Abstract

We study a nonlinear lossless polarizer (NLP), a fiber-based device able to control the polarization of an optical signal while preserving its energy. The NLP exploits the lossless polarization attraction (LPA) generated by the Kerr interactions between the signal and a fully polarized continuous wave (CW) pump. By employing a copropagating pump, we show that the effectiveness of LPA depends on the joint action of the Kerr nonlinearity and the mutual delay between signal and pump. We find the optimal pump wavelength placement and demonstrate that true LPA occurs only within a limited range of delay values. Thus, we explain why the copropagating NLP is more flexible and power efficient compared with the traditional counterpropagating NLP.

© 2015 Chinese Laser Press

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References

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  1. G. Millot and S. Wabnitz, “Nonlinear polarization effects in optical fibers: polarization attraction and modulation instability [Invited],” J. Opt. Soc. Am. B 31, 2754–2768 (2014).
    [Crossref]
  2. Y. Su, L. Mller, C. Xie, R. Ryf, X. Liu, X. Wei, and S. Cabot, “Ultra high-speed data signals with alternating and pairwise alternating optical phases,” J. Lightwave Technol. 23, 26–31 (2005).
    [Crossref]
  3. 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]
  4. M. Barozzi and A. Vannucci, “Lossless polarization attraction of telecom signals: application to all-optical OSNR enhancement,” J. Opt. Soc. Am. B 31, 2712–2720 (2014).
    [Crossref]
  5. V. C. Ribeiro, R. S. Luís, J. M. D. Mendinueta, B. J. Puttman, A. Shahpari, N. J. C. Muga, M. Lima, S. Shinada, N. Wada, and A. Teixeira, “All-optical packet alignment using polarization attraction effect,” IEEE Photon. Technol. Lett. 27, 541–544 (2015).
    [Crossref]
  6. M. Barozzi and A. Vannucci, “Optimal pump wavelength placement in lossless polarization attraction,” in Proceedings of Fotonica (AEIT, 2013).
  7. 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]
  8. M. Barozzi and A. Vannucci, “Performance characterization and guidelines for the design of a counter-propagating nonlinear lossless polarizer,” J. Opt. Soc. Am. B 30, 3102–3112 (2013).
    [Crossref]
  9. M. Barozzi, A. Vannucci, and D. Sperti, “Lossless polarization attraction simulation with a novel and simple counterpropagation algorithm for optical signals,” J. Eur. Opt. Soc. 7, 12042 (2012).
    [Crossref]
  10. 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]
  11. S. Pitois and M. Haelterman, “Optical fiber polarization funnel,” in Nonlinear Guided Waves and Their Applications, OSA Technical Digest Series (Optical Society of America, 2001), pp. 278–280.
  12. 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]
  13. P. K. A. Wai and C. R. Menyuk, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence,” J. Lightwave Technol. 14, 148–157 (1996).
    [Crossref]
  14. A. Bononi, A. Vannucci, A. Orlandini, E. Corbel, S. Lanne, and S. Bigo, “Degree of polarization degradation due to cross-polarization modulation and its impact on polarization-mode dispersion compensator,” J. Lightwave Technol. 21, 1903–1913 (2003).
    [Crossref]
  15. A. Vannucci, A. Bononi, A. Orlandini, E. Corbel, J. Thiéry, S. Lanne, and S. Bigo, “A simple formula for the degree of polarization degraded by XPM and its experimental validation,” in Proceedings of Optical Fiber Communication (OFC 2003) (IEEE, 2003), Vol. 2, pp. 498–499.

2015 (1)

V. C. Ribeiro, R. S. Luís, J. M. D. Mendinueta, B. J. Puttman, A. Shahpari, N. J. C. Muga, M. Lima, S. Shinada, N. Wada, and A. Teixeira, “All-optical packet alignment using polarization attraction effect,” IEEE Photon. Technol. Lett. 27, 541–544 (2015).
[Crossref]

2014 (2)

2013 (2)

2012 (1)

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

2011 (3)

2005 (1)

2003 (1)

1996 (1)

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

Barozzi, M.

