Abstract

We report on a theoretical study of activated polarization pulling and de-correlation of signal and pump states of polarization based on an advanced vector model of a fiber Raman amplifier accounting for random birefringence and two-scale fiber spinning. As a result, we have found that it is possible to provide de-correlation and simultaneously suppress PDG and PMD to 1.2 dB and 0.035 ps/km1/2 respectively.

© 2011 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. C. D. Poole and R. E. Wagner, “Phenomenological approach to polarization dispersion in long single-mode fibers,” Electron. Lett. 22(19), 1029–1030 (1986).
    [CrossRef]
  2. 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(2), 148–157 (1996).
    [CrossRef]
  3. R. H. Stolen, “Polarization effects in fiber Raman and Brillouin lasers,” IEEE J. Quantum Electron. 15(10), 1157–1160 (1979).
    [CrossRef]
  4. Q. Lin and G. P. Agrawal, “Vector theory of stimulated Raman scattering and its application to fiber-based Raman amplifiers,” J. Opt. Soc. Am. B 20(8), 1616–1631 (2003).
    [CrossRef]
  5. S. Sergeyev, S. Popov, and A. T. Friberg, “Spun fiber Raman amplifiers with reduced polarization impairments,” Opt. Express 16(19), 14380–14389 (2008).
    [CrossRef] [PubMed]
  6. S. Sergeyev, S. Popov, and A. T. Friberg, “Virtually isotropic transmission media with fiber Raman amplifier,” IEEE J. Quantum Electron. 46(10), 1492–1497 (2010).
    [CrossRef]
  7. S. Sergeyev and S. Popov, “Two-section fiber optic Raman polarizer for high-speed transmission systems,” in the 13th International Conference on Transparent Optical Networks (June 26–30, 2011) Stockholm, Sweden, Th.A6.7.
  8. M. J. Li and D. A. Nolan, “Fiber spin-profile designs for producing fibers with low polarization mode dispersion,” Opt. Lett. 23(21), 1659–1661 (1998).
    [CrossRef] [PubMed]
  9. A. Galtarossa, L. Palmieri, A. Pizzinat, B. S. Marks, and C. R. Menyuk, “An analytical formula for the mean differential group delay of randomly-birefringent spun fibers,” J. Lightwave Technol. 21(7), 1635–1643 (2003).
    [CrossRef]
  10. M. Martinelli, M. Cirigliano, M. Ferrario, L. Marazzi, and P. Martelli, “Evidence of Raman-induced polarization pulling,” Opt. Express 17(2), 947–955 (2009).
    [CrossRef] [PubMed]
  11. V. V. Kozlov, J. Nuño, J. D. Ania-Castañón, and S. Wabnitz, “Theory of fiber optic Raman polarizers,” Opt. Lett. 35(23), 3970–3972 (2010).
    [CrossRef] [PubMed]
  12. 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(4), 254–256 (2011).
    [CrossRef]
  13. N. J. Muga, M. F. S. Ferreira, and A. N. Pinto, “Broadband polarization pulling using Raman amplification,” Opt. Express 19(19), 18707–18712 (2011).
    [CrossRef] [PubMed]
  14. J. 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(4), 257–259 (2000).
    [CrossRef] [PubMed]
  15. 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(15), 15311–15317 (2010).
    [CrossRef] [PubMed]
  16. 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(26), 21692–21707 (2008).
    [CrossRef] [PubMed]
  17. F. Marino, M. Giudici, S. Barland, and S. Balle, “Experimental evidence of stochastic resonance in an excitable optical system,” Phys. Rev. Lett. 88(4), 040601 (2002).
    [CrossRef]
  18. B. Lindner, J. García-Ojalvo, A. Neimand, and L. Schimansky-Geier, “Effects of noise in excitable systems,” Phys. Rep. 392(6), 321–424 (2004).
    [CrossRef]
  19. M. I. Dykman, B. Golding, L. I. McCann, V. N. Smelyanskiy, D. G. Luchinsky, R. Mannella, and P. V. E. McClintock, “Activated escape of periodically driven systems,” Chaos 11(3), 587–594 (2001).
    [CrossRef] [PubMed]
  20. J. D. Ania-Castañón, V. Karalekas, P. Harper, and S. K. Turitsyn, “Simultaneous spatial and spectral transparency in ultralong fiber lasers,” Phys. Rev. Lett. 101(12), 123903 (2008).
    [CrossRef] [PubMed]
  21. S. A. Babin, V. Karalekas, E. V. Podivilov, V. K. Mezentsev, P. Harper, J. D. Ania-Castanon, and S. K. Turitsyn, “Turbulent broadening of optical spectra in ultralong Raman fiber lasers,” Phys. Rev. A 77(3), 033803 (2008).
    [CrossRef]

