Abstract

We study the performance of a nonlinear lossless polarizer (NLP), the device that transforms an input arbitrary state of polarization (SOP) of a signal beam into one and the same SOP toward the output and, unlike conventional passive polarizers, performs this transformation without polarization-dependent losses. The operation principle of this device is based on the nonlinear rotation of the SOP of the strong signal beam under the interaction with a copropagating strong pump beam in a Kerr medium, which in our case is a telecom fiber. We quantify the performance of this NLP by introducing the notion of instantaneous degree of polarization, which is a natural extension of the conventional notion of the degree of polarization appropriate for CW beams to the case of pulses whose SOP is not constant across the pulse. We pay particular attention to the regime when signal and pump beams experience a walk-off in the dispersive medium. In particular, we demonstrate that a signal pulse experiences much stronger repolarization when the walk-off effect is present as compared with the case of no walk-off. We also study the degradation of the efficiency of the NLP in the presence of polarization mode dispersion.

© 2013 Optical Society of America

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References

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  1. J. E. Heebner, R. S. Bennink, R. W. Boyd, and R. A. Fisher, “Conversion of unpolarized light to polarized light with greater than 50% efficiency by photorefractive two-beam coupling,” Opt. Lett. 25, 257–259 (2000).
    [CrossRef]
  2. V. V. Kozlov, K. Turitsyn, and S. Wabnitz, “Nonlinear repolarization in optical fibers: polarization attraction with copropagating beams,” Opt. Lett. 36, 4050–4052 (2011).
    [CrossRef]
  3. S. Pitois, G. Millot, and S. Wabnitz, “Polarization domain wall solitons with counterpropagating laser beams,” Phys. Rev. Lett. 81, 1409–1412 (1998).
    [CrossRef]
  4. S. Pitois, G. Millot, and S. Wabnitz, “Nonlinear polarization dynamics of counterpropagating waves in an isotropic optical fiber: theory and experiments,” J. Opt. Soc. Am. B 18, 432–443(2001).
    [CrossRef]
  5. S. Pitois, A. Sauter, and G. Millot, “Simultaneous achievement of polarization attraction and Raman amplification in isotropic optical fibers,” Opt. Lett. 29, 599–601 (2004).
    [CrossRef]
  6. S. Pitois, J. Fatome, and G. Millot, “Polarization attraction using counter-propagating waves in optical fiber at telecommunication wavelengths,” Opt. Express 16, 6646–6651 (2008).
    [CrossRef]
  7. S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, “Polarization and modal attractors in conservative counterpropagating four-wave interaction,” Europhys. Lett. 70, 88–94 (2005).
    [CrossRef]
  8. J. Fatome, S. Pitois, P. Morin, and G. Millot, “Observation of light-by-light polarization control and stabilization in optical fibre for telecommunication applications,” Opt. Express 18, 15311–15317 (2010).
    [CrossRef]
  9. P. Morin, J. Fatome, C. Finot, S. Pitois, R. Claveau, and G. Millot, “All-optical nonlinear processing of both polarization state and intensity profile for 40  Gbit/s regeneration applications,” Opt. Express 19, 17158–17166 (2011).
    [CrossRef]
  10. D. Sugny, A. Picozzi, S. Lagrange, and H. R. Jauslin, “Role of singular tori in the dynamics of spatiotemporal nonlinear wave systems,” Phys. Rev. Lett. 103, 034102 (2009).
    [CrossRef]
  11. E. Assémat, S. Lagrange, A. Picozzi, H. R. Jauslin, and D. Sugny, “Complete nonlinear polarization control in an optical fiber system,” Opt. Lett. 35, 2025 (2010).
    [CrossRef]
  12. S. Lagrange, D. Sugny, A. Picozzi, and H. R. Jauslin, “Singular tori as attractors of four-wave-interaction systems,” Phys. Rev. E 81, 016202 (2010).
    [CrossRef]
  13. E. Assémat, S. Lagrange, A. Picozzi, H. R. Jauslin, and D. Sugny, “Complete nonlinear polarization control in an optical fiber system,” Opt. Lett. 35, 2025–2027 (2010).
    [CrossRef]
  14. V. V. Kozlov, J. Nuño, and S. Wabnitz, “Theory of lossless polarization attraction in telecommunication fibers,” J. Opt. Soc. Am. B 28, 100–108 (2011).
    [CrossRef]
  15. E. Assemat, D. Dargent, A. Picozzi, H. R. Jauslin, and D. Sugny, “Polarization control in spun and telecommunication optical fibers,” Opt. Lett. 36, 4038–4040 (2011).
    [CrossRef]
  16. V. V. Kozlov and S. Wabnitz, “Theoretical study of polarization attraction in high-birefringence and spun fibers,” Opt. Lett. 35, 3949–3951 (2010).
    [CrossRef]
  17. V. V. Kozlov, J. Fatome, P. Morin, S. Pitois, G. Millot, and S. Wabnitz, “Nonlinear repolarization dynamics in optical fibers: transient polarization attraction,” J. Opt. Soc. Am. B 28, 1782–1791 (2011).
    [CrossRef]
  18. S. Pitois and M. Haelterman, “Optical fiber polarization funnel,” in Nonlinear Guided Waves and Their Applications, OSA Technical Digest Series (Optical Society of America, 2001), pp. 278–280.
  19. V. V. Kozlov, Javier Nuño, J. D. Ania-Castañón, and S. Wabnitz, “Theory of fiber optics Raman polarizer,” Opt. Lett. 35, 3970–3972 (2010).
    [CrossRef]
  20. S. V. Manakov, “On the theory of two-dimensional stationary self focussing of electromagnetic waves,” Sov. Phys. J. Exper. Theor. Phys. 38, 248–253 (1974).
  21. D. Marcuse, C. R. Menyuk, and P. K. A. Wai, “Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 15, 1735–1746 (1997).
    [CrossRef]
  22. P. Serena, M. Bertolini, and A. Vannucci, “Optilux Toolbox,” http://optilux.sourceforge.net/Documentation/optilux_doc.pdf .
  23. M. Barozzi, A. Vannucci, and D. Sperti, “A simple counter-propagation algorithm for optical signals (SCAOS) to simulate polarization attraction,” in Proceedings of Fotonica 2012(AEIT - Federazione Italiana di Elettrotecnica, Elettronica, Automazione, Informatica e Telecomunicazioni, 2012), A6.4.
  24. M. Barozzi, A. Vannucci, and D. Sperti, “Lossless polarization attraction simulation with a novel and simple counterpropagation algorithm for optical signals,” JEOS RP 7, 12042 (2012).
    [CrossRef]
  25. A. Bononi and A. Vannucci, “Is there life beyond the principal states of polarization?,” Opt. Fiber Technol. 8, 257–294 (2002).
    [CrossRef]
  26. D. Breuer, H.-J. Tessmann, A. Gladisch, H. M. Foisel, G. Neumann, H. Reiner, and H. Cremer, “Measurements of PMD in the installed fiber plant of Deutsche Telekom,” in IEEE LEOS Summer Topical Meetings (IEEE, 2003), pp. MB2.1–MB2.2.
  27. M. Barozzi and A. Vannucci, “Performance analysis of lossless polarization attractors,” in Latin America Optics and Photonics Conference, OSA Technical Digest (online) (Optical Society of America, 2012), paper LM3C.4.

