Abstract

We report the experimental observation of bistability and hysteresis phenomena of the polarization signal in a telecommunication optical fiber. This process occurs in a counterpropagating configuration in which the optical beam nonlinearly interacts with its own Bragg-reflected replica at the fiber output. The proof of principle of optical flip–flop memory and 10Gbit/s routing operation is also reported based on this polarization bistability. Finally, we also provide a general physical understanding of this behavior on the basis of a geometrical analysis of an effective model of the dynamics. Good quantitative agreement between theory and experiment is obtained.

© 2013 Optical Society of America

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  1. 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. M. Martinelli, M. Cirigliano, M. Ferrario, L. Marazzi, and P. Martelli, “Evidence of Raman-induced polarization pulling,” Opt. Express 17, 947–955 (2009).
    [CrossRef]
  3. L. Ursini, M. Santagiustina, and L. Palmieri, “Raman nonlinear polarization pulling in the pump depleted regime in randomly birefringent fibers,” IEEE Photon. Technol. Lett. 23, 254–256 (2011).
    [CrossRef]
  4. V. Kozlov, J. Nuno, J. D. Ania-Castanon, and S. Wabnitz, “Theoretical study of optical fiber Raman polarizers with counterpropagating beams,” IEEE J. Lightwave Technol. 29, 341–347 (2011).
  5. L. Thevenaz, A. Zadok, A. Eyal, and M. Tur, “All-optical polarization control through Brillouin amplification,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OML7.
  6. Z. Shmilovitch, N. Primerov, A. Zadok, A. Eyal, S. Chin, L. Thevenaz, and M. Tur, “Dual-pump push-pull polarization control using stimulated Brillouin scattering,” Opt. Express 19, 25873–25880 (2011).
    [CrossRef]
  7. B. Stiller, P. Morin, D. M. Nguyen, J. Fatome, S. Pitois, E. Lantz, H. Maillotte, C. R. Menyuk, and T. Sylvestre, “Demonstration of polarization pulling using a fiber-optic parametric amplifier,” Opt. Express 20, 27248–27253 (2012).
    [CrossRef]
  8. M. Guasoni, V. Kozlov, and S. Wabnitz, “Theory of polarization attraction in parametric amplifiers based on telecommunication fibers,” J. Opt. Soc. Am. B 29, 2710–2720 (2012).
    [CrossRef]
  9. 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]
  10. 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]
  11. 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]
  12. 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]
  13. V. V. Kozlov, J. Nuno, and S. Wabnitz, “Theory of lossless polarization attraction in telecommunication fibers,” J. Opt. Soc. Am. B 28, 100–108 (2011).
    [CrossRef]
  14. 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]
  15. 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]
  16. E. Assémat, A. Picozzi, H. R. Jauslin, and D. Sugny, “Hamiltonian tools for the analysis of optical polarization control,” J. Opt. Soc. Am. B 29, 559–571 (2012).
    [CrossRef]
  17. 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]
  18. 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]
  19. 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]
  20. D. J. Gauthier, M. S. Malcuit, A. L. Gaeta, and R. W. Boyd, “Polarization bistability of counterpropagating laser beams,” Phys. Rev. Lett. 64, 1721–1724 (1990).
    [CrossRef]
  21. A. L. Gaeta, R. W. Boyd, J. R. Ackerhalt, and P. W. Milonni, “Instabilities and chaos in the polarizations of counterpropagating light fields,” Phys. Rev. Lett. 58, 2432–2435 (1987).
    [CrossRef]
  22. S. Trillo and S. Wabnitz, “Intermittent spatial chaos in the polarization of counterpropagating beams in a birefringent optical fiber,” Phys. Rev. A 36, 3881–3884 (1987).
    [CrossRef]
  23. M. V. Tratnik and J. E. Sipe, “Nonlinear polarization dynamics. II. Counterpropagating-beam equations: new simple solutions and the possibilities for chaos,” Phys. Rev. A 35, 2976–2988 (1987).
    [CrossRef]
  24. S. Pitois, G. Millot, and S. Wabnitz, “Polarization domain wall solitons with counterpropagating laser beams,” Phys. Rev. Lett. 81, 1409–1412 (1998).
    [CrossRef]
  25. D. David, D. D. Holm, and M. V. Tratnik, “Hamiltonian chaos in nonlinear optical polarization dynamics,” Phys. Rep. 187, 281–367 (1990).
    [CrossRef]
  26. V. Kozlov and S. Wabnitz, “Theoretical study of polarization attraction in high-birefringence and spun fibers,” Opt. Lett. 35, 3949–3951 (2010).
    [CrossRef]
  27. J. Fatome, S. Pitois, P. Morin, D. Sugny, E. Assémat, A. Picozzi, H. R. Jauslin, G. Millot, V. V. Kozlov, and S. Wabnitz, “A universal optical all-fiber omnipolarizer,” Sci. Rep. 2, 938 (2012).
  28. H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry-Perot interferometer,” Phys. Rev. Lett. 36, 1135–1138 (1976).
    [CrossRef]
  29. R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).
  30. K. S. Turitsyn and S. Wabnitz, “Stability analysis of polarization attraction in optical fibers,” Opt. Commun. 307, 62–66 (2013).
    [CrossRef]
  31. A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
    [CrossRef]
  32. M. Virtel, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7, 60–65 (2012).
    [CrossRef]
  33. https://www.facebook.com/petal.inside .

