Abstract

In this work, we report the experimental observation of a polarization attraction process which can occur in optical fibers at telecommunication wavelengths. More precisely, we have numerically and experimentally shown that a polarization attractor, based on the injection of two counter-propagating waves around 1.55µm into a 2-m long high nonlinear fiber, can transform any input polarization state into a unique well-defined output polarization state.

© 2008 Optical Society of America

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  1. K. Cvecek, K. Sponsel, R. Ludwig, C. Schubert, C. Stephan, G. Onishchukov, B. Schmauss, and G. Leuchs, "2R-Regeneration of an 80-Gb/s RZ-DQPSK Signal by a Nonlinear Amplifying Loop Mirror," IEEE Photon. Technol. Lett. 19, 146-148 (2007).
    [CrossRef]
  2. S. Boscolo, S. K. Turitsyn, and K. J. Blow, "Nonlinear loop mirror-based all-optical signal processing in fiber-optic communications," Opt. Fiber Technol. Available online 17 March 2008.
  3. E. Ip, A. P. T. Lau, D. J. F. Barros, and J. M. Kahn, "Coherent detection in optical fiber systems, " Opt. Express 16, 753-791 (2008).
    [CrossRef] [PubMed]
  4. E. Ciaramella, F. Curti, and S. Trillo, "All-optical signal reshaping by means of four-wave mixing in optical fibers," IEEE Photon. Technol. Lett. 13, 142-144 (2001).
    [CrossRef]
  5. P. Honzatko, A. Kumpera, and P. Skoda, "Effects of polarization dependent gain and dynamic birefringence of the SOA on the performance of the ultrafast nonlinear interferometer gate, " Opt. Express 15, 2541-2547 (2007).
    [CrossRef] [PubMed]
  6. Y. Takahashi, A. Neogi, and H. Kawaguchi, "Polarization dependent nonlinear gain in semiconductor optical amplifiers," J. Quantum Electron. 34, 1660-1672 (1998).
    [CrossRef]
  7. J. P. Gordon and H. Kogelnik, "PMD fundamentals: Polarization mode dispersion in optical fibers," PNAS 97, 4541-4550 (2000).
    [CrossRef] [PubMed]
  8. J. Garnier, J. Fatome, and G. Le Meur, "Statistical analysis of pulse propagation driven by polarization-mode dispersion," J. Opt. Soc. Am. B 19, 1968-1977 (2002).
    [CrossRef]
  9. 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]
  10. 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]
  11. 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] [PubMed]
  12. 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]

2008

2007

P. Honzatko, A. Kumpera, and P. Skoda, "Effects of polarization dependent gain and dynamic birefringence of the SOA on the performance of the ultrafast nonlinear interferometer gate, " Opt. Express 15, 2541-2547 (2007).
[CrossRef] [PubMed]

K. Cvecek, K. Sponsel, R. Ludwig, C. Schubert, C. Stephan, G. Onishchukov, B. Schmauss, and G. Leuchs, "2R-Regeneration of an 80-Gb/s RZ-DQPSK Signal by a Nonlinear Amplifying Loop Mirror," IEEE Photon. Technol. Lett. 19, 146-148 (2007).
[CrossRef]

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, 88-94 (2005).
[CrossRef]

2004

2002

2001

E. Ciaramella, F. Curti, and S. Trillo, "All-optical signal reshaping by means of four-wave mixing in optical fibers," IEEE Photon. Technol. Lett. 13, 142-144 (2001).
[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]

2000

1998

Y. Takahashi, A. Neogi, and H. Kawaguchi, "Polarization dependent nonlinear gain in semiconductor optical amplifiers," J. Quantum Electron. 34, 1660-1672 (1998).
[CrossRef]

Barros, D. J. F.

Bennink, R. S.

Boyd, R. W.

Ciaramella, E.

E. Ciaramella, F. Curti, and S. Trillo, "All-optical signal reshaping by means of four-wave mixing in optical fibers," IEEE Photon. Technol. Lett. 13, 142-144 (2001).
[CrossRef]

Curti, F.

E. Ciaramella, F. Curti, and S. Trillo, "All-optical signal reshaping by means of four-wave mixing in optical fibers," IEEE Photon. Technol. Lett. 13, 142-144 (2001).
[CrossRef]

Cvecek, K.

