Abstract

We report all-optical regeneration of the state of polarization of a 40Gbit/s return-to-zero telecommunication signal. The device discussed here consists of a 6.2-km-long nonzero dispersion-shifted fiber, with low polarization mode dispersion, pumped from the output end by a backward propagating wave coming from either an external continuous source or a reflection of the signal. An initially scrambled signal acquires a degree of polarization close to 100% toward the polarization generator output. All-optical regeneration is confirmed by means of polarization and bit-error-rate measurements as well as real-time observation of the eye diagrams. We show that the physical mechanism underlying the observed four-wave-mixing-based polarization attraction phenomenon can be described in terms of the geometric approach developed for the study of Hamiltonian singularities.

© 2013 Chinese Laser Press

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  1. M. Reimer, D. Dumas, G. Soliman, D. Yevick, and M. O’Sullivan, “Polarization evolution in dispersion compensation modules,” presented at the Optical Fiber Communications/National Fiber Optic Engineers Conference (OFC/NFOEC), San Diego, California, March22–26, 2009, paper OWD4.
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    [CrossRef]
  3. N. G. Walker and G. R. Walker, “Polarization control for coherent communications,” J. Lightwave Technol. 8, 438–458 (1990).
    [CrossRef]
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    [CrossRef]
  5. B. Koch, R. Noe, V. Mirvoda, H. Griesser, S. Bayer, and H. Wernz, “Record 59 krad/s polarization tracking in 112 Gb/s 640 km PDM-RZ-DQPSK transmission,” IEEE Photon. Technol. Lett. 22, 1407–1409 (2010).
    [CrossRef]
  6. S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16, 804–817 (2008).
    [CrossRef]
  7. S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. 16, 1164–1179 (2010).
    [CrossRef]
  8. D. Taillaert, H. Chong, P. I. Borel, L. H. Frandsen, R. M. De La Rue, and R. Baets, “A compact two-dimensional grating coupler used as a polarization splitter,” IEEE Photon. Technol. Lett. 15, 1249–1251 (2003).
    [CrossRef]
  9. F. Van Laere, T. Stomeo, D. Taillaert, G. Roelkens, D. Van Thourhout, T. F. Krauss, and R. Baets, “Efficient polarization diversity grating couplers in bonded InP-membrane,” IEEE Photon. Technol. Lett. 20, 318–320 (2008).
    [CrossRef]
  10. V. E. Zakharov and A. V. Mikhailov, “Polarization domains in nonlinear optics,” JETP Lett. 45, 349 (1987).
  11. S. Pitois, G. Millot, and S. Wabnitz, “Polarization domain wall solitons with counterpropagating laser beams,” Phys. Rev. Lett. 81, 1409–1412 (1998).
    [CrossRef]
  12. 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]
  13. 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]
  14. 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]
  15. J. Fatome, P. Morin, S. Pitois, and G. Millot, “Light-by-light polarization control of 10 Gb/s RZ and NRZ telecommunication signals,” IEEE J. Sel. Top. Quantum Electron. 18, 621–628 (2012).
    [CrossRef]
  16. J. Fatome, S. Pitois, P. Morin, E. Assémat, D. Sugny, A. Picozzi, H. R. Jauslin, G. Millot, V. V. Kozlov, and S. Wabnitz, “A universal optical all-fiber omnipolarizer,” Sci. Rep. 2, 938 (2012).
    [CrossRef]
  17. S. Pitois and M. Haelterman, “Optical fiber polarization funnel,” in Nonlinear Guided Waves and Their Applications, OSA Technical Digest (Optical Society of America, 2001), paper MC79, pp. 278–280.
  18. M. Martinelli, M. Cirigliano, M. M. Ferrario, L. Marazzi, and P. Martelli, “Evidence of Raman-induced polarization pulling,” Opt. Express 17, 947–955 (2009).
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  19. N. Muga, M. Ferreira, and A. Pinto, “Broadband polarization pulling using Raman amplification,” Opt. Express 19, 18707–18712 (2011).
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  20. F. Chiarello, L. Palmieri, M. Santagiustina, R. Gamatham, and A. Galtarossa, “Experimental characterization of the counter-propagating Raman polarization attraction,” Opt. Express 20, 26050–26055 (2012).
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  22. Z. Shmilovitch, N. Primerov, A. Zadok, A. Eyal, S. Chin, L. Thévenaz, and M. Tur, “Dual-pump push-pull polarization control using stimulated Brillouin scattering,” Opt. Express 19, 25873–25880 (2011).
    [CrossRef]
  23. J. Fatome, S. Pitois, and G. Millot, “Experimental evidence of Brillouin-induced polarization wheeling in highly birefringent optical fibers,” Opt. Express 17, 12612–12618 (2009).
    [CrossRef]
  24. 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]
  25. 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 (2005).
    [CrossRef]
  26. 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]
  27. V. V. Kozlov, J. Nuno, and S. Wabnitz, “Theory of lossless polarization attraction in telecommunication fiber,” J. Opt. Soc. Am. B 28, 100–108 (2011).
    [CrossRef]
  28. 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]
  29. V. V. Kozlov, J. Fatome, P. Morin, S. Pitois, and S. Wabnitz, “Nonlinear optical fiber polarization tracking at 200 krad/s,” presented at the 37th European Conference on Optical Communication (ECOC), 2011, Geneve, Switzerland, September18–22, 2011.
  30. V. V. Kozlov and S. Wabnitz, “Theoretical study of polarization attraction in high-birefringence and spun fibers,” Opt. Lett. 35, 3949–3951 (2010).
    [CrossRef]
  31. 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]
  32. V. V. Kozlov, M. Barozzi, A. Vannucci, and S. Wabnitz, “Lossless polarization attraction of co-propagating beams in telecom fibers,” J. Opt. Soc. Am. B 30, 530–540 (2013).
    [CrossRef]
  33. R. H. Cushman and L. M. Bates, Global Aspects of Classical Integrable Systems (Birkhauser, 1997).
  34. D. Sugny, A. Picozzi, S. Lagrange, and H. R. Jauslin, “On the role of singular tori in the spatio-temporal dynamics of nonlinear wave systems,” Phys. Rev. Lett. 103, 034102 (2009).
    [CrossRef]
  35. 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]
  36. E. Assémat, A. Picozzi, H. R. Jauslin, and D. Sugny, “Hamiltonian tools for the analysis of optical polarization system,” J. Opt. Soc. Am. B 29, 559–571 (2012).
    [CrossRef]
  37. 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]
  38. E. Assémat, 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]
  39. K. Efstathiou and D. A. Sadovskii, “Normalization and global analysis of perturbations of the hydrogen atom,” Rev. Mod. Phys. 82, 2099–2154 (2010).
    [CrossRef]
  40. V. V. Kozlov and S. Wabnitz, “Instability of optical solitons in the boundary value problem for a medium of finite extension,” Lett. Math. Phys. 96, 405–413 (2011).
    [CrossRef]
  41. E. Assemat, A. Picozzi, H. R. Jauslin, and D. Sugny, “Instabilities of optical solitons and Hamiltonian singular solutions in a medium of finite extension,” Phys. Rev. A 84, 013809 (2011).
    [CrossRef]