2012 (1)

M. Barozzi, A. Vannucci, and D. Sperti, “Lossless polarization attraction simulation with a novel and simple counterpropagation algorithm for optical signals,” JEOS RP 7, 12042 (2012).
[CrossRef]

2011 (5)

2010 (6)

2009 (1)

D. Sugny, A. Picozzi, S. Lagrange, and H. R. Jauslin, “Role of singular tori in the dynamics of spatiotemporal nonlinear wave systems,” Phys. Rev. Lett. 103, 034102 (2009).
[CrossRef]

2008 (1)

2005 (1)

S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, “Polarization and modal attractors in conservative counterpropagating four-wave interaction,” Europhys. Lett. 70, 88–94 (2005).
[CrossRef]

2004 (1)

2002 (1)

A. Bononi and A. Vannucci, “Is there life beyond the principal states of polarization?,” Opt. Fiber Technol. 8, 257–294 (2002).
[CrossRef]

2001 (1)

2000 (1)

1998 (1)

S. Pitois, G. Millot, and S. Wabnitz, “Polarization domain wall solitons with counterpropagating laser beams,” Phys. Rev. Lett. 81, 1409–1412 (1998).
[CrossRef]

1997 (1)

D. Marcuse, C. R. Menyuk, and P. K. A. Wai, “Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 15, 1735–1746 (1997).
[CrossRef]

1974 (1)

S. V. Manakov, “On the theory of two-dimensional stationary self focussing of electromagnetic waves,” Sov. Phys. J. Exper. Theor. Phys. 38, 248–253 (1974).