2013 (1)

K. S. Turitsyn and S. Wabnitz, “Stability analysis of polarization attraction in optical fibers,” Opt. Commun. 307, 62–66 (2013).
[CrossRef]

2012 (5)

2011 (7)

2010 (4)

2009 (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]

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

2008 (2)

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]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
[CrossRef]

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]

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]

1990 (2)

D. David, D. D. Holm, and M. V. Tratnik, “Hamiltonian chaos in nonlinear optical polarization dynamics,” Phys. Rep. 187, 281–367 (1990).
[CrossRef]

D. J. Gauthier, M. S. Malcuit, A. L. Gaeta, and R. W. Boyd, “Polarization bistability of counterpropagating laser beams,” Phys. Rev. Lett. 64, 1721–1724 (1990).
[CrossRef]

1987 (3)

A. L. Gaeta, R. W. Boyd, J. R. Ackerhalt, and P. W. Milonni, “Instabilities and chaos in the polarizations of counterpropagating light fields,” Phys. Rev. Lett. 58, 2432–2435 (1987).
[CrossRef]

S. Trillo and S. Wabnitz, “Intermittent spatial chaos in the polarization of counterpropagating beams in a birefringent optical fiber,” Phys. Rev. A 36, 3881–3884 (1987).
[CrossRef]

M. V. Tratnik and J. E. Sipe, “Nonlinear polarization dynamics. II. Counterpropagating-beam equations: new simple solutions and the possibilities for chaos,” Phys. Rev. A 35, 2976–2988 (1987).
[CrossRef]

1976 (1)

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry-Perot interferometer,” Phys. Rev. Lett. 36, 1135–1138 (1976).
[CrossRef]

Ackerhalt, J. R.

A. L. Gaeta, R. W. Boyd, J. R. Ackerhalt, and P. W. Milonni, “Instabilities and chaos in the polarizations of counterpropagating light fields,” Phys. Rev. Lett. 58, 2432–2435 (1987).
[CrossRef]

Amano, K.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
[CrossRef]

Ania-Castanon, J. D.

V. Kozlov, J. Nuno, J. D. Ania-Castanon, and S. Wabnitz, “Theoretical study of optical fiber Raman polarizers with counterpropagating beams,” IEEE J. Lightwave Technol. 29, 341–347 (2011).

Assémat, E.

Bennink, R. S.

Boyd, R. W.