2013

2012

E. Assémat, A. Picozzi, H. R. Jauslin, and D. Sugny, “Hamiltonian tools for the analysis of optical polarization system,” J. Opt. Soc. Am. B 29, 559–571 (2012).
[CrossRef]

F. Chiarello, L. Palmieri, M. Santagiustina, R. Gamatham, and A. Galtarossa, “Experimental characterization of the counter-propagating Raman polarization attraction,” Opt. Express 20, 26050–26055 (2012).
[CrossRef]

J. Fatome, P. Morin, S. Pitois, and G. Millot, “Light-by-light polarization control of 10 Gb/s RZ and NRZ telecommunication signals,” IEEE J. Sel. Top. Quantum Electron. 18, 621–628 (2012).
[CrossRef]

J. Fatome, S. Pitois, P. Morin, E. Assémat, D. Sugny, A. Picozzi, H. R. Jauslin, G. Millot, V. V. Kozlov, and S. Wabnitz, “A universal optical all-fiber omnipolarizer,” Sci. Rep. 2, 938 (2012).
[CrossRef]

2011

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]

N. Muga, M. Ferreira, and A. Pinto, “Broadband polarization pulling using Raman amplification,” Opt. Express 19, 18707–18712 (2011).
[CrossRef]

Z. Shmilovitch, N. Primerov, A. Zadok, A. Eyal, S. Chin, L. Thévenaz, and M. Tur, “Dual-pump push-pull polarization control using stimulated Brillouin scattering,” Opt. Express 19, 25873–25880 (2011).
[CrossRef]

V. V. Kozlov, J. Nuno, and S. Wabnitz, “Theory of lossless polarization attraction in telecommunication fiber,” J. Opt. Soc. Am. B 28, 100–108 (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]

E. Assémat, 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]

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]

V. V. Kozlov and S. Wabnitz, “Instability of optical solitons in the boundary value problem for a medium of finite extension,” Lett. Math. Phys. 96, 405–413 (2011).
[CrossRef]

E. Assemat, A. Picozzi, H. R. Jauslin, and D. Sugny, “Instabilities of optical solitons and Hamiltonian singular solutions in a medium of finite extension,” Phys. Rev. A 84, 013809 (2011).
[CrossRef]

2010

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]

K. Efstathiou and D. A. Sadovskii, “Normalization and global analysis of perturbations of the hydrogen atom,” Rev. Mod. Phys. 82, 2099–2154 (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]

V. V. Kozlov and S. Wabnitz, “Theoretical study of polarization attraction in high-birefringence and spun fibers,” Opt. Lett. 35, 3949–3951 (2010).
[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]

B. Koch, R. Noe, V. Mirvoda, H. Griesser, S. Bayer, and H. Wernz, “Record 59 krad/s polarization tracking in 112 Gb/s 640 km PDM-RZ-DQPSK transmission,” IEEE Photon. Technol. Lett. 22, 1407–1409 (2010).
[CrossRef]

S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. 16, 1164–1179 (2010).
[CrossRef]

2009

2008

2006

2005

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 (2005).
[CrossRef]

