Abstract

We experimentally observe polarization-locked vector solitons in a passively mode-locked fiber laser. The vector soliton pulse is composed of components along both principal polarization axes of the linearly birefringent laser cavity. For certain values of birefringence and pulse energy these components propagate with a constant relative optical phase of ±π/2, and hence the pulse has a fixed elliptical polarization state. The linear birefringence of the cavity is canceled by the nonlinear birefringence created by the unequal amplitudes of the two polarization components. This dynamic equalization of the phase velocities of the components results in the stable propagation of an elliptically polarized vector soliton pulse. Under different conditions we also observe the nonlinear instability of the fast principal axis as an intracavity pulse linearly polarized along the slow axis of the cavity. We present the experimental characterization of both the polarization-locked vector soliton and the fast axis instability and discuss the nonlinear mechanism creating both phenomena.

© 2000 Optical Society of America

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  6. C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, “Polarization dispersion and principal states in a 147-km undersea lightwave cable,” J. Lightwave Technol. 6, 1185–1190 (1988).
    [CrossRef]
  7. C. R. Menyuk, “Nonlinear pulse-propagation in birefringent optical fiber,” IEEE J. Quantum Electron. QE-23, 174–176 (1987).
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  8. C. R. Menyuk, “Stability of soliton in birefringent optical fibers. 1. Equal propagation amplitudes,” Opt. Lett. 12, 614–616 (1988).
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  12. S. G. Evangelides, Jr., L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10, 28–35 (1992).
    [CrossRef]
  13. M. V. Tratnik and J. E. Sipe, “Bound solitary waves in a birefringent optical fiber,” Phys. Rev. A 38, 2011–2017 (1988).
    [CrossRef] [PubMed]
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    [CrossRef]
  15. N. Akhmediev and J. M. Soto-Crespo, “Dynamics of solitonlike pulse propagation in birefringent optical fibers,” Phys. Rev. E 49, 5742–5754 (1994).
    [CrossRef]
  16. N. N. Akhmediev, A. V. Buryak, J. M. Soto-Crespo, and D. R. Andersen, “Phase-locked stationary soliton states in birefringent nonlinear optical fibers,” J. Opt. Soc. Am. B 12, 434–439 (1995).
    [CrossRef]
  17. J. M. Soto-Crespo, N. Akhmediev, and A. Ankiewicz, “Stationary solitonlike pulses in biefringent optical fiber,” Phys. Rev. E 51, 3547–3555 (1995).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  20. J. M. Soto-Crespo, N. N. Akhmediev, B. C. Collings, S. T. Cundiff, K. Bergman, and W. H. Knox, “Polarization-locked temporal vector solitons in a fiber laser: theory,” J. Opt. Soc. Am. B 17, 366–372 (2000).
    [CrossRef]
  21. B. C. Collings, K. Bergman, S. T. Cundiff, S. Tsuda, J. N. Kutz, M. Koch, and W. H. Knox, “Short cavity erbium/ytterbium fiber lasers mode-locked with a saturable Bragg reflector,” IEEE J. Sel. Top. Quantum Electron. 3, 1065–1075 (1997).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  24. Y. Barad and Y. Silberberg, “Polarization evolution and polarization instability of solitons in a birefringent optical fiber,” Phys. Rev. Lett. 78, 3290–3293 (1997).
    [CrossRef]
  25. S. V. Manakov, “On the theory of two-dimensional self-focusing of electromagnetic waves,” Sov. Phys. JETP 38, 248–253 (1974).
  26. J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, “Observation of Manakov spatial solitons in AlGaAs planar waveguides,” Phys. Rev. Lett. 76, 3699–3702 (1996).
    [CrossRef] [PubMed]
  27. L. F. Mollenauer, K. Smith, J. P. Gordon, and C. R. Menyuk, “Resistance of solitons to the effects of polarization dispersion in optical fibers,” Opt. Lett. 14, 1219–1221 (1989).
    [CrossRef] [PubMed]
  28. S. Tsuda, W. H. Knox, S. T. Cundiff, W. Y. Jan, and J. E. Cunningham, “Mode-locking ultrafast solid-state lasers with saturable Bragg reflectors,” IEEE J. Sel. Top. Quantum Electron. 2, 454–464 (1996).
    [CrossRef]
  29. J. N. Kutz, B. C. Collings, K. Bergman, S. Tsuda, S. Cundiff, W. H. Knox, P. Holmes, and M. I. Weinstein, “Mode-locking pulse dynamics in a fiber laser with a saturable Bragg reflector,” J. Opt. Soc. Am. B 14, 2681–2690 (1997).
    [CrossRef]
  30. N. N. Akhmediev, J. M. Soto-Crespo, S. T. Cundiff, B. C. Collings, and W. H. Knox, “Phase locking and periodic evolution of solitons in passively mode-locked fiber lasers with a semiconductor saturable absorber,” Opt. Lett. 23, 852–854 (1998).
    [CrossRef]
  31. S. M. J. Kelley, “Characteristic side-band instability of periodically amplified average soliton,” Electron. Lett. 28, 806–807 (1992).
    [CrossRef]
  32. J. P. Gordon, “Dispersive perturbation of solitons of the nonlinear Schrödinger-equation,” J. Opt. Soc. Am. B 9, 91–97 (1992).
    [CrossRef]
  33. H. C. Lefevre, “Single-mode fiber fractional wave devices and polarization controllers,” Electron. Lett. 16, 778–780 (1980).
    [CrossRef]
  34. S. T. Cundiff, B. C. Collings, and W. H. Knox, “Polarization locking in an isotropic, mode-locked soliton Er/Yb fiber laser,” Opt. Express 1, 12–20 (1997); http://epubs.osa.org/opticsexpress.
    [CrossRef] [PubMed]