Ania-Castañón, J. D.

Assemat, E.

Assémat, E.

Barozzi, M.

M. Barozzi, A. Vannucci, and D. Sperti, “Lossless polarization attraction simulation with a novel and simple counterpropagation algorithm for optical signals,” JEOS RP 7, 12042 (2012).
[CrossRef]

M. Barozzi, A. Vannucci, and D. Sperti, “A simple counter-propagation algorithm for optical signals (SCAOS) to simulate polarization attraction,” in Proceedings of Fotonica 2012(AEIT - Federazione Italiana di Elettrotecnica, Elettronica, Automazione, Informatica e Telecomunicazioni, 2012), A6.4.

M. Barozzi and A. Vannucci, “Performance analysis of lossless polarization attractors,” in Latin America Optics and Photonics Conference, OSA Technical Digest (online) (Optical Society of America, 2012), paper LM3C.4.

Bennink, R. S.

Bononi, A.

A. Bononi and A. Vannucci, “Is there life beyond the principal states of polarization?,” Opt. Fiber Technol. 8, 257–294 (2002).
[CrossRef]

Boyd, R. W.

Breuer, D.

D. Breuer, H.-J. Tessmann, A. Gladisch, H. M. Foisel, G. Neumann, H. Reiner, and H. Cremer, “Measurements of PMD in the installed fiber plant of Deutsche Telekom,” in IEEE LEOS Summer Topical Meetings (IEEE, 2003), pp. MB2.1–MB2.2.

Claveau, R.

Cremer, H.

D. Breuer, H.-J. Tessmann, A. Gladisch, H. M. Foisel, G. Neumann, H. Reiner, and H. Cremer, “Measurements of PMD in the installed fiber plant of Deutsche Telekom,” in IEEE LEOS Summer Topical Meetings (IEEE, 2003), pp. MB2.1–MB2.2.

Dargent, D.

Fatome, J.

Finot, C.

Fisher, R. A.

Foisel, H. M.

D. Breuer, H.-J. Tessmann, A. Gladisch, H. M. Foisel, G. Neumann, H. Reiner, and H. Cremer, “Measurements of PMD in the installed fiber plant of Deutsche Telekom,” in IEEE LEOS Summer Topical Meetings (IEEE, 2003), pp. MB2.1–MB2.2.

Gladisch, A.

D. Breuer, H.-J. Tessmann, A. Gladisch, H. M. Foisel, G. Neumann, H. Reiner, and H. Cremer, “Measurements of PMD in the installed fiber plant of Deutsche Telekom,” in IEEE LEOS Summer Topical Meetings (IEEE, 2003), pp. MB2.1–MB2.2.

Haelterman, M.

S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, “Polarization and modal attractors in conservative counterpropagating four-wave interaction,” Europhys. Lett. 70, 88–94 (2005).
[CrossRef]

S. Pitois and M. Haelterman, “Optical fiber polarization funnel,” in Nonlinear Guided Waves and Their Applications, OSA Technical Digest Series (Optical Society of America, 2001), pp. 278–280.

Heebner, J. E.

Jauslin, H. R.

E. Assemat, D. Dargent, A. Picozzi, H. R. Jauslin, and D. Sugny, “Polarization control in spun and telecommunication optical fibers,” Opt. Lett. 36, 4038–4040 (2011).
[CrossRef]

E. Assémat, S. Lagrange, A. Picozzi, H. R. Jauslin, and D. Sugny, “Complete nonlinear polarization control in an optical fiber system,” Opt. Lett. 35, 2025 (2010).
[CrossRef]

E. Assémat, S. Lagrange, A. Picozzi, H. R. Jauslin, and D. Sugny, “Complete nonlinear polarization control in an optical fiber system,” Opt. Lett. 35, 2025–2027 (2010).
[CrossRef]

S. Lagrange, D. Sugny, A. Picozzi, and H. R. Jauslin, “Singular tori as attractors of four-wave-interaction systems,” Phys. Rev. E 81, 016202 (2010).
[CrossRef]

D. Sugny, A. Picozzi, S. Lagrange, and H. R. Jauslin, “Role of singular tori in the dynamics of spatiotemporal nonlinear wave systems,” Phys. Rev. Lett. 103, 034102 (2009).
[CrossRef]

S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, “Polarization and modal attractors in conservative counterpropagating four-wave interaction,” Europhys. Lett. 70, 88–94 (2005).
[CrossRef]

Kozlov, V. V.