2004

2003

D. Taillaert, H. Chong, P. I. Borel, L. H. Frandsen, R. M. De La Rue, and R. Baets, “A compact two-dimensional grating coupler used as a polarization splitter,” IEEE Photon. Technol. Lett. 15, 1249–1251 (2003).
[CrossRef]

2001

1998

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

1990

N. G. Walker and G. R. Walker, “Polarization control for coherent communications,” J. Lightwave Technol. 8, 438–458 (1990).
[CrossRef]

1988

R. Noe, H. Heidrich, and D. Hoffmann, “Endless polarization control systems for coherent optics,” J. Lightwave Technol. 6, 1199–1208 (1988).
[CrossRef]

1987

V. E. Zakharov and A. V. Mikhailov, “Polarization domains in nonlinear optics,” JETP Lett. 45, 349 (1987).

Assemat, E.

E. Assemat, A. Picozzi, H. R. Jauslin, and D. Sugny, “Instabilities of optical solitons and Hamiltonian singular solutions in a medium of finite extension,” Phys. Rev. A 84, 013809 (2011).
[CrossRef]

Assémat, E.

Baets, R.

F. Van Laere, T. Stomeo, D. Taillaert, G. Roelkens, D. Van Thourhout, T. F. Krauss, and R. Baets, “Efficient polarization diversity grating couplers in bonded InP-membrane,” IEEE Photon. Technol. Lett. 20, 318–320 (2008).
[CrossRef]

D. Taillaert, H. Chong, P. I. Borel, L. H. Frandsen, R. M. De La Rue, and R. Baets, “A compact two-dimensional grating coupler used as a polarization splitter,” IEEE Photon. Technol. Lett. 15, 1249–1251 (2003).
[CrossRef]

Barozzi, M.

Bates, L. M.

R. H. Cushman and L. M. Bates, Global Aspects of Classical Integrable Systems (Birkhauser, 1997).

Bayer, S.

B. Koch, R. Noe, V. Mirvoda, H. Griesser, S. Bayer, and H. Wernz, “Record 59 krad/s polarization tracking in 112 Gb/s 640 km PDM-RZ-DQPSK transmission,” IEEE Photon. Technol. Lett. 22, 1407–1409 (2010).
[CrossRef]

Borel, P. I.

D. Taillaert, H. Chong, P. I. Borel, L. H. Frandsen, R. M. De La Rue, and R. Baets, “A compact two-dimensional grating coupler used as a polarization splitter,” IEEE Photon. Technol. Lett. 15, 1249–1251 (2003).
[CrossRef]

Chiarello, F.

Chin, S.

Chong, H.

D. Taillaert, H. Chong, P. I. Borel, L. H. Frandsen, R. M. De La Rue, and R. Baets, “A compact two-dimensional grating coupler used as a polarization splitter,” IEEE Photon. Technol. Lett. 15, 1249–1251 (2003).
[CrossRef]

Cirigliano, M.

Claveau, R.

Cushman, R. H.

R. H. Cushman and L. M. Bates, Global Aspects of Classical Integrable Systems (Birkhauser, 1997).

Dargent, D.

De La Rue, R. M.

D. Taillaert, H. Chong, P. I. Borel, L. H. Frandsen, R. M. De La Rue, and R. Baets, “A compact two-dimensional grating coupler used as a polarization splitter,” IEEE Photon. Technol. Lett. 15, 1249–1251 (2003).
[CrossRef]

Dumas, D.

M. Reimer, D. Dumas, G. Soliman, D. Yevick, and M. O’Sullivan, “Polarization evolution in dispersion compensation modules,” presented at the Optical Fiber Communications/National Fiber Optic Engineers Conference (OFC/NFOEC), San Diego, California, March22–26, 2009, paper OWD4.

Efstathiou, K.

K. Efstathiou and D. A. Sadovskii, “Normalization and global analysis of perturbations of the hydrogen atom,” Rev. Mod. Phys. 82, 2099–2154 (2010).
[CrossRef]

Eyal, A.

Fatome, J.

J. Fatome, S. Pitois, P. Morin, E. Assémat, D. Sugny, A. Picozzi, H. R. Jauslin, G. Millot, V. V. Kozlov, and S. Wabnitz, “A universal optical all-fiber omnipolarizer,” Sci. Rep. 2, 938 (2012).
[CrossRef]

J. Fatome, P. Morin, S. Pitois, and G. Millot, “Light-by-light polarization control of 10 Gb/s RZ and NRZ telecommunication signals,” IEEE J. Sel. Top. Quantum Electron. 18, 621–628 (2012).
[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]

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]

J. Fatome, S. Pitois, and G. Millot, “Experimental evidence of Brillouin-induced polarization wheeling in highly birefringent optical fibers,” Opt. Express 17, 12612–12618 (2009).
[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]

V. V. Kozlov, J. Fatome, P. Morin, S. Pitois, and S. Wabnitz, “Nonlinear optical fiber polarization tracking at 200 krad/s,” presented at the 37th European Conference on Optical Communication (ECOC), 2011, Geneve, Switzerland, September18–22, 2011.

Ferrario, M. M.

Ferreira, M.

Finot, C.

Frandsen, L. H.

