the spectral degree of coherence of a partially coherent beam propagating through a gradient-index fiber," J. Opt. Soc. Am. A 23, 940-948 (2006).
[CrossRef]

H. Roychowdhury, S. Ponomarenko, and E. Wolf, "Change in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmostphere," J. Mod. Opt. 52, 1611-1618 (2005).
[CrossRef]

Santarsiero, M.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, "Partially polarized Gaussian Schell-model beams," J. Opt. A, Pure Appl. Opt. 3, 1-9 (2001).
[CrossRef]

Seong, T. Y.

J. Cho, J. W. Lee, J. S. Im, C. Sone, Y. Park, D. Kim, H. Jeon, E. Yoon, D. S. Leem, and T. Y. Seong, "Recent developments in patterned structure light-emitting diodes," Proc. SPIE 5941, 11-18 (2005).

Sereda, L.

Shi, L.

Q. D. Liu, L. Shi, P. P. Ho, and R. R. Alfano, "Nonlinear vector rotation and depolarization of femtosecond laser pulses propagating in non-birefringent single-mode optical fibers," Opt. Commun. 138, 45-48 (1997).
[CrossRef]

Silvestre, E.

Simon, R.

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, "Partially polarized Gaussian Schell-model beams," J. Opt. A, Pure Appl. Opt. 3, 1-9 (2001).
[CrossRef]

Sone, C.

J. Cho, J. W. Lee, J. S. Im, C. Sone, Y. Park, D. Kim, H. Jeon, E. Yoon, D. S. Leem, and T. Y. Seong, "Recent developments in patterned structure light-emitting diodes," Proc. SPIE 5941, 11-18 (2005).

Tervo, J.

H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, "Spectrally partially coherent pulses in dispersive media," Opt. Commun. 255, 12-20 (2005).
[CrossRef]

Torres-Company, V.

Turunen, J.

H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, "Spectrally partially coherent pulses in dispersive media," Opt. Commun. 255, 12-20 (2005).
[CrossRef]

P. Paakkonen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, "Partially coherent Gaussian pulses," Opt. Commun. 204, 53-58 (2002).
[CrossRef]

Vahimaa, P.

H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, "Spectrally partially coherent pulses in dispersive media," Opt. Commun. 255, 12-20 (2005).
[CrossRef]

P. Paakkonen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, "Partially coherent Gaussian pulses," Opt. Commun. 204, 53-58 (2002).
[CrossRef]

Wang, L.

Q. Lin, L. Wang, and S. Zhu, "Partially coherent light pulse and its propagation," Opt. Commun. 219, 67-70 (2003).
[CrossRef]

Wolf, E.

H. Roychowdhury, G. P. Agrawal, and E. Wolf, "Changes in the spectrum, in the spectral degree of polarization, and in the spectral degree of coherence of a partially coherent beam propagating through a gradient-index fiber," J. Opt. Soc. Am. A 23, 940-948 (2006).
[CrossRef]

H. Roychowdhury, S. Ponomarenko, and E. Wolf, "Change in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmostphere," J. Mod. Opt. 52, 1611-1618 (2005).
[CrossRef]

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, "Degree of polarization of statistically stationary electromagnetic fields," Opt. Commun. 248, 333-337 (2005).
[CrossRef]

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, "Correlation matrix of a completely polarized, statistically stationary electromagnetic field," Opt. Lett. 29, 1536-1538 (2004).
[CrossRef] [PubMed]

S. A. Ponomarenko, G. P. Agrawal, and E. Wolf, "Energy spectrum of a nonstationary ensemble of pulses," Opt. Lett. 29, 394-396 (2004).
[CrossRef] [PubMed]

E. Wolf, "Correlation-induced changes in the degree of polarization, the degree of coherence, and the spectrum of random electromagnetic beams on propagation," Opt. Lett. 28, 1078-1080 (2003).
[CrossRef] [PubMed]

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

G. P. Agrawal and E. Wolf, "Propagation-induced polarization changes in partially coherent optical beams," J. Opt. Soc. Am. A 17, 2019-2023 (2000).
[CrossRef]

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

Wyrowski, F.

H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, "Spectrally partially coherent pulses in dispersive media," Opt. Commun. 255, 12-20 (2005).
[CrossRef]

P. Paakkonen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, "Partially coherent Gaussian pulses," Opt. Commun. 204, 53-58 (2002).
[CrossRef]

Yoon, E.