Bigo, S.

A. Bononi, A. Vannucci, A. Orlandini, E. Corbel, S. Lanne, and S. Bigo, “Degree of polarization degradation due to cross-polarization modulation and its impact on polarization-mode dispersion compensator,” J. Lightwave Technol. 21, 1903–1913 (2003).
[Crossref]

A. Vannucci, A. Bononi, A. Orlandini, E. Corbel, J. Thiéry, S. Lanne, and S. Bigo, “A simple formula for the degree of polarization degraded by XPM and its experimental validation,” in Proceedings of Optical Fiber Communication (OFC 2003) (IEEE, 2003), Vol. 2, pp. 498–499.

Bononi, A.

A. Bononi, A. Vannucci, A. Orlandini, E. Corbel, S. Lanne, and S. Bigo, “Degree of polarization degradation due to cross-polarization modulation and its impact on polarization-mode dispersion compensator,” J. Lightwave Technol. 21, 1903–1913 (2003).
[Crossref]

A. Vannucci, A. Bononi, A. Orlandini, E. Corbel, J. Thiéry, S. Lanne, and S. Bigo, “A simple formula for the degree of polarization degraded by XPM and its experimental validation,” in Proceedings of Optical Fiber Communication (OFC 2003) (IEEE, 2003), Vol. 2, pp. 498–499.

Cabot, S.

Claveau, R.

Corbel, E.

A. Bononi, A. Vannucci, A. Orlandini, E. Corbel, S. Lanne, and S. Bigo, “Degree of polarization degradation due to cross-polarization modulation and its impact on polarization-mode dispersion compensator,” J. Lightwave Technol. 21, 1903–1913 (2003).
[Crossref]

A. Vannucci, A. Bononi, A. Orlandini, E. Corbel, J. Thiéry, S. Lanne, and S. Bigo, “A simple formula for the degree of polarization degraded by XPM and its experimental validation,” in Proceedings of Optical Fiber Communication (OFC 2003) (IEEE, 2003), Vol. 2, pp. 498–499.

Fatome, J.

Finot, C.

Haelterman, M.

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

Kozlov, V. V.

Lanne, S.

A. Bononi, A. Vannucci, A. Orlandini, E. Corbel, S. Lanne, and S. Bigo, “Degree of polarization degradation due to cross-polarization modulation and its impact on polarization-mode dispersion compensator,” J. Lightwave Technol. 21, 1903–1913 (2003).
[Crossref]

A. Vannucci, A. Bononi, A. Orlandini, E. Corbel, J. Thiéry, S. Lanne, and S. Bigo, “A simple formula for the degree of polarization degraded by XPM and its experimental validation,” in Proceedings of Optical Fiber Communication (OFC 2003) (IEEE, 2003), Vol. 2, pp. 498–499.

Lima, M.

V. C. Ribeiro, R. S. Luís, J. M. D. Mendinueta, B. J. Puttman, A. Shahpari, N. J. C. Muga, M. Lima, S. Shinada, N. Wada, and A. Teixeira, “All-optical packet alignment using polarization attraction effect,” IEEE Photon. Technol. Lett. 27, 541–544 (2015).
[Crossref]

Liu, X.

Luís, R. S.

V. C. Ribeiro, R. S. Luís, J. M. D. Mendinueta, B. J. Puttman, A. Shahpari, N. J. C. Muga, M. Lima, S. Shinada, N. Wada, and A. Teixeira, “All-optical packet alignment using polarization attraction effect,” IEEE Photon. Technol. Lett. 27, 541–544 (2015).
[Crossref]

Mendinueta, J. M. D.

V. C. Ribeiro, R. S. Luís, J. M. D. Mendinueta, B. J. Puttman, A. Shahpari, N. J. C. Muga, M. Lima, S. Shinada, N. Wada, and A. Teixeira, “All-optical packet alignment using polarization attraction effect,” IEEE Photon. Technol. Lett. 27, 541–544 (2015).
[Crossref]

Menyuk, C. R.