D. Taillaert, H. Chong, P. I. Borel, L. H. Frandsen, R. M. De La Rue, and R. Baets, “A compact two-dimensional grating coupler used as a polarization splitter,” IEEE Photon. Technol. Lett. 15, 1249–1251 (2003).
[CrossRef]

Galtarossa, A.

Gamatham, R.

Griesser, H.

B. Koch, R. Noe, V. Mirvoda, H. Griesser, S. Bayer, and H. Wernz, “Record 59 krad/s polarization tracking in 112 Gb/s 640 km PDM-RZ-DQPSK transmission,” IEEE Photon. Technol. Lett. 22, 1407–1409 (2010).
[CrossRef]

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 (2005).
[CrossRef]

S. Pitois and M. Haelterman, “Optical fiber polarization funnel,” in Nonlinear Guided Waves and Their Applications, OSA Technical Digest (Optical Society of America, 2001), paper MC79, pp. 278–280.

Heidrich, H.

R. Noe, H. Heidrich, and D. Hoffmann, “Endless polarization control systems for coherent optics,” J. Lightwave Technol. 6, 1199–1208 (1988).
[CrossRef]

Hoffmann, D.

R. Noe, H. Heidrich, and D. Hoffmann, “Endless polarization control systems for coherent optics,” J. Lightwave Technol. 6, 1199–1208 (1988).
[CrossRef]

Jauslin, H. R.

J. Fatome, S. Pitois, P. Morin, E. Assémat, D. Sugny, A. Picozzi, H. R. Jauslin, G. Millot, V. V. Kozlov, and S. Wabnitz, “A universal optical all-fiber omnipolarizer,” Sci. Rep. 2, 938 (2012).
[CrossRef]

E. Assémat, A. Picozzi, H. R. Jauslin, and D. Sugny, “Hamiltonian tools for the analysis of optical polarization system,” J. Opt. Soc. Am. B 29, 559–571 (2012).
[CrossRef]

E. Assemat, A. Picozzi, H. R. Jauslin, and D. Sugny, “Instabilities of optical solitons and Hamiltonian singular solutions in a medium of finite extension,” Phys. Rev. A 84, 013809 (2011).
[CrossRef]

E. Assémat, 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, 2025–2027 (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, “On the role of singular tori in the spatio-temporal dynamics of 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 (2005).
[CrossRef]

Koch, B.

B. Koch, R. Noe, V. Mirvoda, H. Griesser, S. Bayer, and H. Wernz, “Record 59 krad/s polarization tracking in 112 Gb/s 640 km PDM-RZ-DQPSK transmission,” IEEE Photon. Technol. Lett. 22, 1407–1409 (2010).
[CrossRef]

Kozlov, V. V.

V. V. Kozlov, M. Barozzi, A. Vannucci, and S. Wabnitz, “Lossless polarization attraction of co-propagating beams in telecom fibers,” J. Opt. Soc. Am. B 30, 530–540 (2013).
[CrossRef]

J. Fatome, S. Pitois, P. Morin, E. Assémat, D. Sugny, A. Picozzi, H. R. Jauslin, G. Millot, V. V. Kozlov, and S. Wabnitz, “A universal optical all-fiber omnipolarizer,” Sci. Rep. 2, 938 (2012).
[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]

V. V. Kozlov, J. Nuno, and S. Wabnitz, “Theory of lossless polarization attraction in telecommunication fiber,” J. Opt. Soc. Am. B 28, 100–108 (2011).
[CrossRef]

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]

V. V. Kozlov and S. Wabnitz, “Instability of optical solitons in the boundary value problem for a medium of finite extension,” Lett. Math. Phys. 96, 405–413 (2011).
[CrossRef]

V. V. Kozlov and S. Wabnitz, “Theoretical study of polarization attraction in high-birefringence and spun fibers,” Opt. Lett. 35, 3949–3951 (2010).
[CrossRef]

V. V. Kozlov, J. Fatome, P. Morin, S. Pitois, and S. Wabnitz, “Nonlinear optical fiber polarization tracking at 200 krad/s,” presented at the 37th European Conference on Optical Communication (ECOC), 2011, Geneve, Switzerland, September18–22, 2011.

Krauss, T. F.

F. Van Laere, T. Stomeo, D. Taillaert, G. Roelkens, D. Van Thourhout, T. F. Krauss, and R. Baets, “Efficient polarization diversity grating couplers in bonded InP-membrane,” IEEE Photon. Technol. Lett. 20, 318–320 (2008).
[CrossRef]

Lagrange, S.

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]

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]

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

Marazzi, L.

Martelli, P.

Martinelli, M.

Mikhailov, A. V.

V. E. Zakharov and A. V. Mikhailov, “Polarization domains in nonlinear optics,” JETP Lett. 45, 349 (1987).

Millot, G.

J. Fatome, S. Pitois, P. Morin, E. Assémat, D. Sugny, A. Picozzi, H. R. Jauslin, G. Millot, V. V. Kozlov, and S. Wabnitz, “A universal optical all-fiber omnipolarizer,” Sci. Rep. 2, 938 (2012).
[CrossRef]

J. Fatome, P. Morin, S. Pitois, and G. Millot, “Light-by-light polarization control of 10 Gb/s RZ and NRZ telecommunication signals,” IEEE J. Sel. Top. Quantum Electron. 18, 621–628 (2012).
[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]

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]

J. Fatome, S. Pitois, and G. Millot, “Experimental evidence of Brillouin-induced polarization wheeling in highly birefringent optical fibers,” Opt. Express 17, 12612–12618 (2009).
[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 (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]

Mirvoda, V.