2000 (1)

1999 (1)

S. T. Cundiff, B. C. Collings, N. N. Akhmediev, J. M. Soto-Crespo, K. Bergman, and W. H. Knox, “Observation of polarization-locked vector solitons in optical fiber,” Phys. Rev. Lett. 82, 3988–3991 (1999).
[CrossRef]

1998 (1)

1997 (5)

1996 (2)

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, “Observation of Manakov spatial solitons in AlGaAs planar waveguides,” Phys. Rev. Lett. 76, 3699–3702 (1996).
[CrossRef] [PubMed]

S. Tsuda, W. H. Knox, S. T. Cundiff, W. Y. Jan, and J. E. Cunningham, “Mode-locking ultrafast solid-state lasers with saturable Bragg reflectors,” IEEE J. Sel. Top. Quantum Electron. 2, 454–464 (1996).
[CrossRef]

1995 (2)

N. N. Akhmediev, A. V. Buryak, J. M. Soto-Crespo, and D. R. Andersen, “Phase-locked stationary soliton states in birefringent nonlinear optical fibers,” J. Opt. Soc. Am. B 12, 434–439 (1995).
[CrossRef]

J. M. Soto-Crespo, N. Akhmediev, and A. Ankiewicz, “Stationary solitonlike pulses in biefringent optical fiber,” Phys. Rev. E 51, 3547–3555 (1995).
[CrossRef]

1994 (2)

N. Akhmediev, A. Buryak, and J. M. Soto-Crespo, “Elliptically polarized solitons in birefringent optical fibers,” Opt. Commun. 112, 278–282 (1994).
[CrossRef]

N. Akhmediev and J. M. Soto-Crespo, “Dynamics of solitonlike pulse propagation in birefringent optical fibers,” Phys. Rev. E 49, 5742–5754 (1994).
[CrossRef]

1992 (3)

S. G. Evangelides, Jr., L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10, 28–35 (1992).
[CrossRef]

S. M. J. Kelley, “Characteristic side-band instability of periodically amplified average soliton,” Electron. Lett. 28, 806–807 (1992).
[CrossRef]

J. P. Gordon, “Dispersive perturbation of solitons of the nonlinear Schrödinger-equation,” J. Opt. Soc. Am. B 9, 91–97 (1992).
[CrossRef]

1989 (2)

1988 (5)

1987 (2)