K. Cvecek, K. Sponsel, R. Ludwig, C. Schubert, C. Stephan, G. Onishchukov, B. Schmauss, and G. Leuchs, "2R-Regeneration of an 80-Gb/s RZ-DQPSK Signal by a Nonlinear Amplifying Loop Mirror," IEEE Photon. Technol. Lett. 19, 146-148 (2007).
[CrossRef]

Fatome, J.

Fisher, R. A.

Garnier, J.

Gordon, J. P.

J. P. Gordon and H. Kogelnik, "PMD fundamentals: Polarization mode dispersion in optical fibers," PNAS 97, 4541-4550 (2000).
[CrossRef] [PubMed]

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.

Honzatko, P.

Ip, E.

Jauslin, H. R.

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]

Kahn, J. M.

Kawaguchi, H.

Y. Takahashi, A. Neogi, and H. Kawaguchi, "Polarization dependent nonlinear gain in semiconductor optical amplifiers," J. Quantum Electron. 34, 1660-1672 (1998).
[CrossRef]

Kogelnik, H.

J. P. Gordon and H. Kogelnik, "PMD fundamentals: Polarization mode dispersion in optical fibers," PNAS 97, 4541-4550 (2000).
[CrossRef] [PubMed]

Kumpera, A.

Lau, A. P. T.

Le Meur, G.

Leuchs, G.

K. Cvecek, K. Sponsel, R. Ludwig, C. Schubert, C. Stephan, G. Onishchukov, B. Schmauss, and G. Leuchs, "2R-Regeneration of an 80-Gb/s RZ-DQPSK Signal by a Nonlinear Amplifying Loop Mirror," IEEE Photon. Technol. Lett. 19, 146-148 (2007).
[CrossRef]

Ludwig, R.

K. Cvecek, K. Sponsel, R. Ludwig, C. Schubert, C. Stephan, G. Onishchukov, B. Schmauss, and G. Leuchs, "2R-Regeneration of an 80-Gb/s RZ-DQPSK Signal by a Nonlinear Amplifying Loop Mirror," IEEE Photon. Technol. Lett. 19, 146-148 (2007).
[CrossRef]

Millot, G.

Neogi, A.

Y. Takahashi, A. Neogi, and H. Kawaguchi, "Polarization dependent nonlinear gain in semiconductor optical amplifiers," J. Quantum Electron. 34, 1660-1672 (1998).
[CrossRef]

Onishchukov, G.

K. Cvecek, K. Sponsel, R. Ludwig, C. Schubert, C. Stephan, G. Onishchukov, B. Schmauss, and G. Leuchs, "2R-Regeneration of an 80-Gb/s RZ-DQPSK Signal by a Nonlinear Amplifying Loop Mirror," IEEE Photon. Technol. Lett. 19, 146-148 (2007).
[CrossRef]

Picozzi, A.

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.

Sauter, A.

Schmauss, B.

K. Cvecek, K. Sponsel, R. Ludwig, C. Schubert, C. Stephan, G. Onishchukov, B. Schmauss, and G. Leuchs, "2R-Regeneration of an 80-Gb/s RZ-DQPSK Signal by a Nonlinear Amplifying Loop Mirror," IEEE Photon. Technol. Lett. 19, 146-148 (2007).
[CrossRef]

Schubert, C.

K. Cvecek, K. Sponsel, R. Ludwig, C. Schubert, C. Stephan, G. Onishchukov, B. Schmauss, and G. Leuchs, "2R-Regeneration of an 80-Gb/s RZ-DQPSK Signal by a Nonlinear Amplifying Loop Mirror," IEEE Photon. Technol. Lett. 19, 146-148 (2007).
[CrossRef]

Skoda, P.

Sponsel, K.

K. Cvecek, K. Sponsel, R. Ludwig, C. Schubert, C. Stephan, G. Onishchukov, B. Schmauss, and G. Leuchs, "2R-Regeneration of an 80-Gb/s RZ-DQPSK Signal by a Nonlinear Amplifying Loop Mirror," IEEE Photon. Technol. Lett. 19, 146-148 (2007).
[CrossRef]

Stephan, C.