B. Koch, R. Noe, V. Mirvoda, H. Griesser, S. Bayer, and H. Wernz, “Record 59 krad/s polarization tracking in 112 Gb/s 640 km PDM-RZ-DQPSK transmission,” IEEE Photon. Technol. Lett. 22, 1407–1409 (2010).
[CrossRef]

Morin, P.

J. Fatome, P. Morin, S. Pitois, and G. Millot, “Light-by-light polarization control of 10 Gb/s RZ and NRZ telecommunication signals,” IEEE J. Sel. Top. Quantum Electron. 18, 621–628 (2012).
[CrossRef]

J. Fatome, S. Pitois, P. Morin, E. Assémat, D. Sugny, A. Picozzi, H. R. Jauslin, G. Millot, V. V. Kozlov, and S. Wabnitz, “A universal optical all-fiber omnipolarizer,” Sci. Rep. 2, 938 (2012).
[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]

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]

V. V. Kozlov, J. Fatome, P. Morin, S. Pitois, and S. Wabnitz, “Nonlinear optical fiber polarization tracking at 200 krad/s,” presented at the 37th European Conference on Optical Communication (ECOC), 2011, Geneve, Switzerland, September18–22, 2011.

Muga, N.

Noe, R.

B. Koch, R. Noe, V. Mirvoda, H. Griesser, S. Bayer, and H. Wernz, “Record 59 krad/s polarization tracking in 112 Gb/s 640 km PDM-RZ-DQPSK transmission,” IEEE Photon. Technol. Lett. 22, 1407–1409 (2010).
[CrossRef]

R. Noe, H. Heidrich, and D. Hoffmann, “Endless polarization control systems for coherent optics,” J. Lightwave Technol. 6, 1199–1208 (1988).
[CrossRef]

Nuno, J.

O’Sullivan, M.

M. Reimer, D. Dumas, G. Soliman, D. Yevick, and M. O’Sullivan, “Polarization evolution in dispersion compensation modules,” presented at the Optical Fiber Communications/National Fiber Optic Engineers Conference (OFC/NFOEC), San Diego, California, March22–26, 2009, paper OWD4.

Palmieri, L.

Picozzi, A.

E. Assémat, A. Picozzi, H. R. Jauslin, and D. Sugny, “Hamiltonian tools for the analysis of optical polarization system,” J. Opt. Soc. Am. B 29, 559–571 (2012).
[CrossRef]

J. Fatome, S. Pitois, P. Morin, E. Assémat, D. Sugny, A. Picozzi, H. R. Jauslin, G. Millot, V. V. Kozlov, and S. Wabnitz, “A universal optical all-fiber omnipolarizer,” Sci. Rep. 2, 938 (2012).
[CrossRef]

E. Assémat, 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. Assemat, A. Picozzi, H. R. Jauslin, and D. Sugny, “Instabilities of optical solitons and Hamiltonian singular solutions in a medium of finite extension,” Phys. Rev. A 84, 013809 (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, 2025–2027 (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, “On the role of singular tori in the spatio-temporal dynamics of 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 (2005).
[CrossRef]

Pietralunga, S. M.

Pinto, A.

Pitois, S.

J. Fatome, P. Morin, S. Pitois, and G. Millot, “Light-by-light polarization control of 10 Gb/s RZ and NRZ telecommunication signals,” IEEE J. Sel. Top. Quantum Electron. 18, 621–628 (2012).
[CrossRef]

J. Fatome, S. Pitois, P. Morin, E. Assémat, D. Sugny, A. Picozzi, H. R. Jauslin, G. Millot, V. V. Kozlov, and S. Wabnitz, “A universal optical all-fiber omnipolarizer,” Sci. Rep. 2, 938 (2012).
[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]

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]

J. Fatome, S. Pitois, and G. Millot, “Experimental evidence of Brillouin-induced polarization wheeling in highly birefringent optical fibers,” Opt. Express 17, 12612–12618 (2009).
[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 (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 (Optical Society of America, 2001), paper MC79, pp. 278–280.

V. V. Kozlov, J. Fatome, P. Morin, S. Pitois, and S. Wabnitz, “Nonlinear optical fiber polarization tracking at 200 krad/s,” presented at the 37th European Conference on Optical Communication (ECOC), 2011, Geneve, Switzerland, September18–22, 2011.

Primerov, N.

Reimer, M.

M. Reimer, D. Dumas, G. Soliman, D. Yevick, and M. O’Sullivan, “Polarization evolution in dispersion compensation modules,” presented at the Optical Fiber Communications/National Fiber Optic Engineers Conference (OFC/NFOEC), San Diego, California, March22–26, 2009, paper OWD4.

Roelkens, G.