J. Cho, J. W. Lee, J. S. Im, C. Sone, Y. Park, D. Kim, H. Jeon, E. Yoon, D. S. Leem, and T. Y. Seong, "Recent developments in patterned structure light-emitting diodes," Proc. SPIE 5941, 11-18 (2005).

Zhu, S.

Q. Lin, L. Wang, and S. Zhu, "Partially coherent light pulse and its propagation," Opt. Commun. 219, 67-70 (2003).
[CrossRef]

J. Mod. Opt. (2)

J. Pérez-Téllez, F. Mendieta-Jiménez, and A. Arvizu-Mondragón, "Degree of polarization and heterodyne spectrum in coherent detection of partially polarized wavefield," J. Mod. Opt. 52, 2511-2522 (2005).
[CrossRef]

H. Roychowdhury, S. Ponomarenko, and E. Wolf, "Change in the polarization of partially coherent electromagnetic beams propagating through the turbulent atmostphere," J. Mod. Opt. 52, 1611-1618 (2005).
[CrossRef]

J. Opt. A, Pure Appl. Opt. (1)

F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, "Partially polarized Gaussian Schell-model beams," J. Opt. A, Pure Appl. Opt. 3, 1-9 (2001).
[CrossRef]

J. Opt. Soc. Am. A (5)

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

Nuovo Cimento B (1)

A. K. Jaiswal, G. P. Agrawal, and C. L. Mehta, "Coherence functions in the far-field diffraction plane," Nuovo Cimento B 15, 295-307 (1973).
[CrossRef]

Opt. Commun. (5)

Q. D. Liu, L. Shi, P. P. Ho, and R. R. Alfano, "Nonlinear vector rotation and depolarization of femtosecond laser pulses propagating in non-birefringent single-mode optical fibers," Opt. Commun. 138, 45-48 (1997).
[CrossRef]

Q. Lin, L. Wang, and S. Zhu, "Partially coherent light pulse and its propagation," Opt. Commun. 219, 67-70 (2003).
[CrossRef]

P. Paakkonen, J. Turunen, P. Vahimaa, A. T. Friberg, and F. Wyrowski, "Partially coherent Gaussian pulses," Opt. Commun. 204, 53-58 (2002).
[CrossRef]

J. Ellis, A. Dogariu, S. Ponomarenko, and E. Wolf, "Degree of polarization of statistically stationary electromagnetic fields," Opt. Commun. 248, 333-337 (2005).
[CrossRef]

H. Lajunen, J. Turunen, P. Vahimaa, J. Tervo, and F. Wyrowski, "Spectrally partially coherent pulses in dispersive media," Opt. Commun. 255, 12-20 (2005).
[CrossRef]

Opt. Lett. (5)

Phys. Lett. A (1)

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

Proc. SPIE (2)

J. Cho, J. W. Lee, J. S. Im, C. Sone, Y. Park, D. Kim, H. Jeon, E. Yoon, D. S. Leem, and T. Y. Seong, "Recent developments in patterned structure light-emitting diodes," Proc. SPIE 5941, 11-18 (2005).

S. Robinson and I. Ashdown, "Polychromatic optical feedback: Control, stability, and dimming," Proc. SPIE 6337, 633714(1-10) (2005).

Pure Appl. Opt. (1)

M. Bertolotti, L. Sereda, and A. Ferrari, "Application of the spectral representation of stochastic processes to the study of nonstationary light radiation: A tutorial," Pure Appl. Opt. 6153-171 (1997).
[CrossRef]

Other (2)

G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, 2007).

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

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Figures (4)

Fig. 1
Fig. 1

Degree of polarization P as a function of fiber length z for (a) σ c = 100 ps , (b) σ c = 20 ps , (c) σ c = 5 ps , and (d) σ c = 1 ps . The solid, dotted–dashed, and dotted curves correspond to δ = 2.6 , 0.52, and 0.13 ps km , respectively.

Fig. 2
Fig. 2

Variations of the degree of polarization with τ for (a) σ c = 100 ps , (b) σ c = 20 ps , (c) σ c = 5 ps , and (d) σ c = 1 ps . The solid, dotted–dashed, and dotted curves correspond to z = 2 , 6, and 12 km , respectively.