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

Millot, G.

Mller, L.

Morin, P.

Muga, N. J. C.

V. C. Ribeiro, R. S. Luís, J. M. D. Mendinueta, B. J. Puttman, A. Shahpari, N. J. C. Muga, M. Lima, S. Shinada, N. Wada, and A. Teixeira, “All-optical packet alignment using polarization attraction effect,” IEEE Photon. Technol. Lett. 27, 541–544 (2015).
[Crossref]

Orlandini, A.

A. Bononi, A. Vannucci, A. Orlandini, E. Corbel, S. Lanne, and S. Bigo, “Degree of polarization degradation due to cross-polarization modulation and its impact on polarization-mode dispersion compensator,” J. Lightwave Technol. 21, 1903–1913 (2003).
[Crossref]

A. Vannucci, A. Bononi, A. Orlandini, E. Corbel, J. Thiéry, S. Lanne, and S. Bigo, “A simple formula for the degree of polarization degraded by XPM and its experimental validation,” in Proceedings of Optical Fiber Communication (OFC 2003) (IEEE, 2003), Vol. 2, pp. 498–499.

Pitois, S.

Puttman, B. J.

V. C. Ribeiro, R. S. Luís, J. M. D. Mendinueta, B. J. Puttman, A. Shahpari, N. J. C. Muga, M. Lima, S. Shinada, N. Wada, and A. Teixeira, “All-optical packet alignment using polarization attraction effect,” IEEE Photon. Technol. Lett. 27, 541–544 (2015).
[Crossref]

Ribeiro, V. C.

V. C. Ribeiro, R. S. Luís, J. M. D. Mendinueta, B. J. Puttman, A. Shahpari, N. J. C. Muga, M. Lima, S. Shinada, N. Wada, and A. Teixeira, “All-optical packet alignment using polarization attraction effect,” IEEE Photon. Technol. Lett. 27, 541–544 (2015).
[Crossref]

Ryf, R.

Shahpari, A.

V. C. Ribeiro, R. S. Luís, J. M. D. Mendinueta, B. J. Puttman, A. Shahpari, N. J. C. Muga, M. Lima, S. Shinada, N. Wada, and A. Teixeira, “All-optical packet alignment using polarization attraction effect,” IEEE Photon. Technol. Lett. 27, 541–544 (2015).
[Crossref]

Shinada, S.

V. C. Ribeiro, R. S. Luís, J. M. D. Mendinueta, B. J. Puttman, A. Shahpari, N. J. C. Muga, M. Lima, S. Shinada, N. Wada, and A. Teixeira, “All-optical packet alignment using polarization attraction effect,” IEEE Photon. Technol. Lett. 27, 541–544 (2015).
[Crossref]

Sperti, D.

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

Su, Y.

Teixeira, A.

V. C. Ribeiro, R. S. Luís, J. M. D. Mendinueta, B. J. Puttman, A. Shahpari, N. J. C. Muga, M. Lima, S. Shinada, N. Wada, and A. Teixeira, “All-optical packet alignment using polarization attraction effect,” IEEE Photon. Technol. Lett. 27, 541–544 (2015).
[Crossref]

Thiéry, J.

A. Vannucci, A. Bononi, A. Orlandini, E. Corbel, J. Thiéry, S. Lanne, and S. Bigo, “A simple formula for the degree of polarization degraded by XPM and its experimental validation,” in Proceedings of Optical Fiber Communication (OFC 2003) (IEEE, 2003), Vol. 2, pp. 498–499.

Turitsyn, K.

Vannucci, A.