F. Van Laere, T. Stomeo, D. Taillaert, G. Roelkens, D. Van Thourhout, T. F. Krauss, and R. Baets, “Efficient polarization diversity grating couplers in bonded InP-membrane,” IEEE Photon. Technol. Lett. 20, 318–320 (2008).
[CrossRef]

Sadovskii, D. A.

K. Efstathiou and D. A. Sadovskii, “Normalization and global analysis of perturbations of the hydrogen atom,” Rev. Mod. Phys. 82, 2099–2154 (2010).
[CrossRef]

Santagiustina, M.

Sauter, A.

Savory, S. J.

S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. 16, 1164–1179 (2010).
[CrossRef]

S. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16, 804–817 (2008).
[CrossRef]

Shmilovitch, Z.

Soliman, G.

M. Reimer, D. Dumas, G. Soliman, D. Yevick, and M. O’Sullivan, “Polarization evolution in dispersion compensation modules,” presented at the Optical Fiber Communications/National Fiber Optic Engineers Conference (OFC/NFOEC), San Diego, California, March22–26, 2009, paper OWD4.

Stomeo, T.

F. Van Laere, T. Stomeo, D. Taillaert, G. Roelkens, D. Van Thourhout, T. F. Krauss, and R. Baets, “Efficient polarization diversity grating couplers in bonded InP-membrane,” IEEE Photon. Technol. Lett. 20, 318–320 (2008).
[CrossRef]

Sugny, D.

J. Fatome, S. Pitois, P. Morin, E. Assémat, D. Sugny, A. Picozzi, H. R. Jauslin, G. Millot, V. V. Kozlov, and S. Wabnitz, “A universal optical all-fiber omnipolarizer,” Sci. Rep. 2, 938 (2012).
[CrossRef]

E. Assémat, A. Picozzi, H. R. Jauslin, and D. Sugny, “Hamiltonian tools for the analysis of optical polarization system,” J. Opt. Soc. Am. B 29, 559–571 (2012).
[CrossRef]

E. Assemat, A. Picozzi, H. R. Jauslin, and D. Sugny, “Instabilities of optical solitons and Hamiltonian singular solutions in a medium of finite extension,” Phys. Rev. A 84, 013809 (2011).
[CrossRef]

E. Assémat, 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, 2025–2027 (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, “On the role of singular tori in the spatio-temporal dynamics of nonlinear wave systems,” Phys. Rev. Lett. 103, 034102 (2009).
[CrossRef]

Taillaert, D.

F. Van Laere, T. Stomeo, D. Taillaert, G. Roelkens, D. Van Thourhout, T. F. Krauss, and R. Baets, “Efficient polarization diversity grating couplers in bonded InP-membrane,” IEEE Photon. Technol. Lett. 20, 318–320 (2008).
[CrossRef]

D. Taillaert, H. Chong, P. I. Borel, L. H. Frandsen, R. M. De La Rue, and R. Baets, “A compact two-dimensional grating coupler used as a polarization splitter,” IEEE Photon. Technol. Lett. 15, 1249–1251 (2003).
[CrossRef]

Thévenaz, L.

Tur, M.

Turitsyn, K.

Van Laere, F.

F. Van Laere, T. Stomeo, D. Taillaert, G. Roelkens, D. Van Thourhout, T. F. Krauss, and R. Baets, “Efficient polarization diversity grating couplers in bonded InP-membrane,” IEEE Photon. Technol. Lett. 20, 318–320 (2008).
[CrossRef]

Van Thourhout, D.

F. Van Laere, T. Stomeo, D. Taillaert, G. Roelkens, D. Van Thourhout, T. F. Krauss, and R. Baets, “Efficient polarization diversity grating couplers in bonded InP-membrane,” IEEE Photon. Technol. Lett. 20, 318–320 (2008).
[CrossRef]

Vannucci, A.

Wabnitz, S.

V. V. Kozlov, M. Barozzi, A. Vannucci, and S. Wabnitz, “Lossless polarization attraction of co-propagating beams in telecom fibers,” J. Opt. Soc. Am. B 30, 530–540 (2013).
[CrossRef]

J. Fatome, S. Pitois, P. Morin, E. Assémat, D. Sugny, A. Picozzi, H. R. Jauslin, G. Millot, V. V. Kozlov, and S. Wabnitz, “A universal optical all-fiber omnipolarizer,” Sci. Rep. 2, 938 (2012).
[CrossRef]

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]

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]

V. V. Kozlov, J. Nuno, and S. Wabnitz, “Theory of lossless polarization attraction in telecommunication fiber,” J. Opt. Soc. Am. B 28, 100–108 (2011).
[CrossRef]

V. V. Kozlov and S. Wabnitz, “Instability of optical solitons in the boundary value problem for a medium of finite extension,” Lett. Math. Phys. 96, 405–413 (2011).
[CrossRef]

V. V. Kozlov and S. Wabnitz, “Theoretical study of polarization attraction in high-birefringence and spun fibers,” Opt. Lett. 35, 3949–3951 (2010).
[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]

V. V. Kozlov, J. Fatome, P. Morin, S. Pitois, and S. Wabnitz, “Nonlinear optical fiber polarization tracking at 200 krad/s,” presented at the 37th European Conference on Optical Communication (ECOC), 2011, Geneve, Switzerland, September18–22, 2011.

