Abstract

We characterize the performance of a nonlinear lossless polarizer, an all-optical fiber-based device that allows for the control of the state of polarization of an optical signal. The device relies on the lossless polarization attraction generated by the nonlinear interaction between the controlled signal and a controlling pump. Choosing a counter-propagating pump, we quantify its performance by introducing the degree of attraction (DOA), which highlights the trade-off between the average attraction of the signal polarization and the unavoidable degradation of its degree of polarization (DOP). We investigate, by numerical simulations, the dependence of the DOA on the injected power and on the fiber length, thus providing the design guidelines to reach the desired performance. We find that an effective attraction can occur even for strongly unbalanced signal and pump power levels, and that fibers longer than a few kilometers yield only a marginal improvement of the DOA.

© 2013 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  11. M. Barozzi and A. Vannucci, “All-optical noise cleaning based on co-propagating lossless polarization attraction,” in Proceedings of IEEE International Conference on Photonics (ICP 2013), doc. ID 1569795661 (2013), paper D3-AM1-C.2.
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  14. S. V. Sergeyev, “Activated polarization pulling and de-correlation of signal and pump states of polarization in a fiber Raman amplifier,” Opt. Express 19, 24268–24279 (2011).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  22. M. Barozzi and A. Vannucci, “Optimal pump wavelength placement in lossless polarization attraction,” in Proceedings of Fotonica 2013 (AEIT - Federazione Italiana di Elettrotecnica, Elettronica, Automazione, Informatica e Telecomunicazioni, 2013), paper P.12.
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  24. P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” IEEE J. Lightwave Technol. 14, 148–157 (1996).
  25. P. Serena, M. Bertolini, and A. Vannucci, “Optilux toolbox,” http://optilux.sourceforge.net/Documentation/optilux_doc.pdf .
  26. C. D. Poole and D. L. Favin, “Polarization-mode dispersion measurements based on transmission spectra through a polarizer,” IEEE J. Lightwave Technol. 12, 917–929 (1994).
    [CrossRef]

2013

2012

S. Sergeyev and S. Popov, “Two-section fiber optic Raman polarizer,” IEEE J. Quantum Electron. 48, 56–60 (2012).
[CrossRef]

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

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

2011

2010

2009

2008

2000

1996

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” IEEE J. Lightwave Technol. 14, 148–157 (1996).

1994

C. D. Poole and D. L. Favin, “Polarization-mode dispersion measurements based on transmission spectra through a polarizer,” IEEE J. Lightwave Technol. 12, 917–929 (1994).
[CrossRef]

Assémat, E.

Barozzi, M.

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

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

M. Barozzi and A. Vannucci, “A novel device to enhance the OSNR based on lossless polarization attraction,” in Proceedings of Fotonica 2013 (AEIT-Federazione Italiana di Elettrotecnica, Elettronica, Automazione, Informatica e Telecomunicazioni, 2013), paper C6.5.

M. Barozzi and A. Vannucci, “Optimal pump wavelength placement in lossless polarization attraction,” in Proceedings of Fotonica 2013 (AEIT - Federazione Italiana di Elettrotecnica, Elettronica, Automazione, Informatica e Telecomunicazioni, 2013), paper P.12.

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

M. Barozzi and A. Vannucci, “All-optical noise cleaning based on co-propagating lossless polarization attraction,” in Proceedings of IEEE International Conference on Photonics (ICP 2013), doc. ID 1569795661 (2013), paper D3-AM1-C.2.

Bennink, R. S.

Boyd, R. W.

Cirigliano, M.

Claveau, R.

Eyal, A.

Fatome, J.

Favin, D. L.

C. D. Poole and D. L. Favin, “Polarization-mode dispersion measurements based on transmission spectra through a polarizer,” IEEE J. Lightwave Technol. 12, 917–929 (1994).
[CrossRef]

Ferrario, M.

Ferreira, M. F. S.

Finot, C.

Fisher, R. A.

Friberg, A. T.