2011 (2)

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(4), 254–256 (2011).
[CrossRef]

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

2010 (3)

2009 (1)

2008 (4)

J. D. Ania-Castañón, V. Karalekas, P. Harper, and S. K. Turitsyn, “Simultaneous spatial and spectral transparency in ultralong fiber lasers,” Phys. Rev. Lett. 101(12), 123903 (2008).
[CrossRef] [PubMed]

S. A. Babin, V. Karalekas, E. V. Podivilov, V. K. Mezentsev, P. Harper, J. D. Ania-Castanon, and S. K. Turitsyn, “Turbulent broadening of optical spectra in ultralong Raman fiber lasers,” Phys. Rev. A 77(3), 033803 (2008).
[CrossRef]

S. Sergeyev, S. Popov, and A. T. Friberg, “Spun fiber Raman amplifiers with reduced polarization impairments,” Opt. Express 16(19), 14380–14389 (2008).
[CrossRef] [PubMed]

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(26), 21692–21707 (2008).
[CrossRef] [PubMed]

2004 (1)

B. Lindner, J. García-Ojalvo, A. Neimand, and L. Schimansky-Geier, “Effects of noise in excitable systems,” Phys. Rep. 392(6), 321–424 (2004).
[CrossRef]

2003 (2)

2002 (1)

F. Marino, M. Giudici, S. Barland, and S. Balle, “Experimental evidence of stochastic resonance in an excitable optical system,” Phys. Rev. Lett. 88(4), 040601 (2002).
[CrossRef]

2001 (1)

M. I. Dykman, B. Golding, L. I. McCann, V. N. Smelyanskiy, D. G. Luchinsky, R. Mannella, and P. V. E. McClintock, “Activated escape of periodically driven systems,” Chaos 11(3), 587–594 (2001).
[CrossRef] [PubMed]

2000 (1)

1998 (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(2), 148–157 (1996).
[CrossRef]

1986 (1)

C. D. Poole and R. E. Wagner, “Phenomenological approach to polarization dispersion in long single-mode fibers,” Electron. Lett. 22(19), 1029–1030 (1986).
[CrossRef]

1979 (1)

R. H. Stolen, “Polarization effects in fiber Raman and Brillouin lasers,” IEEE J. Quantum Electron. 15(10), 1157–1160 (1979).
[CrossRef]

Agrawal, G. P.

Ania-Castanon, J. D.

S. A. Babin, V. Karalekas, E. V. Podivilov, V. K. Mezentsev, P. Harper, J. D. Ania-Castanon, and S. K. Turitsyn, “Turbulent broadening of optical spectra in ultralong Raman fiber lasers,” Phys. Rev. A 77(3), 033803 (2008).
[CrossRef]

Ania-Castañón, J. D.

V. V. Kozlov, J. Nuño, J. D. Ania-Castañón, and S. Wabnitz, “Theory of fiber optic Raman polarizers,” Opt. Lett. 35(23), 3970–3972 (2010).
[CrossRef] [PubMed]

J. D. Ania-Castañón, V. Karalekas, P. Harper, and S. K. Turitsyn, “Simultaneous spatial and spectral transparency in ultralong fiber lasers,” Phys. Rev. Lett. 101(12), 123903 (2008).
[CrossRef] [PubMed]

Babin, S. A.

S. A. Babin, V. Karalekas, E. V. Podivilov, V. K. Mezentsev, P. Harper, J. D. Ania-Castanon, and S. K. Turitsyn, “Turbulent broadening of optical spectra in ultralong Raman fiber lasers,” Phys. Rev. A 77(3), 033803 (2008).
[CrossRef]

Balle, S.

F. Marino, M. Giudici, S. Barland, and S. Balle, “Experimental evidence of stochastic resonance in an excitable optical system,” Phys. Rev. Lett. 88(4), 040601 (2002).
[CrossRef]

Barland, S.