Lagrange, S.

E. Assémat, S. Lagrange, A. Picozzi, H. R. Jauslin, and D. Sugny, “Complete nonlinear polarization control in an optical fiber system,” Opt. Lett. 35, 2025–2027 (2010).
[CrossRef]

E. Assémat, S. Lagrange, A. Picozzi, H. R. Jauslin, and D. Sugny, “Complete nonlinear polarization control in an optical fiber system,” Opt. Lett. 35, 2025 (2010).
[CrossRef]

S. Lagrange, D. Sugny, A. Picozzi, and H. R. Jauslin, “Singular tori as attractors of four-wave-interaction systems,” Phys. Rev. E 81, 016202 (2010).
[CrossRef]

D. Sugny, A. Picozzi, S. Lagrange, and H. R. Jauslin, “Role of singular tori in the dynamics of spatiotemporal nonlinear wave systems,” Phys. Rev. Lett. 103, 034102 (2009).
[CrossRef]

Manakov, S. V.

S. V. Manakov, “On the theory of two-dimensional stationary self focussing of electromagnetic waves,” Sov. Phys. J. Exper. Theor. Phys. 38, 248–253 (1974).

Marcuse, D.

D. Marcuse, C. R. Menyuk, and P. K. A. Wai, “Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 15, 1735–1746 (1997).
[CrossRef]

Menyuk, C. R.

D. Marcuse, C. R. Menyuk, and P. K. A. Wai, “Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 15, 1735–1746 (1997).
[CrossRef]

Millot, G.

V. V. Kozlov, J. Fatome, P. Morin, S. Pitois, G. Millot, and S. Wabnitz, “Nonlinear repolarization dynamics in optical fibers: transient polarization attraction,” J. Opt. Soc. Am. B 28, 1782–1791 (2011).
[CrossRef]

P. Morin, J. Fatome, C. Finot, S. Pitois, R. Claveau, and G. Millot, “All-optical nonlinear processing of both polarization state and intensity profile for 40  Gbit/s regeneration applications,” Opt. Express 19, 17158–17166 (2011).
[CrossRef]

J. Fatome, S. Pitois, P. Morin, and G. Millot, “Observation of light-by-light polarization control and stabilization in optical fibre for telecommunication applications,” Opt. Express 18, 15311–15317 (2010).
[CrossRef]

S. Pitois, J. Fatome, and G. Millot, “Polarization attraction using counter-propagating waves in optical fiber at telecommunication wavelengths,” Opt. Express 16, 6646–6651 (2008).
[CrossRef]

S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, “Polarization and modal attractors in conservative counterpropagating four-wave interaction,” Europhys. Lett. 70, 88–94 (2005).
[CrossRef]

S. Pitois, A. Sauter, and G. Millot, “Simultaneous achievement of polarization attraction and Raman amplification in isotropic optical fibers,” Opt. Lett. 29, 599–601 (2004).
[CrossRef]

S. Pitois, G. Millot, and S. Wabnitz, “Nonlinear polarization dynamics of counterpropagating waves in an isotropic optical fiber: theory and experiments,” J. Opt. Soc. Am. B 18, 432–443(2001).
[CrossRef]

S. Pitois, G. Millot, and S. Wabnitz, “Polarization domain wall solitons with counterpropagating laser beams,” Phys. Rev. Lett. 81, 1409–1412 (1998).
[CrossRef]

Morin, P.

Neumann, G.

D. Breuer, H.-J. Tessmann, A. Gladisch, H. M. Foisel, G. Neumann, H. Reiner, and H. Cremer, “Measurements of PMD in the installed fiber plant of Deutsche Telekom,” in IEEE LEOS Summer Topical Meetings (IEEE, 2003), pp. MB2.1–MB2.2.