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]

D. J. Gauthier, M. S. Malcuit, A. L. Gaeta, and R. W. Boyd, “Polarization bistability of counterpropagating laser beams,” Phys. Rev. Lett. 64, 1721–1724 (1990).
[CrossRef]

A. L. Gaeta, R. W. Boyd, J. R. Ackerhalt, and P. W. Milonni, “Instabilities and chaos in the polarizations of counterpropagating light fields,” Phys. Rev. Lett. 58, 2432–2435 (1987).
[CrossRef]

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

Chin, S.

Cirigliano, M.

Claveau, R.

Dargent, D.

David, D.

D. David, D. D. Holm, and M. V. Tratnik, “Hamiltonian chaos in nonlinear optical polarization dynamics,” Phys. Rep. 187, 281–367 (1990).
[CrossRef]

Davis, P.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
[CrossRef]

Eyal, A.

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

L. Thevenaz, A. Zadok, A. Eyal, and M. Tur, “All-optical polarization control through Brillouin amplification,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OML7.

Fatome, J.

Ferrario, M.

Finot, C.

Fisher, R. A.

Gaeta, A. L.

D. J. Gauthier, M. S. Malcuit, A. L. Gaeta, and R. W. Boyd, “Polarization bistability of counterpropagating laser beams,” Phys. Rev. Lett. 64, 1721–1724 (1990).
[CrossRef]

A. L. Gaeta, R. W. Boyd, J. R. Ackerhalt, and P. W. Milonni, “Instabilities and chaos in the polarizations of counterpropagating light fields,” Phys. Rev. Lett. 58, 2432–2435 (1987).
[CrossRef]

Gauthier, D. J.

D. J. Gauthier, M. S. Malcuit, A. L. Gaeta, and R. W. Boyd, “Polarization bistability of counterpropagating laser beams,” Phys. Rev. Lett. 64, 1721–1724 (1990).
[CrossRef]

Gibbs, H. M.

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry-Perot interferometer,” Phys. Rev. Lett. 36, 1135–1138 (1976).
[CrossRef]

Guasoni, M.

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]

Heebner, E.

Hirano, K.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
[CrossRef]

Holm, D. D.

D. David, D. D. Holm, and M. V. Tratnik, “Hamiltonian chaos in nonlinear optical polarization dynamics,” Phys. Rep. 187, 281–367 (1990).
[CrossRef]

Inoue, M.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
[CrossRef]

Jauslin, H. R.

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

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

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]

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, “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.

Kozlov, V. V.

Kurashige, T.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
[CrossRef]

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]

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]

Lantz, E.

Maillotte, H.

Malcuit, M. S.

D. J. Gauthier, M. S. Malcuit, A. L. Gaeta, and R. W. Boyd, “Polarization bistability of counterpropagating laser beams,” Phys. Rev. Lett. 64, 1721–1724 (1990).
[CrossRef]

Marazzi, L.

Martelli, P.

Martinelli, M.

McCall, S. L.

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry-Perot interferometer,” Phys. Rev. Lett. 36, 1135–1138 (1976).
[CrossRef]

Menyuk, C. R.

Millot, G.

Milonni, P. W.

A. L. Gaeta, R. W. Boyd, J. R. Ackerhalt, and P. W. Milonni, “Instabilities and chaos in the polarizations of counterpropagating light fields,” Phys. Rev. Lett. 58, 2432–2435 (1987).
[CrossRef]

Morin, P.

Naito, S.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
[CrossRef]

Nguyen, D. M.

Nuno, J.

V. Kozlov, J. Nuno, J. D. Ania-Castanon, and S. Wabnitz, “Theoretical study of optical fiber Raman polarizers with counterpropagating beams,” IEEE J. Lightwave Technol. 29, 341–347 (2011).

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

Oowada, I.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
[CrossRef]

Palmieri, L.