F. Marino, M. Giudici, S. Barland, and S. Balle, “Experimental evidence of stochastic resonance in an excitable optical system,” Phys. Rev. Lett. 88(4), 040601 (2002).
[CrossRef]

Bennink, R. S.

Boyd, R. W.

Cirigliano, M.

Dykman, M. I.

M. I. Dykman, B. Golding, L. I. McCann, V. N. Smelyanskiy, D. G. Luchinsky, R. Mannella, and P. V. E. McClintock, “Activated escape of periodically driven systems,” Chaos 11(3), 587–594 (2001).
[CrossRef] [PubMed]

Eyal, A.

Fatome, J.

Ferrario, M.

Ferreira, M. F. S.

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(10), 1492–1497 (2010).
[CrossRef]

S. Sergeyev, S. Popov, and A. T. Friberg, “Spun fiber Raman amplifiers with reduced polarization impairments,” Opt. Express 16(19), 14380–14389 (2008).
[CrossRef] [PubMed]

Galtarossa, A.

García-Ojalvo, J.

B. Lindner, J. García-Ojalvo, A. Neimand, and L. Schimansky-Geier, “Effects of noise in excitable systems,” Phys. Rep. 392(6), 321–424 (2004).
[CrossRef]

Giudici, M.

F. Marino, M. Giudici, S. Barland, and S. Balle, “Experimental evidence of stochastic resonance in an excitable optical system,” Phys. Rev. Lett. 88(4), 040601 (2002).
[CrossRef]

Golding, B.

M. I. Dykman, B. Golding, L. I. McCann, V. N. Smelyanskiy, D. G. Luchinsky, R. Mannella, and P. V. E. McClintock, “Activated escape of periodically driven systems,” Chaos 11(3), 587–594 (2001).
[CrossRef] [PubMed]

Harper, P.

J. D. Ania-Castañón, V. Karalekas, P. Harper, and S. K. Turitsyn, “Simultaneous spatial and spectral transparency in ultralong fiber lasers,” Phys. Rev. Lett. 101(12), 123903 (2008).
[CrossRef] [PubMed]

S. A. Babin, V. Karalekas, E. V. Podivilov, V. K. Mezentsev, P. Harper, J. D. Ania-Castanon, and S. K. Turitsyn, “Turbulent broadening of optical spectra in ultralong Raman fiber lasers,” Phys. Rev. A 77(3), 033803 (2008).
[CrossRef]

Heebner, J. E.

Karalekas, V.

S. A. Babin, V. Karalekas, E. V. Podivilov, V. K. Mezentsev, P. Harper, J. D. Ania-Castanon, and S. K. Turitsyn, “Turbulent broadening of optical spectra in ultralong Raman fiber lasers,” Phys. Rev. A 77(3), 033803 (2008).
[CrossRef]

J. D. Ania-Castañón, V. Karalekas, P. Harper, and S. K. Turitsyn, “Simultaneous spatial and spectral transparency in ultralong fiber lasers,” Phys. Rev. Lett. 101(12), 123903 (2008).
[CrossRef] [PubMed]

Kozlov, V. V.

Li, M. J.

Lin, Q.

Lindner, B.

B. Lindner, J. García-Ojalvo, A. Neimand, and L. Schimansky-Geier, “Effects of noise in excitable systems,” Phys. Rep. 392(6), 321–424 (2004).
[CrossRef]

Luchinsky, D. G.

M. I. Dykman, B. Golding, L. I. McCann, V. N. Smelyanskiy, D. G. Luchinsky, R. Mannella, and P. V. E. McClintock, “Activated escape of periodically driven systems,” Chaos 11(3), 587–594 (2001).
[CrossRef] [PubMed]

Mannella, R.

M. I. Dykman, B. Golding, L. I. McCann, V. N. Smelyanskiy, D. G. Luchinsky, R. Mannella, and P. V. E. McClintock, “Activated escape of periodically driven systems,” Chaos 11(3), 587–594 (2001).
[CrossRef] [PubMed]

Marazzi, L.

Marino, F.

F. Marino, M. Giudici, S. Barland, and S. Balle, “Experimental evidence of stochastic resonance in an excitable optical system,” Phys. Rev. Lett. 88(4), 040601 (2002).
[CrossRef]

Marks, B. S.