K. Cvecek, K. Sponsel, R. Ludwig, C. Schubert, C. Stephan, G. Onishchukov, B. Schmauss, and G. Leuchs, "2R-Regeneration of an 80-Gb/s RZ-DQPSK Signal by a Nonlinear Amplifying Loop Mirror," IEEE Photon. Technol. Lett. 19, 146-148 (2007).
[CrossRef]

Takahashi, Y.

Y. Takahashi, A. Neogi, and H. Kawaguchi, "Polarization dependent nonlinear gain in semiconductor optical amplifiers," J. Quantum Electron. 34, 1660-1672 (1998).
[CrossRef]

Trillo, S.

E. Ciaramella, F. Curti, and S. Trillo, "All-optical signal reshaping by means of four-wave mixing in optical fibers," IEEE Photon. Technol. Lett. 13, 142-144 (2001).
[CrossRef]

Wabnitz, S.

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, 88-94 (2005).
[CrossRef]

IEEE Photon. Technol. Lett.

K. Cvecek, K. Sponsel, R. Ludwig, C. Schubert, C. Stephan, G. Onishchukov, B. Schmauss, and G. Leuchs, "2R-Regeneration of an 80-Gb/s RZ-DQPSK Signal by a Nonlinear Amplifying Loop Mirror," IEEE Photon. Technol. Lett. 19, 146-148 (2007).
[CrossRef]

E. Ciaramella, F. Curti, and S. Trillo, "All-optical signal reshaping by means of four-wave mixing in optical fibers," IEEE Photon. Technol. Lett. 13, 142-144 (2001).
[CrossRef]

J. Opt. Soc. Am. B

J. Quantum Electron.

Y. Takahashi, A. Neogi, and H. Kawaguchi, "Polarization dependent nonlinear gain in semiconductor optical amplifiers," J. Quantum Electron. 34, 1660-1672 (1998).
[CrossRef]

Opt. Express

Opt. Lett.

PNAS

J. P. Gordon and H. Kogelnik, "PMD fundamentals: Polarization mode dispersion in optical fibers," PNAS 97, 4541-4550 (2000).
[CrossRef] [PubMed]

Other

S. Boscolo, S. K. Turitsyn, and K. J. Blow, "Nonlinear loop mirror-based all-optical signal processing in fiber-optic communications," Opt. Fiber Technol. Available online 17 March 2008.

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Figures (4)

Fig. 1.
Fig. 1.

Experimental set-up. HNLF : Highly Nonlinear Fiber, λ/4 : quaterwave-plate, Pol : Polarizer.

Fig. 2.
Fig. 2.

Simulation results: (a) Evolution of the energy ratio contained in the right circular polarization (solid line) and in the left (dashed line) circular polarization as a function of the pump/signal power for different initial signal polarizations. (b) Evolution of the signal polarization state on the Poincaré sphere for four different input signal polarization states. The counter-propagating pump wave is injected with a right circular polarization (S2=1).

Fig. 3.
Fig. 3.

(a). Experimental evolution of the energy ratio contained in the right (solid line) and in the left (dashed line) circular polarization as a function of the pump/signal power for four different initial signal polarization states. Output scrambled signal at P=1 W (b) and at P=45W (c).

Fig. 4.
Fig. 4.

Output pump (a1) and signal (a2) for P=1 W after scrambling of the input signal polarization. Output pump (a3) and signal (a4) for P=45 W after scrambling of the input signal polarization. (b1), (b2), (b3) and (b4) are numerical simulations corresponding Figs. (a1), (a2), (a3) and (a4), respectively.

Equations (4)

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u t + v g u z = i 2 3 v g γ [ ( u 2 + 2 v 2 ) u + ( 2 u ¯ 2 + 2 v ¯ 2 ) u + 2 u ¯ v ¯ * v ]
v t + v g v z = i 2 3 v g γ [ ( v 2 + 2 u 2 ) v + ( 2 u ¯ 2 + 2 v ¯ 2 ) v + 2 v ¯ u ¯ * u ]
u ¯ t v g u ¯ z = i 2 3 v g γ [ ( u ¯ 2 + 2 v ¯ 2 ) u ¯ + ( 2 u 2 + 2 v 2 ) u ¯ + 2 u v * v ¯ ]
v ¯ t v g v ¯ z = i 2 3 v g γ [ ( v ¯ 2 + 2 u ¯ 2 ) v ¯ + ( 2 u 2 + 2 v 2 ) v ¯ + 2 v u * u ¯ ]

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