L. Ursini, M. Santagiustina, and L. Palmieri, “Raman nonlinear polarization pulling in the pump depleted regime in randomly birefringent fibers,” IEEE Photon. Technol. Lett. 23, 254–256 (2011).
[CrossRef]

Panajotov, K.

M. Virtel, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7, 60–65 (2012).
[CrossRef]

Picozzi, A.

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

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

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, “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.

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

B. Stiller, P. Morin, D. M. Nguyen, J. Fatome, S. Pitois, E. Lantz, H. Maillotte, C. R. Menyuk, and T. Sylvestre, “Demonstration of polarization pulling using a fiber-optic parametric amplifier,” Opt. Express 20, 27248–27253 (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]

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

Primerov, N.

Santagiustina, M.

L. Ursini, M. Santagiustina, and L. Palmieri, “Raman nonlinear polarization pulling in the pump depleted regime in randomly birefringent fibers,” IEEE Photon. Technol. Lett. 23, 254–256 (2011).
[CrossRef]

Sciamanna, M.

M. Virtel, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7, 60–65 (2012).
[CrossRef]

Shiki, M.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
[CrossRef]

Shmilovitch, Z.

Sipe, J. E.

M. V. Tratnik and J. E. Sipe, “Nonlinear polarization dynamics. II. Counterpropagating-beam equations: new simple solutions and the possibilities for chaos,” Phys. Rev. A 35, 2976–2988 (1987).
[CrossRef]

Someya, H.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
[CrossRef]

Stiller, B.

Sugny, D.

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

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

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]

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, “Role of singular tori in the dynamics of spatiotemporal nonlinear wave systems,” Phys. Rev. Lett. 103, 034102 (2009).
[CrossRef]

Sylvestre, T.

Thevenaz, L.

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

L. Thevenaz, A. Zadok, A. Eyal, and M. Tur, “All-optical polarization control through Brillouin amplification,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OML7.

Thienpont, H.

M. Virtel, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7, 60–65 (2012).
[CrossRef]

Tratnik, M. V.

D. David, D. D. Holm, and M. V. Tratnik, “Hamiltonian chaos in nonlinear optical polarization dynamics,” Phys. Rep. 187, 281–367 (1990).
[CrossRef]

M. V. Tratnik and J. E. Sipe, “Nonlinear polarization dynamics. II. Counterpropagating-beam equations: new simple solutions and the possibilities for chaos,” Phys. Rev. A 35, 2976–2988 (1987).
[CrossRef]

Trillo, S.

S. Trillo and S. Wabnitz, “Intermittent spatial chaos in the polarization of counterpropagating beams in a birefringent optical fiber,” Phys. Rev. A 36, 3881–3884 (1987).
[CrossRef]

Tur, M.

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

L. Thevenaz, A. Zadok, A. Eyal, and M. Tur, “All-optical polarization control through Brillouin amplification,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OML7.

Turitsyn, K. S.

K. S. Turitsyn and S. Wabnitz, “Stability analysis of polarization attraction in optical fibers,” Opt. Commun. 307, 62–66 (2013).
[CrossRef]

Uchida, A.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
[CrossRef]

Ursini, L.

L. Ursini, M. Santagiustina, and L. Palmieri, “Raman nonlinear polarization pulling in the pump depleted regime in randomly birefringent fibers,” IEEE Photon. Technol. Lett. 23, 254–256 (2011).
[CrossRef]

Venkatesan, T. N. C.

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry-Perot interferometer,” Phys. Rev. Lett. 36, 1135–1138 (1976).
[CrossRef]

Virtel, M.

M. Virtel, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7, 60–65 (2012).
[CrossRef]

Wabnitz, S.