Martelli, P.

Martinelli, M.

McCann, L. I.

M. I. Dykman, B. Golding, L. I. McCann, V. N. Smelyanskiy, D. G. Luchinsky, R. Mannella, and P. V. E. McClintock, “Activated escape of periodically driven systems,” Chaos 11(3), 587–594 (2001).
[CrossRef] [PubMed]

McClintock, P. V. E.

M. I. Dykman, B. Golding, L. I. McCann, V. N. Smelyanskiy, D. G. Luchinsky, R. Mannella, and P. V. E. McClintock, “Activated escape of periodically driven systems,” Chaos 11(3), 587–594 (2001).
[CrossRef] [PubMed]

Menyuk, C. R.

A. Galtarossa, L. Palmieri, A. Pizzinat, B. S. Marks, and C. R. Menyuk, “An analytical formula for the mean differential group delay of randomly-birefringent spun fibers,” J. Lightwave Technol. 21(7), 1635–1643 (2003).
[CrossRef]

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(2), 148–157 (1996).
[CrossRef]

Mezentsev, V. K.

S. A. Babin, V. Karalekas, E. V. Podivilov, V. K. Mezentsev, P. Harper, J. D. Ania-Castanon, and S. K. Turitsyn, “Turbulent broadening of optical spectra in ultralong Raman fiber lasers,” Phys. Rev. A 77(3), 033803 (2008).
[CrossRef]

Millot, G.

Morin, P.

Muga, N. J.

Neimand, A.

B. Lindner, J. García-Ojalvo, A. Neimand, and L. Schimansky-Geier, “Effects of noise in excitable systems,” Phys. Rep. 392(6), 321–424 (2004).
[CrossRef]

Nolan, D. A.

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(4), 254–256 (2011).
[CrossRef]

A. Galtarossa, L. Palmieri, A. Pizzinat, B. S. Marks, and C. R. Menyuk, “An analytical formula for the mean differential group delay of randomly-birefringent spun fibers,” J. Lightwave Technol. 21(7), 1635–1643 (2003).
[CrossRef]

Pinto, A. N.

Pitois, S.

Pizzinat, A.

Podivilov, E. V.

S. A. Babin, V. Karalekas, E. V. Podivilov, V. K. Mezentsev, P. Harper, J. D. Ania-Castanon, and S. K. Turitsyn, “Turbulent broadening of optical spectra in ultralong Raman fiber lasers,” Phys. Rev. A 77(3), 033803 (2008).
[CrossRef]

Poole, C. D.

C. D. Poole and R. E. Wagner, “Phenomenological approach to polarization dispersion in long single-mode fibers,” Electron. Lett. 22(19), 1029–1030 (1986).
[CrossRef]

Popov, S.

S. Sergeyev, S. Popov, and A. T. Friberg, “Virtually isotropic transmission media with fiber Raman amplifier,” IEEE J. Quantum Electron. 46(10), 1492–1497 (2010).
[CrossRef]

S. Sergeyev, S. Popov, and A. T. Friberg, “Spun fiber Raman amplifiers with reduced polarization impairments,” Opt. Express 16(19), 14380–14389 (2008).
[CrossRef] [PubMed]

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(4), 254–256 (2011).
[CrossRef]

Schimansky-Geier, L.

B. Lindner, J. García-Ojalvo, A. Neimand, and L. Schimansky-Geier, “Effects of noise in excitable systems,” Phys. Rep. 392(6), 321–424 (2004).
[CrossRef]

Sergeyev, S.

S. Sergeyev, S. Popov, and A. T. Friberg, “Virtually isotropic transmission media with fiber Raman amplifier,” IEEE J. Quantum Electron. 46(10), 1492–1497 (2010).
[CrossRef]

S. Sergeyev, S. Popov, and A. T. Friberg, “Spun fiber Raman amplifiers with reduced polarization impairments,” Opt. Express 16(19), 14380–14389 (2008).
[CrossRef] [PubMed]

Smelyanskiy, V. N.

M. I. Dykman, B. Golding, L. I. McCann, V. N. Smelyanskiy, D. G. Luchinsky, R. Mannella, and P. V. E. McClintock, “Activated escape of periodically driven systems,” Chaos 11(3), 587–594 (2001).
[CrossRef] [PubMed]

Stolen, R. H.