S. Sergeyev, S. Popov, and A. T. Friberg, “Virtually isotropic transmission media with fiber Raman amplifier,” IEEE J. Quantum Electron. 46, 1492–1497 (2010).
[CrossRef]

Heebner, J. E.

Huard, S.

S. Huard, Polarisation de la Lumière (Masson Ed., 1994).

Jauslin, H. R.

Kozlov, V. V.

Marazzi, L.

Martelli, P.

Martinelli, M.

Menyuk, C. R.

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” IEEE J. Lightwave Technol. 14, 148–157 (1996).

Millot, G.

Morin, P.

Muga, N. J.

Nuño, J.

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]

Picozzi, A.

Pinto, A. N.

Pitois, S.

Poole, C. D.

C. D. Poole and D. L. Favin, “Polarization-mode dispersion measurements based on transmission spectra through a polarizer,” IEEE J. Lightwave Technol. 12, 917–929 (1994).
[CrossRef]

Popov, S.

S. Sergeyev and S. Popov, “Two-section fiber optic Raman polarizer,” IEEE J. Quantum Electron. 48, 56–60 (2012).
[CrossRef]

S. Sergeyev, S. Popov, and A. T. Friberg, “Virtually isotropic transmission media with fiber Raman amplifier,” IEEE J. Quantum Electron. 46, 1492–1497 (2010).
[CrossRef]

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]

Sergeyev, S.

S. Sergeyev and S. Popov, “Two-section fiber optic Raman polarizer,” IEEE J. Quantum Electron. 48, 56–60 (2012).
[CrossRef]

S. Sergeyev, S. Popov, and A. T. Friberg, “Virtually isotropic transmission media with fiber Raman amplifier,” IEEE J. Quantum Electron. 46, 1492–1497 (2010).
[CrossRef]

Sergeyev, S. V.

Sperti, D.

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

Sungy, D.

Thévenaz, L.

Tur, M.

Turitsyn, K.

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]

Vannucci, A.

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

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

M. Barozzi and A. Vannucci, “A novel device to enhance the OSNR based on lossless polarization attraction,” in Proceedings of Fotonica 2013 (AEIT-Federazione Italiana di Elettrotecnica, Elettronica, Automazione, Informatica e Telecomunicazioni, 2013), paper C6.5.

M. Barozzi and A. Vannucci, “Optimal pump wavelength placement in lossless polarization attraction,” in Proceedings of Fotonica 2013 (AEIT - Federazione Italiana di Elettrotecnica, Elettronica, Automazione, Informatica e Telecomunicazioni, 2013), paper P.12.

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

M. Barozzi and A. Vannucci, “All-optical noise cleaning based on co-propagating lossless polarization attraction,” in Proceedings of IEEE International Conference on Photonics (ICP 2013), doc. ID 1569795661 (2013), paper D3-AM1-C.2.

Wabnitz, S.

Wai, P. K. A.

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” IEEE J. Lightwave Technol. 14, 148–157 (1996).

Zadok, A.

Zilka, E.

IEEE J. Lightwave Technol.

P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” IEEE J. Lightwave Technol. 14, 148–157 (1996).

C. D. Poole and D. L. Favin, “Polarization-mode dispersion measurements based on transmission spectra through a polarizer,” IEEE J. Lightwave Technol. 12, 917–929 (1994).
[CrossRef]

IEEE J. Quantum Electron.

S. Sergeyev and S. Popov, “Two-section fiber optic Raman polarizer,” IEEE J. Quantum Electron. 48, 56–60 (2012).
[CrossRef]

S. Sergeyev, S. Popov, and A. T. Friberg, “Virtually isotropic transmission media with fiber Raman amplifier,” IEEE J. Quantum Electron. 46, 1492–1497 (2010).
[CrossRef]

IEEE Photon. Technol. Lett.

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. Europ. Opt. Soc. Rap. Public.

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

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Other

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

M. Barozzi and A. Vannucci, “A novel device to enhance the OSNR based on lossless polarization attraction,” in Proceedings of Fotonica 2013 (AEIT-Federazione Italiana di Elettrotecnica, Elettronica, Automazione, Informatica e Telecomunicazioni, 2013), paper C6.5.