M. Barozzi and A. Vannucci, “Lossless polarization attraction of telecom signals: application to all-optical OSNR enhancement,” J. Opt. Soc. Am. B 31, 2712–2720 (2014).
[Crossref]

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 and A. Vannucci, “Performance characterization and guidelines for the design of a counter-propagating nonlinear lossless polarizer,” J. Opt. Soc. Am. B 30, 3102–3112 (2013).
[Crossref]

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

A. Bononi, A. Vannucci, A. Orlandini, E. Corbel, S. Lanne, and S. Bigo, “Degree of polarization degradation due to cross-polarization modulation and its impact on polarization-mode dispersion compensator,” J. Lightwave Technol. 21, 1903–1913 (2003).
[Crossref]

A. Vannucci, A. Bononi, A. Orlandini, E. Corbel, J. Thiéry, S. Lanne, and S. Bigo, “A simple formula for the degree of polarization degraded by XPM and its experimental validation,” in Proceedings of Optical Fiber Communication (OFC 2003) (IEEE, 2003), Vol. 2, pp. 498–499.

M. Barozzi and A. Vannucci, “Optimal pump wavelength placement in lossless polarization attraction,” in Proceedings of Fotonica (AEIT, 2013).

Wabnitz, S.

Wada, N.

V. C. Ribeiro, R. S. Luís, J. M. D. Mendinueta, B. J. Puttman, A. Shahpari, N. J. C. Muga, M. Lima, S. Shinada, N. Wada, and A. Teixeira, “All-optical packet alignment using polarization attraction effect,” IEEE Photon. Technol. Lett. 27, 541–544 (2015).
[Crossref]

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,” J. Lightwave Technol. 14, 148–157 (1996).
[Crossref]

Wei, X.

Xie, C.

IEEE Photon. Technol. Lett. (1)

V. C. Ribeiro, R. S. Luís, J. M. D. Mendinueta, B. J. Puttman, A. Shahpari, N. J. C. Muga, M. Lima, S. Shinada, N. Wada, and A. Teixeira, “All-optical packet alignment using polarization attraction effect,” IEEE Photon. Technol. Lett. 27, 541–544 (2015).
[Crossref]

J. Eur. Opt. Soc. (1)

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

J. Lightwave Technol. (3)

J. Opt. Soc. Am. B (5)

Opt. Express (1)

Opt. Lett. (1)

Other (3)

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

A. Vannucci, A. Bononi, A. Orlandini, E. Corbel, J. Thiéry, S. Lanne, and S. Bigo, “A simple formula for the degree of polarization degraded by XPM and its experimental validation,” in Proceedings of Optical Fiber Communication (OFC 2003) (IEEE, 2003), Vol. 2, pp. 498–499.

M. Barozzi and A. Vannucci, “Optimal pump wavelength placement in lossless polarization attraction,” in Proceedings of Fotonica (AEIT, 2013).

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Figures (4)

Fig. 1.
Fig. 1. System setup of a copropagating NLP.
Fig. 2.
Fig. 2. Evolution of the average signal SOP along the NLP. Here, the input signal and pump SOP are rightcircular (s^3) and linear-horizontal (s^1), respectively (marked by red and blue vectors, in figure). A (a) too small (τd=0) or (c) too large (τd=32) walk-off induces polarization rotation, while true polarization attraction only occurs for (b) intermediate values (τd=5). (See Section 4 for the definition of τd.)
Fig. 3.
Fig. 3. Performance of a copropagating NLP: output signal DOP versus the mutual signal–pump walk-off delay Td. (a) Results obtained for different pulse durations Ts obey a scaling law, so that (b) DOP only depends on the normalized delay τdTd/Ts.
Fig. 4.
Fig. 4. Performance of a copropagating NLP: DOP versus τd for different values of the signal power (Ps=Pp). The six tested values are 0.2, 0.4, 0.8, 1.6, 1.8, and 2 W.

Equations (2)

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{Ssz+1vsSstjβ2s22Sst2=j89γeαz[|Ss|2+|Sp|2+SpSp]SsSpz+1vpSptjβ2p22Spt2=j89γeαz[|Sp|2+|Ss|2+SsSs]Sp.
{ssz+12vwossτ=89γeαz[sp×ss]spz12vwospτ=89γeαz[ss×sp],

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