R. H. Stolen, “Polarization effects in fiber Raman and Brillouin lasers,” IEEE J. Quantum Electron. 15(10), 1157–1160 (1979).
[CrossRef]

Thévenaz, L.

Tur, M.

Turitsyn, S. K.

J. D. Ania-Castañón, V. Karalekas, P. Harper, and S. K. Turitsyn, “Simultaneous spatial and spectral transparency in ultralong fiber lasers,” Phys. Rev. Lett. 101(12), 123903 (2008).
[CrossRef] [PubMed]

S. A. Babin, V. Karalekas, E. V. Podivilov, V. K. Mezentsev, P. Harper, J. D. Ania-Castanon, and S. K. Turitsyn, “Turbulent broadening of optical spectra in ultralong Raman fiber lasers,” Phys. Rev. A 77(3), 033803 (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(4), 254–256 (2011).
[CrossRef]

Wabnitz, S.

Wagner, R. E.

C. D. Poole and R. E. Wagner, “Phenomenological approach to polarization dispersion in long single-mode fibers,” Electron. Lett. 22(19), 1029–1030 (1986).
[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(2), 148–157 (1996).
[CrossRef]

Zadok, A.

Zilka, E.

Chaos (1)

M. I. Dykman, B. Golding, L. I. McCann, V. N. Smelyanskiy, D. G. Luchinsky, R. Mannella, and P. V. E. McClintock, “Activated escape of periodically driven systems,” Chaos 11(3), 587–594 (2001).
[CrossRef] [PubMed]

Electron. Lett. (1)

C. D. Poole and R. E. Wagner, “Phenomenological approach to polarization dispersion in long single-mode fibers,” Electron. Lett. 22(19), 1029–1030 (1986).
[CrossRef]

IEEE J. Quantum Electron. (2)

R. H. Stolen, “Polarization effects in fiber Raman and Brillouin lasers,” IEEE J. Quantum Electron. 15(10), 1157–1160 (1979).
[CrossRef]

S. Sergeyev, S. Popov, and A. T. Friberg, “Virtually isotropic transmission media with fiber Raman amplifier,” IEEE J. Quantum Electron. 46(10), 1492–1497 (2010).
[CrossRef]

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(4), 254–256 (2011).
[CrossRef]

J. Lightwave Technol. (2)

A. Galtarossa, L. Palmieri, A. Pizzinat, B. S. Marks, and C. R. Menyuk, “An analytical formula for the mean differential group delay of randomly-birefringent spun fibers,” J. Lightwave Technol. 21(7), 1635–1643 (2003).
[CrossRef]

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(2), 148–157 (1996).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Express (5)

Opt. Lett. (3)

Phys. Rep. (1)

B. Lindner, J. García-Ojalvo, A. Neimand, and L. Schimansky-Geier, “Effects of noise in excitable systems,” Phys. Rep. 392(6), 321–424 (2004).
[CrossRef]

Phys. Rev. A (1)

S. A. Babin, V. Karalekas, E. V. Podivilov, V. K. Mezentsev, P. Harper, J. D. Ania-Castanon, and S. K. Turitsyn, “Turbulent broadening of optical spectra in ultralong Raman fiber lasers,” Phys. Rev. A 77(3), 033803 (2008).
[CrossRef]

Phys. Rev. Lett. (2)

J. D. Ania-Castañón, V. Karalekas, P. Harper, and S. K. Turitsyn, “Simultaneous spatial and spectral transparency in ultralong fiber lasers,” Phys. Rev. Lett. 101(12), 123903 (2008).
[CrossRef] [PubMed]

F. Marino, M. Giudici, S. Barland, and S. Balle, “Experimental evidence of stochastic resonance in an excitable optical system,” Phys. Rev. Lett. 88(4), 040601 (2002).
[CrossRef]

Other (1)

S. Sergeyev and S. Popov, “Two-section fiber optic Raman polarizer for high-speed transmission systems,” in the 13th International Conference on Transparent Optical Networks (June 26–30, 2011) Stockholm, Sweden, Th.A6.7.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Evolution of the pump p ^ and the signal s ^ states of polarization on the Poincaré sphere, as well as the fluctuations of the local birefringence vector Wi = (2bicosθ, 2bisinθ,0)T . Vectors s ^ and p ^ rotate around the local axis (W) at rates bp and bs, while vector (W) rotates randomly in the equatorial plane at the rate σ = Lc-1/2 (Lc is the correlation length), Φ is an angle between pump and signal SOPs.