Fig. 3
Fig. 3

Variations of the degree of polarization across the pulse for (a) δ = 0 and (b) δ = 0.26 ps km . The degree of polarization as a function of z for (c) δ = 0 and (d) δ = 0.26 ps km for partially coherent light with σ c x = 12 ps and σ c y = 16 ps . In parts (a) and (b), the solid, dotted–dashed, and dotted curves correspond to z = 5 , 20, and 40 km , respectively; they correspond to τ = 0 , 20, and 80 ps , respectively, in parts (c) and (d).

Fig. 4
Fig. 4

Normalized intensity of the whole pulse (solid curve) and of the two polarization modes (dashed curves) as a function of τ at z = 10 km . The degree of polarization P is also plotted for comparison (dotted curve).

Equations (25)

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E ( t , r ) = ( A x ( t , z ) A y ( t , z ) ) F ( x , y ) e i ( β 0 z ω 0 t ) ,
Γ j l ( t 1 , t 2 , z ) = A j * ( t 1 , z ) A l ( t 2 , z ) ,
A j z + β 1 j A j t + i 2 β 2 j 2 A j t 2 = i ( β 0 j β 0 ) A j ,
ξ = ω 0 β 2 z , τ j = t z β 1 j , A ̃ j ( τ j , ξ ) = A j ( t , z ) exp [ i ( β 0 j β 0 ) z ] ,
2 i ω 0 A ̃ j ξ = 2 A ̃ j τ j 2 .
A ̃ j ( ξ , τ j ) = i ω 0 2 π ξ A ̃ j 0 ( τ ) exp [ i ω 0 2 ξ ( τ j τ ) 2 ] d τ ,
Γ j l ( t 1 , t 2 , z ) = Γ ̃ j l ( τ j 1 , τ l 2 , ξ ) e i ( β 0 l β 0 j ) z ,
Γ ̃ j l ( τ j 1 , τ l 2 , ξ ) A ̃ j * ( τ j 1 , ξ ) A ̃ l ( τ l 2 , ξ ) ,
Γ ̃ j l 0 ( τ 1 , τ 2 ) = A 2 δ j l exp [ ( τ 1 2 + τ 2 2 ) 4 σ t 2 ] exp [ ( τ 1 τ 2 ) 2 2 σ c j 2 ] .
Γ ̃ j l ( τ j 1 , τ l 2 , ξ ) = A 2 δ j l Δ j ( ξ ) exp [ γ j τ j 1 2 + γ j * τ l 2 2 2 β j τ j 1 τ l 2 σ t 2 ρ j 2 Δ j 2 ( ξ ) ] ,
1 ρ j 2 = 1 4 σ t 2 + 1 σ c j 2 , γ j = α j i ξ 2 ω 0 ,
α j = a j 4 ( a j 2 b j 2 ) , β j = b j 4 ( a j 2 b j 2 ) ,
a j = 1 4 σ t 2 + 1 2 σ c j 2 , b j = 1 2 σ c j 2 ,
Δ j ( ξ ) = 1 + ξ 2 ( ω 0 σ t ρ j ) 2 .
P ( t , z ) = ( 1 4 det [ J ( t , z ) ] { tr [ J ( t , z ) ] } 2 ) 1 2 ,
J j l ( t , z ) = Γ ̃ j l ( t z β 1 j , t z β 1 l , ω 0 β 2 z ) e i ( β 0 l β 0 j ) z .
J ( t , z = 0 ) = I 0 ( t ) [ 1 0 0 1 ] ,
J ( t , z ) = [ I x ( t , z ) 0 0 I y ( t , z ) ] ,
I j ( t , z ) = A 2 Λ j ( z ) exp [ ( t z β 1 j ) 2 2 σ t 2 Λ j 2 ( z ) ] ,
Λ j ( z ) = 1 + ( β 2 z 2 σ t 2 ) 2 + ( β 2 z σ t σ c j ) 2 .
P ( τ , z ) = I x ( τ , z ) I y ( τ , z ) I x ( τ , z ) + I y ( τ , z ) ,
I j ( τ , z ) = A 2 Λ j ( z ) exp [ ( τ ± δ z ) 2 2 σ t 2 Λ j 2 ( z ) ] .
τ c j ( z ) = σ t 2 + β 2 2 z 2 σ t 2 ( 1 4 + σ t 2 σ c j 2 ) ,
P ( τ , z ) = tanh [ τ δ z σ t 2 Λ 2 ( z ) ] .
P = tanh [ δ 2 β 2 2 ( 1 4 σ t 2 + 1 σ c 2 ) 1 ] .

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