Nuño, J.

Nuño, Javier

Picozzi, A.

E. Assemat, D. Dargent, A. Picozzi, H. R. Jauslin, and D. Sugny, “Polarization control in spun and telecommunication optical fibers,” Opt. Lett. 36, 4038–4040 (2011).
[CrossRef]

E. Assémat, S. Lagrange, A. Picozzi, H. R. Jauslin, and D. Sugny, “Complete nonlinear polarization control in an optical fiber system,” Opt. Lett. 35, 2025 (2010).
[CrossRef]

E. Assémat, S. Lagrange, A. Picozzi, H. R. Jauslin, and D. Sugny, “Complete nonlinear polarization control in an optical fiber system,” Opt. Lett. 35, 2025–2027 (2010).
[CrossRef]

S. Lagrange, D. Sugny, A. Picozzi, and H. R. Jauslin, “Singular tori as attractors of four-wave-interaction systems,” Phys. Rev. E 81, 016202 (2010).
[CrossRef]

D. Sugny, A. Picozzi, S. Lagrange, and H. R. Jauslin, “Role of singular tori in the dynamics of spatiotemporal nonlinear wave systems,” Phys. Rev. Lett. 103, 034102 (2009).
[CrossRef]

S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, “Polarization and modal attractors in conservative counterpropagating four-wave interaction,” Europhys. Lett. 70, 88–94 (2005).
[CrossRef]

Pitois, S.

P. Morin, J. Fatome, C. Finot, S. Pitois, R. Claveau, and G. Millot, “All-optical nonlinear processing of both polarization state and intensity profile for 40  Gbit/s regeneration applications,” Opt. Express 19, 17158–17166 (2011).
[CrossRef]

V. V. Kozlov, J. Fatome, P. Morin, S. Pitois, G. Millot, and S. Wabnitz, “Nonlinear repolarization dynamics in optical fibers: transient polarization attraction,” J. Opt. Soc. Am. B 28, 1782–1791 (2011).
[CrossRef]

J. Fatome, S. Pitois, P. Morin, and G. Millot, “Observation of light-by-light polarization control and stabilization in optical fibre for telecommunication applications,” Opt. Express 18, 15311–15317 (2010).
[CrossRef]

S. Pitois, J. Fatome, and G. Millot, “Polarization attraction using counter-propagating waves in optical fiber at telecommunication wavelengths,” Opt. Express 16, 6646–6651 (2008).
[CrossRef]

S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, “Polarization and modal attractors in conservative counterpropagating four-wave interaction,” Europhys. Lett. 70, 88–94 (2005).
[CrossRef]

S. Pitois, A. Sauter, and G. Millot, “Simultaneous achievement of polarization attraction and Raman amplification in isotropic optical fibers,” Opt. Lett. 29, 599–601 (2004).
[CrossRef]

S. Pitois, G. Millot, and S. Wabnitz, “Nonlinear polarization dynamics of counterpropagating waves in an isotropic optical fiber: theory and experiments,” J. Opt. Soc. Am. B 18, 432–443(2001).
[CrossRef]

S. Pitois, G. Millot, and S. Wabnitz, “Polarization domain wall solitons with counterpropagating laser beams,” Phys. Rev. Lett. 81, 1409–1412 (1998).
[CrossRef]

S. Pitois and M. Haelterman, “Optical fiber polarization funnel,” in Nonlinear Guided Waves and Their Applications, OSA Technical Digest Series (Optical Society of America, 2001), pp. 278–280.

Reiner, H.

D. Breuer, H.-J. Tessmann, A. Gladisch, H. M. Foisel, G. Neumann, H. Reiner, and H. Cremer, “Measurements of PMD in the installed fiber plant of Deutsche Telekom,” in IEEE LEOS Summer Topical Meetings (IEEE, 2003), pp. MB2.1–MB2.2.

Sauter, A.

Sperti, D.

M. Barozzi, A. Vannucci, and D. Sperti, “Lossless polarization attraction simulation with a novel and simple counterpropagation algorithm for optical signals,” JEOS RP 7, 12042 (2012).
[CrossRef]

M. Barozzi, A. Vannucci, and D. Sperti, “A simple counter-propagation algorithm for optical signals (SCAOS) to simulate polarization attraction,” in Proceedings of Fotonica 2012(AEIT - Federazione Italiana di Elettrotecnica, Elettronica, Automazione, Informatica e Telecomunicazioni, 2012), A6.4.