Walker, G. R.

N. G. Walker and G. R. Walker, “Polarization control for coherent communications,” J. Lightwave Technol. 8, 438–458 (1990).
[CrossRef]

Walker, N. G.

N. G. Walker and G. R. Walker, “Polarization control for coherent communications,” J. Lightwave Technol. 8, 438–458 (1990).
[CrossRef]

Wernz, H.

B. Koch, R. Noe, V. Mirvoda, H. Griesser, S. Bayer, and H. Wernz, “Record 59 krad/s polarization tracking in 112 Gb/s 640 km PDM-RZ-DQPSK transmission,” IEEE Photon. Technol. Lett. 22, 1407–1409 (2010).
[CrossRef]

Yevick, D.

M. Reimer, D. Dumas, G. Soliman, D. Yevick, and M. O’Sullivan, “Polarization evolution in dispersion compensation modules,” presented at the Optical Fiber Communications/National Fiber Optic Engineers Conference (OFC/NFOEC), San Diego, California, March22–26, 2009, paper OWD4.

Zadok, A.

Zakharov, V. E.

V. E. Zakharov and A. V. Mikhailov, “Polarization domains in nonlinear optics,” JETP Lett. 45, 349 (1987).

Zilka, E.

Europhys. Lett.

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 (2005).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

S. J. Savory, “Digital coherent optical receivers: algorithms and subsystems,” IEEE J. Sel. Top. Quantum Electron. 16, 1164–1179 (2010).
[CrossRef]

J. Fatome, P. Morin, S. Pitois, and G. Millot, “Light-by-light polarization control of 10 Gb/s RZ and NRZ telecommunication signals,” IEEE J. Sel. Top. Quantum Electron. 18, 621–628 (2012).
[CrossRef]

IEEE Photon. Technol. Lett.

D. Taillaert, H. Chong, P. I. Borel, L. H. Frandsen, R. M. De La Rue, and R. Baets, “A compact two-dimensional grating coupler used as a polarization splitter,” IEEE Photon. Technol. Lett. 15, 1249–1251 (2003).
[CrossRef]

F. Van Laere, T. Stomeo, D. Taillaert, G. Roelkens, D. Van Thourhout, T. F. Krauss, and R. Baets, “Efficient polarization diversity grating couplers in bonded InP-membrane,” IEEE Photon. Technol. Lett. 20, 318–320 (2008).
[CrossRef]

B. Koch, R. Noe, V. Mirvoda, H. Griesser, S. Bayer, and H. Wernz, “Record 59 krad/s polarization tracking in 112 Gb/s 640 km PDM-RZ-DQPSK transmission,” IEEE Photon. Technol. Lett. 22, 1407–1409 (2010).
[CrossRef]

J. Lightwave Technol.

R. Noe, H. Heidrich, and D. Hoffmann, “Endless polarization control systems for coherent optics,” J. Lightwave Technol. 6, 1199–1208 (1988).
[CrossRef]

N. G. Walker and G. R. Walker, “Polarization control for coherent communications,” J. Lightwave Technol. 8, 438–458 (1990).
[CrossRef]

M. Martinelli, P. Martelli, and S. M. Pietralunga, “Polarization stabilization in optical communications systems,” J. Lightwave Technol. 24, 4172–4183 (2006).
[CrossRef]

J. Opt. Soc. Am. B

JETP Lett.

V. E. Zakharov and A. V. Mikhailov, “Polarization domains in nonlinear optics,” JETP Lett. 45, 349 (1987).

Lett. Math. Phys.

V. V. Kozlov and S. Wabnitz, “Instability of optical solitons in the boundary value problem for a medium of finite extension,” Lett. Math. Phys. 96, 405–413 (2011).
[CrossRef]

Opt. Express

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. J. Savory, “Digital filters for coherent optical receivers,” Opt. Express 16, 804–817 (2008).
[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]

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]

M. Martinelli, M. Cirigliano, M. M. Ferrario, L. Marazzi, and P. Martelli, “Evidence of Raman-induced polarization pulling,” Opt. Express 17, 947–955 (2009).
[CrossRef]

N. Muga, M. Ferreira, and A. Pinto, “Broadband polarization pulling using Raman amplification,” Opt. Express 19, 18707–18712 (2011).
[CrossRef]

F. Chiarello, L. Palmieri, M. Santagiustina, R. Gamatham, and A. Galtarossa, “Experimental characterization of the counter-propagating Raman polarization attraction,” Opt. Express 20, 26050–26055 (2012).
[CrossRef]

A. Zadok, E. Zilka, A. Eyal, L. Thévenaz, and M. Tur, “Vector analysis of stimulated Brillouin scattering amplification in standard single-mode fibers,” Opt. Express 16, 21692–21707 (2008).
[CrossRef]

Z. Shmilovitch, N. Primerov, A. Zadok, A. Eyal, S. Chin, L. Thévenaz, and M. Tur, “Dual-pump push-pull polarization control using stimulated Brillouin scattering,” Opt. Express 19, 25873–25880 (2011).
[CrossRef]

J. Fatome, S. Pitois, and G. Millot, “Experimental evidence of Brillouin-induced polarization wheeling in highly birefringent optical fibers,” Opt. Express 17, 12612–12618 (2009).
[CrossRef]

Opt. Lett.