Fig. 2
Fig. 2

a): x ^ 0 (solid line) and y ^ 0 (dotted line) and b): Im( Λ 1 ),Im( Λ 2 ), (dotted line), Re( Λ 1 ) (solid line) and Re( Λ 2 ) (dashed line) as a function of correlation length Lc. Parameters: L = 10 km, αs = 0.2 dB/km, λp = 1460 nm, λs = 1550 nm, g = 2.3 dBW−1km−1, Pin = 5 W, Lb = 8.3 m, A0 = 3 (in units of rad), khf = 6π/Lbp, klf = 0, Lc = [5m…205m].

Fig. 3
Fig. 3

Polarization dependent gain PDG (a, b), parameter R for the p ˜ ^ ( 0 )= s ˜ max ( 0 )=(1,0,0) (c, d) and PMD parameter Dp (e, f) as a function of fiber spinning frequency klf and correlation length Lc . Low-frequency amplitude (a, c, e) and phase modulated (b, d, f) fiber spinning. Parameters are the same as for Fig. 2. De-correlation of pump and signal SOPs (minimum in PDG with an arrow): Lc = 105 m and klf = 6 km−1 (Figs. 3 (a, c)), Lc = 110 m and klf = 3 km−1 (Figs. 3 (b, d)); polarization pulling (maximum in PDG with an arrow): Lc = 35 m and klf = 30 km−1 (Figs. 3 (a, c)), Lc = 110 m and klf = 22 km−1 (Figs. 3 (b, d)).

Fig. 4
Fig. 4

Polarization pulling metrics cosΦ as a function of distance along the fiber z for low-frequency amplitude (a) and phase modulated (b) fiber spinning. Dotted line: s ˜ max ( 0 )=(1,0,0) , solid line s ˜ min ( 0 )=(1,0,0) . Thick lines and thin lines correspond to the maximum and minimum in PDG shown by arrows.

Fig. 5
Fig. 5

PDG (a,b), parameter R (c, d) and PMD parameter Dp (e, f) as a function of modulation frequency kl,f (a, c) and correlation length Lc (b, d) for amplitude (thick lines) and phase modulated (thin lines) of fiber spinning. Parameters in Figs. 5 (a, c, d): Lc = 35 m (thick solid line), Lc = 105 m (thick dotted line), Lc = 55 m (thin solid line), Lc = 115 m (thin dotted line), Parameters in Figs. 5 (b, d, f): klf = 6 km−1 (thick solid line), klf = 30 km−1 (thick dotted line), klf = 3 km−1 (thin solid line), klf = 22 km−1 (thin dotted line).

Equations (19)