Sugny, D.

Tessmann, H.-J.

D. Breuer, H.-J. Tessmann, A. Gladisch, H. M. Foisel, G. Neumann, H. Reiner, and H. Cremer, “Measurements of PMD in the installed fiber plant of Deutsche Telekom,” in IEEE LEOS Summer Topical Meetings (IEEE, 2003), pp. MB2.1–MB2.2.

Turitsyn, K.

Vannucci, A.

M. Barozzi, A. Vannucci, and D. Sperti, “Lossless polarization attraction simulation with a novel and simple counterpropagation algorithm for optical signals,” JEOS RP 7, 12042 (2012).
[CrossRef]

A. Bononi and A. Vannucci, “Is there life beyond the principal states of polarization?,” Opt. Fiber Technol. 8, 257–294 (2002).
[CrossRef]

M. Barozzi, A. Vannucci, and D. Sperti, “A simple counter-propagation algorithm for optical signals (SCAOS) to simulate polarization attraction,” in Proceedings of Fotonica 2012(AEIT - Federazione Italiana di Elettrotecnica, Elettronica, Automazione, Informatica e Telecomunicazioni, 2012), A6.4.

M. Barozzi and A. Vannucci, “Performance analysis of lossless polarization attractors,” in Latin America Optics and Photonics Conference, OSA Technical Digest (online) (Optical Society of America, 2012), paper LM3C.4.

Wabnitz, S.

Wai, P. K. A.

D. Marcuse, C. R. Menyuk, and P. K. A. Wai, “Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 15, 1735–1746 (1997).
[CrossRef]

Europhys. Lett. (1)

S. Pitois, A. Picozzi, G. Millot, H. R. Jauslin, and M. Haelterman, “Polarization and modal attractors in conservative counterpropagating four-wave interaction,” Europhys. Lett. 70, 88–94 (2005).
[CrossRef]

J. Lightwave Technol. (1)

D. Marcuse, C. R. Menyuk, and P. K. A. Wai, “Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 15, 1735–1746 (1997).
[CrossRef]

J. Opt. Soc. Am. B (3)

JEOS RP (1)

M. Barozzi, A. Vannucci, and D. Sperti, “Lossless polarization attraction simulation with a novel and simple counterpropagation algorithm for optical signals,” JEOS RP 7, 12042 (2012).
[CrossRef]

Opt. Express (3)

Opt. Fiber Technol. (1)

A. Bononi and A. Vannucci, “Is there life beyond the principal states of polarization?,” Opt. Fiber Technol. 8, 257–294 (2002).
[CrossRef]

Opt. Lett. (8)

Phys. Rev. E (1)

S. Lagrange, D. Sugny, A. Picozzi, and H. R. Jauslin, “Singular tori as attractors of four-wave-interaction systems,” Phys. Rev. E 81, 016202 (2010).
[CrossRef]

Phys. Rev. Lett. (2)

D. Sugny, A. Picozzi, S. Lagrange, and H. R. Jauslin, “Role of singular tori in the dynamics of spatiotemporal nonlinear wave systems,” Phys. Rev. Lett. 103, 034102 (2009).
[CrossRef]

S. Pitois, G. Millot, and S. Wabnitz, “Polarization domain wall solitons with counterpropagating laser beams,” Phys. Rev. Lett. 81, 1409–1412 (1998).
[CrossRef]

Sov. Phys. J. Exper. Theor. Phys. (1)

S. V. Manakov, “On the theory of two-dimensional stationary self focussing of electromagnetic waves,” Sov. Phys. J. Exper. Theor. Phys. 38, 248–253 (1974).

Other (5)

D. Breuer, H.-J. Tessmann, A. Gladisch, H. M. Foisel, G. Neumann, H. Reiner, and H. Cremer, “Measurements of PMD in the installed fiber plant of Deutsche Telekom,” in IEEE LEOS Summer Topical Meetings (IEEE, 2003), pp. MB2.1–MB2.2.

M. Barozzi and A. Vannucci, “Performance analysis of lossless polarization attractors,” in Latin America Optics and Photonics Conference, OSA Technical Digest (online) (Optical Society of America, 2012), paper LM3C.4.