Phys. Rev. A

E. Assemat, A. Picozzi, H. R. Jauslin, and D. Sugny, “Instabilities of optical solitons and Hamiltonian singular solutions in a medium of finite extension,” Phys. Rev. A 84, 013809 (2011).
[CrossRef]

Phys. Rev. E

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.

D. Sugny, A. Picozzi, S. Lagrange, and H. R. Jauslin, “On the role of singular tori in the spatio-temporal dynamics of 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]

Rev. Mod. Phys.

K. Efstathiou and D. A. Sadovskii, “Normalization and global analysis of perturbations of the hydrogen atom,” Rev. Mod. Phys. 82, 2099–2154 (2010).
[CrossRef]

Sci. Rep.

J. Fatome, S. Pitois, P. Morin, E. Assémat, D. Sugny, A. Picozzi, H. R. Jauslin, G. Millot, V. V. Kozlov, and S. Wabnitz, “A universal optical all-fiber omnipolarizer,” Sci. Rep. 2, 938 (2012).
[CrossRef]

Other

S. Pitois and M. Haelterman, “Optical fiber polarization funnel,” in Nonlinear Guided Waves and Their Applications, OSA Technical Digest (Optical Society of America, 2001), paper MC79, pp. 278–280.

M. Reimer, D. Dumas, G. Soliman, D. Yevick, and M. O’Sullivan, “Polarization evolution in dispersion compensation modules,” presented at the Optical Fiber Communications/National Fiber Optic Engineers Conference (OFC/NFOEC), San Diego, California, March22–26, 2009, paper OWD4.

R. H. Cushman and L. M. Bates, Global Aspects of Classical Integrable Systems (Birkhauser, 1997).

V. V. Kozlov, J. Fatome, P. Morin, S. Pitois, and S. Wabnitz, “Nonlinear optical fiber polarization tracking at 200 krad/s,” presented at the 37th European Conference on Optical Communication (ECOC), 2011, Geneve, Switzerland, September18–22, 2011.

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Figures (7)

Fig. 1.
Fig. 1.

Experimental setup.

Fig. 2.
Fig. 2.

Experimental DOP as a function of pump power.

Fig. 3.
Fig. 3.

(a) SOP and (b) eye diagram behind a polarizer of the 40Gbit/s signal after polarization scrambling (1) without and (2) with the counterpropagating pump wave. (c) Evolution of the BER as a function of the received average power in BB configuration (dark squares)—at the output of the system with (open circles) and without (dark circles) the counterpropagating pump wave.

Fig. 4.
Fig. 4.

(a) Evolution of the signal SOP at the omnipolarizer output for different values of the reflection coefficient R. (b) DOP of the output signal as a function of the average power of the reflected signal (and similarly as a function of R).

Fig. 5.
Fig. 5.

Eye diagram behind a polarizer of the 40Gbit/s signal after polarization scrambling (a1) without and (a2) with the reflected signal wave. (b) Evolution of the BER as a function of the received average power in the BB configuration (dark squares)—at the output of the system with (open circles) and without (dark circles) the reflected signal (RS) wave.

Fig. 6.
Fig. 6.

Trajectories followed by the signal SOP to reach the final polarization state (SOP attractor), represented (a), (b) in the energy momentum representation and (c), (d) on the surface of the Poincaré sphere. As indicated in (a), (b), each regular point of the energy momentum diagram refers to a torus (see the text for details). In (a) and (c), the evolution of the input S(z=0)=[0.30,0.60,0.74] (red) is shown for a transient time τtr of the same order as the time required to propagate throughout the omnipolarizer, τtrτL=2L/vg; the signal SOP exhibits an erratic polarization dynamics before reaching its attractor polarization state. In (b) and (d), the evolution of the three inputs S(z=0)=[0.30,0.60,0.74] (red), S(0)=[0.50,0.50,0.70] (blue), and S(0)=[0.90,0.0,0.43] (green) is shown for τtr=103τL; the signal SOP adiabatically relaxes to its attractor polarization state. The arrows show the direction in which the trajectories travel.

Fig. 7.
Fig. 7.

(a) Theoretical Poincaré representation obtained by numerically solving the spatiotemporal SOP evolution defined by Eq. (1). We considered a set of 64 different input signal SOPs, uniformly distributed over the Poincaré sphere. The blue dots represent output SOPs. The first row refers to a fiber length of L=5Λ0, and the second row to L=20Λ0. For the traditional two-source configuration [(a) and (c)], the signal is attracted toward a single SOP, which is determined by the injected pump SOP (green dot). For the omnipolarizer configuration [(b) and (d)], the input SOP ellipticity determines the two basins of attraction of the omnipolarizer, corresponding to the two hemispheres of the Poincaré sphere.

Equations (3)

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S⃗t+S⃗z=S⃗×(IJ⃗)J⃗tJ⃗z=J⃗×(IS⃗).
Sxz=SyJz+SzJySyz=SxJzSzJxSzz=SxJy+SyJxandJxz=SyJzSzJyJyz=SxJz+SzJxJzz=SxJy+SyJx.
H=SxJx+SyJySzJz.

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