M. Barozzi and A. Vannucci, “All-optical noise cleaning based on co-propagating lossless polarization attraction,” in Proceedings of IEEE International Conference on Photonics (ICP 2013), doc. ID 1569795661 (2013), paper D3-AM1-C.2.

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

M. Barozzi and A. Vannucci, “Optimal pump wavelength placement in lossless polarization attraction,” in Proceedings of Fotonica 2013 (AEIT - Federazione Italiana di Elettrotecnica, Elettronica, Automazione, Informatica e Telecomunicazioni, 2013), paper P.12.

S. Huard, Polarisation de la Lumière (Masson Ed., 1994).

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Figures (8)

Fig. 1.
Fig. 1.

System setup of the NLP. The NLP is composed of the fiber along with the (fully polarized) pump laser, with power Pp, and the optical circulators.

Fig. 2.
Fig. 2.

LPA effectiveness as a function of equal pump and signal power (P) and of effective fiber length (Leff) for (a) DOA, (b) DOPs, and (c) MSA. The angular distance between the input signal and pump SOPs is χin=90° (on the Poincaré sphere).

Fig. 3.
Fig. 3.

LPA effectiveness as a function of the effective fiber length (Leff), with equal signal and pump power P=2W for (a) DOA, (b) DOPs, and (c) MSA. Lines refer to an angular distance between the input signal and pump SOPs that varies (top to bottom) from χin=0° to χin=180°, in 30° steps.

Fig. 4.
Fig. 4.

LPA effectiveness as a function of signal and pump power for (a) DOA, (b) DOPs, and (c) MSA. The angular distance between the input signal and pump SOPs is χin=90° (on the Poincaré sphere).

Fig. 5.
Fig. 5.

LPA effectiveness as a function of the geometric mean power P=(PsPp)1/2 for (a) DOA, (b) DOPs, and (c) MSA. Lines refer to an angular distance between the input signal and pump SOPs that varies (top to bottom) from χin=0° to χin=180°, in 30° steps.

Fig. 6.
Fig. 6.

SOP of the signal at the output of the NLP, for an equal signal and pump power of (a) 1 W, (b) 1.6 W, and (c) 2.2 W. The angular distance between the input signal and pump SOPs is χin=90°. The angle between the average output signal SOP (red) and input pump SOP s^1 (blue) is (a) χ¯=40°, (b) χ¯=8°, and (c) χ¯=4°, while the output signal DOPs is (a) 0.89, (b) 0.82, and (c) 0.89.

Fig. 7.
Fig. 7.

First- and second-order moments of the quantities used to characterize the performance of a NLP, as a function of (geometric) mean power for (a) and (d) DOA, (b) and (e) DOPs, and (c) and (f) MSA. In (a) and (d), thick dashed lines report the first- and second-order statistics evaluated by assuming that DOPs and MSA are uncorrelated random variables.

Fig. 8.
Fig. 8.

Graphical picture of LPA toward the input pump SOP s^1 (blue), for 100 random input signal SOPs. Average output signal SOPs (red) are plotted for increasing transmitted power for (a) 600 mW, (b) 1.6 W, and (c) 2.2 W.

Equations (7)

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DOAmaxτ{s⃗p(t+τ)·s⃗s(t)s0p(t+τ)s0s(t)},
DOA=s0p(t)s0s(t)s0p(t)s0s(t)s^p(t)·s^s(t)=w(t)cos(φ(t)),
DOA=s⃗s(t)s0s(t)·s^p=DOPs×MSA.
MSA=s⃗s(t)s⃗s(t)·s^p=m^s·s^p=cos(χ).
DOA¯=E[s⃗s(t)s0s(t)·s^p]=E[s⃗s(t)]s0s(t)·s^p,
DOA¯in=E[cos(χin)]=0πcos(χin)sin(χin)2dχin=0.
σDOAin2=E[cos2(χin)]=0πcos2(χin)sin(χin)2dχin=13,

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