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

dθ dz =β(z), β(z) =0, β(z)β(z') = σ 2 δ(zz'),
R 3 ( γ )=[ cosγ sinγ 0 sinγ cosγ 0 0 0 1 ].
S= s 0 G ave s ^ ,P= P 0 ( z ) p ^ .
ΔG10log( S 0 ( L ) S 0 ( 0 ) / G ave )=10log( s 0 ( L ) s 0 ( 0 ) ),
PDG10log( s 0,max ( L ) / s 0,min ( L ) ),
R=5log( s 0,max(min) 2 ( L ) s 0,max(min) ( L ) 2 / s 0,max(min) ( L ) 2 ).
ds dz = g 2 P 0 ( z ) s 0 p ^ +( W s + W s (NL) )×s , d p ^ dz =( W p + W p (NL) )× p ^ .
d s 0 d z = ε 1 exp( ε 2 z ) x , d x d z = ε 1 exp( ε 2 z ) s 0 ε 3 y ( δ p δ s )exp( ε 2 z ) p ˜ ^ 3 ( p ˜ ^ 2 s ˜ 1 p ˜ ^ 1 s ˜ 2 ) , d y d z = ε 3 [ x p ˜ ^ 1 s ˜ 1 ]2α(z') u y L 2 L c + ε 4 p ˜ ^ 2 s ˜ 1 ε 5 p ˜ ^ 1 s ˜ 2 ( δ p δ s )exp( ε 2 z ) p ˜ ^ 3 p ˜ ^ 1 s ˜ 3 δ s exp( ε 2 z ) p ˜ ^ 2 ( p ˜ ^ 2 s ˜ 1 p ˜ ^ 1 s ˜ 2 ) , d u d z =2α(z') y u 2 +( δ p δ s )exp( ε 2 z ) p ˜ ^ 3 p ˜ ^ 2 s ˜ 3 δ s exp( ε 2 z ) p ˜ ^ 1 ( p ˜ ^ 2 s ˜ 1 p ˜ ^ 1 s ˜ 2 ) .
R i (z)=( 1 0 0 0 cos( 2 b i z ) sin( 2 b i z ) 0 sin( 2 b i z ) cos( 2 b i z ) ),( i=s,p ).
d h 1 f 1 dz' = ε 1 exp( ε 2 z ) s 0 f 1 2 L L c h 1 f 1 .
p ˜ ^ 1 s ˜ 1 = h 1 f 1 = p ˜ ^ 1 ( 0 ) s ˜ 1 ( 0 )exp( z'L/ L c ).
d s 0 2 d z =2 ε 1 exp( ε 2 z ) s 0 x , d s 0 x d z = ε 1 exp( ε 2 z )( s 0 2 + x 2 ) ε 3 y s 0 , d s 0 y d z = ε 1 exp( ε 2 z ) xy + ε 3 [ s 0 x y 2 s 0 p ˜ ^ 1 s ˜ 1 ]2α(z') s 0 u s 0 y L 2 L c , d x 2 d z =2 ε 1 exp( ε 2 z ) s 0 x 2 ε 3 xy , d xy d z = ε 1 exp( ε 2 z ) s 0 y + ε 3 [ x 2 x p ˜ ^ 1 s ˜ 1 ]2α(z') xu xy L 2 L c , d u s 0 d z = ε 1 exp( ε 2 z ) xu +2α(z') y s 0 u s 0 L 2 L c , d xu d z = ε 1 exp( ε 2 z ) s 0 u ε 3 yu +2α(z') xy xu L 2 L c , d yu d z = ε 3 ( xu u p ˜ ^ 1 s ˜ 1 )+2α(z')( y 2 u 2 )+ L yu 2 L c , d u 2 d z =2α(z') yu + L L c ( y 2 u 2 ), d y 2 d z =2 ε 3 [ yx y p ˜ ^ 1 s ˜ 1 ]2α(z') yu L L c ( y 2 u 2 ).
dΩ dz = W s ω + W s ×Ω,SIRF= | Ω( L ) | sp 2 / | Ω( L ) | un 2 ,
dSIR F 2 d z = Ω ^ 1 , d Ω ^ 1 d z = Ω ^ 1 L/ L c +2α(z) Ω ^ 2 +L/ L c , d Ω ^ 2 d z =2α(z) Ω ^ 1 Ω ^ 2 L/ L c ε 5 Ω ^ 3 , d Ω ^ 3 d z = ε 5 Ω ^ 2 .
D ps = λ s 2 L c L bs c SIRF.
α am (z')= A 0 k hf Lcos( k lf Lz')cos( k hf Lz'), α pm (z')= A 0 k hf Lcos( k hf ( Lz'+ a 0 cos( k lf Lz') ) ).
d x ^ d z = ε 1 exp( ε 2 z )( 1 x ^ 2 ) ε 3 y ^ , d y ^ d z =( J 0 ( 2 A 0 ) 2 ε 3 ε 1 exp( ε 2 z ) y ^ ) x ^ y ^ L 2 L c .
Δ x ^ 0 2 3 +Δ x ^ 0 2 +( Δ 1 2 Δ2 ) x ^ 0 Δ=0, y ^ 0 = J 0 ( 2 A 0 ) Δ 1 x ^ 0 Δ x ^ 0 +1 .
Λ 1,2 = 1 4 L c ( 3Δ< x ^ 0 >+1 )± 1 4 L c 1+ Δ 2 < x ^ 0 > 2 2Δ< x ^ 0 >4 Δ 1 2 +Δ Δ 1 y ^ 0 .

Metrics