S. Pitois and M. Haelterman, “Optical fiber polarization funnel,” in Nonlinear Guided Waves and Their Applications, OSA Technical Digest Series (Optical Society of America, 2001), pp. 278–280.

P. Serena, M. Bertolini, and A. Vannucci, “Optilux Toolbox,” http://optilux.sourceforge.net/Documentation/optilux_doc.pdf .

M. Barozzi, A. Vannucci, and D. Sperti, “A simple counter-propagation algorithm for optical signals (SCAOS) to simulate polarization attraction,” in Proceedings of Fotonica 2012(AEIT - Federazione Italiana di Elettrotecnica, Elettronica, Automazione, Informatica e Telecomunicazioni, 2012), A6.4.

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Figures (6)

Fig. 1.
Fig. 1.

Signal power (solid black), instantaneous DOP (solid red), and instantaneous alignment parameter (dashed red) at the output of the fiber, all versus retarded time: (a) fiber length L=2.6km, pump power Pp=1W, no walk-off; (b) L=2.6km, Pp=2W, total delay TD=42ps; (c) L=5.2km, Pp=2W, TD=42ps; and (d) L=10.4km, Pp=2W, TD=42ps.

Fig. 2.
Fig. 2.

Degree of polarization (dashed curves) and alignment parameter (solid curves) as a function of total delay in the case of fibers without PMD. Results are plotted for fiber lengths L=2.6, 5.2, 10.4, and 20.8 km in (a)–(d), respectively, and different pump powers Pp=0.5, 1, 1.5, and 2 W (identified by the following symbols, respectively: circle, square, diamond, star). Note that solid and dashed curves coincide.

Fig. 3.
Fig. 3.

DOP of the NLP driven by incoherent (“noisy”) pump with mean power Ppt: 0.25 W (magenta dotted curve), 0.5 W (black solid curve), and 1 W (red dashed curve). Fiber losses are not taken into account.

Fig. 4.
Fig. 4.

Degree of polarization (dashed curves) and alignment parameter (solid curves) as a function of total delay in the case of modern fibers with a small PMD coefficient Dp=0.05ps/km0.5. Results are plotted for fiber lengths L=2.6, 5.2, 10.4, and 20.8 km in (a)–(d), respectively, and different pump powers Pp=0.5, 1, 1.5, and 2 W (identified by the following symbols, respectively: circle, square, diamond, star).

Fig. 5.
Fig. 5.

Degree of polarization (dashed curves) and alignment parameter (solid curves) as a function of total delay in the case of legacy fibers with a large PMD coefficient Dp=0.2ps/km. Results are plotted for fiber lengths L=2.6, 5.2, 10.4, and 20.8 km in (a)–(d), respectively, and different pump powers Pp=0.5, 1, 1.5, and 2 W (identified by the following symbols, respectively: circle, square, diamond, star).

Fig. 6.
Fig. 6.

Distribution of 50 (initially) random signal SOPs after the NLP with a 20.8 km long fiber, with the pump power Pp=2W and the input pump SOP on S^1 (see plots). Without PMD (left), the SOPs surround the pump SOP, which acts as the attraction SOP. With large PMD (right), the attraction SOP S(a)(k)/S(a)(k) no longer coincides with the pump SOP.

Equations (12)

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(zvst)S(s)=γeαzS(s)×Jx(z)S(p),
(zvpt)S(p)=γeαzS(p)×Jx(z)S(s),
(zvst)S(s)=γ¯eαzS(p)×S(s),
(zvpt)S(p)=γ¯eαzS(s)×S(p),
IDOP(t)=S(s)(t)SOPS0(s)(t)
DOP=S(s)(t)tSOPS0(s)(t)t
IA0L(t)=S(s)(t)SOPS0(s)(t)·S(p)(0)S0(p)(0),
A0L=S(s)(t)tSOPS0(s)(t)t·S(p)(0)S0(p)(0).
A0LPMD=S(s)(t)tSOPPMDS0(s)(t)t·S(p)(0)S0(p)(0)=PS1S(s)(t)tSOPPMD,
DOPPMD=PS1S(s)(t)tSOPPMD.
DOP=S(a)(k)PMD
A0L=S(a)(k)·S(p)(0)S0(p)(0)PMD=S(a)(k)cos(θk)PMD,

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