K. S. Turitsyn and S. Wabnitz, “Stability analysis of polarization attraction in optical fibers,” Opt. Commun. 307, 62–66 (2013).
[CrossRef]

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

M. Guasoni, V. Kozlov, and S. Wabnitz, “Theory of polarization attraction in parametric amplifiers based on telecommunication fibers,” J. Opt. Soc. Am. B 29, 2710–2720 (2012).
[CrossRef]

V. Kozlov, J. Nuno, J. D. Ania-Castanon, and S. Wabnitz, “Theoretical study of optical fiber Raman polarizers with counterpropagating beams,” IEEE J. Lightwave Technol. 29, 341–347 (2011).

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 fibers,” J. Opt. Soc. Am. B 28, 100–108 (2011).
[CrossRef]

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

S. Trillo and S. Wabnitz, “Intermittent spatial chaos in the polarization of counterpropagating beams in a birefringent optical fiber,” Phys. Rev. A 36, 3881–3884 (1987).
[CrossRef]

Yoshimori, S.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
[CrossRef]

Yoshimura, K.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
[CrossRef]

Zadok, A.

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

L. Thevenaz, A. Zadok, A. Eyal, and M. Tur, “All-optical polarization control through Brillouin amplification,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OML7.

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]

IEEE J. Lightwave Technol. (1)

V. Kozlov, J. Nuno, J. D. Ania-Castanon, and S. Wabnitz, “Theoretical study of optical fiber Raman polarizers with counterpropagating beams,” IEEE J. Lightwave Technol. 29, 341–347 (2011).

IEEE Photon. Technol. Lett. (1)

L. Ursini, M. Santagiustina, and L. Palmieri, “Raman nonlinear polarization pulling in the pump depleted regime in randomly birefringent fibers,” IEEE Photon. Technol. Lett. 23, 254–256 (2011).
[CrossRef]

J. Opt. Soc. Am. B (4)

Nat. Photonics (2)

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728–732 (2008).
[CrossRef]

M. Virtel, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7, 60–65 (2012).
[CrossRef]

Opt. Commun. (1)

K. S. Turitsyn and S. Wabnitz, “Stability analysis of polarization attraction in optical fibers,” Opt. Commun. 307, 62–66 (2013).
[CrossRef]

Opt. Express (6)

Opt. Lett. (4)

Phys. Rep. (1)

D. David, D. D. Holm, and M. V. Tratnik, “Hamiltonian chaos in nonlinear optical polarization dynamics,” Phys. Rep. 187, 281–367 (1990).
[CrossRef]

Phys. Rev. A (2)

S. Trillo and S. Wabnitz, “Intermittent spatial chaos in the polarization of counterpropagating beams in a birefringent optical fiber,” Phys. Rev. A 36, 3881–3884 (1987).
[CrossRef]

M. V. Tratnik and J. E. Sipe, “Nonlinear polarization dynamics. II. Counterpropagating-beam equations: new simple solutions and the possibilities for chaos,” Phys. Rev. A 35, 2976–2988 (1987).
[CrossRef]

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. (5)

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]

D. J. Gauthier, M. S. Malcuit, A. L. Gaeta, and R. W. Boyd, “Polarization bistability of counterpropagating laser beams,” Phys. Rev. Lett. 64, 1721–1724 (1990).
[CrossRef]

A. L. Gaeta, R. W. Boyd, J. R. Ackerhalt, and P. W. Milonni, “Instabilities and chaos in the polarizations of counterpropagating light fields,” Phys. Rev. Lett. 58, 2432–2435 (1987).
[CrossRef]

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

H. M. Gibbs, S. L. McCall, and T. N. C. Venkatesan, “Differential gain and bistability using a sodium-filled Fabry-Perot interferometer,” Phys. Rev. Lett. 36, 1135–1138 (1976).
[CrossRef]

Sci. Rep. (1)

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

Other (3)

R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, 2008).

https://www.facebook.com/petal.inside .

L. Thevenaz, A. Zadok, A. Eyal, and M. Tur, “All-optical polarization control through Brillouin amplification,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference, OSA Technical Digest (CD) (Optical Society of America, 2008), paper OML7.

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Figures (9)

Fig. 1.
Fig. 1.

Numerical simulations of the spatiotemporal Eq. (1) on the Poincaré sphere. We considered a set of 64 different input signal SOPs (S⃗(ξ=0)), uniformly distributed over the Poincaré sphere (blue and green dots). The red dots represent the SOPs at the fiber output, S⃗(ξ=L), once the system has reached the stationary state. The ellipticity of the input SOPs determines two basins of attraction: green (blue) dots are attracted to the north (south) pole of the Poincaré sphere. Parameters are ρ=0.98 and L=6.

Fig. 2.
Fig. 2.

(a) Plot of S3(L) as a function of S3(0) for the stationary solutions of Eq. (1). The reflection coefficient is ρ=1, and the normalized fiber length is L=Lc. (b) Same as (a) with normalized fiber length L=3; the solid (blue), dashed (red), and dotted lines represent, respectively, the stable, metastable, and unstable stationary states (see text for details).

Fig. 3.
Fig. 3.

Illustration of the stability of the stationary solutions: initial (dotted lines) and final (plain lines) SOP of S⃗(ξ) along the fiber coordinate obtained by integrating numerically the space-time Eq. (1). The S1, S2, and S3 components are represented in red, blue, and green, respectively. The normalized fiber length is L=10.

Fig. 4.
Fig. 4.

Experimental setup. ASE, amplified spontaneous noise emission; Pol, inline polarizer; PS, polarization scrambler; EDFA, erbium-doped fiber amplifier; PM, power meter; NZDSF, nonzero dispersion fiber; FBG, fiber Bragg grating; PC, polarization controller; PBS, polarization beam splitter.

Fig. 5.
Fig. 5.

(a) Input signal SOP represented on the Poincaré sphere. (b) Output SOP for an input power of 570 mW. (c) Stokes parameters of the input signal as a function of time. (d) Stokes parameters of the output signal as a function of time for an input average power of 570 mW.

Fig. 6.
Fig. 6.

(a) Initial polarization trajectory represented onto the Poincaré sphere. (b) Evolution of the Stokes parameter S3 at the output of the system in linear regime (green solid line) and at high power (570 mW, blue line) as a function of time. (c) Output polarization trajectory represented onto the Poincaré sphere for an input average power of 570 mW. (d) Hysteresis: evolution of the Stokes parameter S3 at the output of the system at high power (570 mW) as a function of the input (equivalent of the linear regime).

Fig. 7.
Fig. 7.

(a)–(f) Hysteresis evolution of the Stokes parameter S3 at the output of the system as a function of input power. Experimental results (red solid lines) are compared with numerical simulations (black lines). (a) 70 mW, (b) 141 mW, (c) 283 mW, (d) 353 mW, (e) 424 mW, and (f) 495 mW.

Fig. 8.
Fig. 8.

(a) Triggering set/reset S3 sequence injected into the system. (b) Temporal response of the flip–flop memory: output S3 parameter. (c) Corresponding intensity profile at the output of the memory detected though a PBS on axis 1 of the PBS (top) and on axis 2 (bottom), respectively. (d) Temporal transition diagram of the flip–flop optical memory recorded in persistence mode of the oscilloscope at port 1 of the PBS.

Fig. 9.
Fig. 9.

(a1) Temporal evolution of the intensity profile at the output of the device detected though a PBS in the linear regime (input power 10 mW). (b1) At high power (570 mW) and on axis 1 of the PBS. (c1) At high power (570 mW) and on axis 2 of the PBS. (a2), (b2), (c2) Corresponding 10Gbit/s eye diagrams.

Equations (3)

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

{S⃗τ+S⃗ξ=(DJ⃗)×S⃗J⃗τJ⃗ξ=(DS⃗)×J⃗,
S⃗ξ=(DJ⃗)×S⃗,J⃗ξ=(DS⃗)×J⃗.
S⃗ξ=K⃗×S⃗.

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