C. R. Menyuk, “Nonlinear pulse-propagation in birefringent optical fiber,” IEEE J. Quantum Electron. QE-23, 174–176 (1987).
[CrossRef]

K. J. Blow, N. J. Doran, and D. Wood, “Polarization instabilities for solitons in birefringent fibers,” Opt. Lett. 12, 202–204 (1987).
[CrossRef] [PubMed]

1986 (1)

1981 (1)

I. P. Kaminow, “Polarization in optical fibers,” IEEE J. Quantum Electron. QE-17, 15–22 (1981).
[CrossRef]

1980 (2)

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

H. C. Lefevre, “Single-mode fiber fractional wave devices and polarization controllers,” Electron. Lett. 16, 778–780 (1980).
[CrossRef]

1974 (1)

S. V. Manakov, “On the theory of two-dimensional self-focusing of electromagnetic waves,” Sov. Phys. JETP 38, 248–253 (1974).

1973 (1)

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear pulses in dispersive dielectric fiber. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

Aitchison, J. S.

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, “Observation of Manakov spatial solitons in AlGaAs planar waveguides,” Phys. Rev. Lett. 76, 3699–3702 (1996).
[CrossRef] [PubMed]

Akhmediev, N.

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, “Observation of Manakov spatial solitons in AlGaAs planar waveguides,” Phys. Rev. Lett. 76, 3699–3702 (1996).
[CrossRef] [PubMed]

J. M. Soto-Crespo, N. Akhmediev, and A. Ankiewicz, “Stationary solitonlike pulses in biefringent optical fiber,” Phys. Rev. E 51, 3547–3555 (1995).
[CrossRef]

N. Akhmediev and J. M. Soto-Crespo, “Dynamics of solitonlike pulse propagation in birefringent optical fibers,” Phys. Rev. E 49, 5742–5754 (1994).
[CrossRef]

N. Akhmediev, A. Buryak, and J. M. Soto-Crespo, “Elliptically polarized solitons in birefringent optical fibers,” Opt. Commun. 112, 278–282 (1994).
[CrossRef]

Akhmediev, N. N.

Andersen, D. R.

Ankiewicz, A.

J. M. Soto-Crespo, N. Akhmediev, and A. Ankiewicz, “Stationary solitonlike pulses in biefringent optical fiber,” Phys. Rev. E 51, 3547–3555 (1995).
[CrossRef]

Atai, J.

Barad, Y.

Y. Barad and Y. Silberberg, “Polarization evolution and polarization instability of solitons in a birefringent optical fiber,” Phys. Rev. Lett. 78, 3290–3293 (1997).
[CrossRef]

Bergano, N. S.

S. G. Evangelides, Jr., L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10, 28–35 (1992).
[CrossRef]

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, “Polarization dispersion and principal states in a 147-km undersea lightwave cable,” J. Lightwave Technol. 6, 1185–1190 (1988).
[CrossRef]

Bergman, K.

J. M. Soto-Crespo, N. N. Akhmediev, B. C. Collings, S. T. Cundiff, K. Bergman, and W. H. Knox, “Polarization-locked temporal vector solitons in a fiber laser: theory,” J. Opt. Soc. Am. B 17, 366–372 (2000).
[CrossRef]

S. T. Cundiff, B. C. Collings, N. N. Akhmediev, J. M. Soto-Crespo, K. Bergman, and W. H. Knox, “Observation of polarization-locked vector solitons in optical fiber,” Phys. Rev. Lett. 82, 3988–3991 (1999).
[CrossRef]

B. C. Collings, K. Bergman, S. T. Cundiff, S. Tsuda, J. N. Kutz, M. Koch, and W. H. Knox, “Short cavity erbium/ytterbium fiber lasers mode-locked with a saturable Bragg reflector,” IEEE J. Sel. Top. Quantum Electron. 3, 1065–1075 (1997).
[CrossRef]

J. N. Kutz, B. C. Collings, K. Bergman, S. Tsuda, S. Cundiff, W. H. Knox, P. Holmes, and M. I. Weinstein, “Mode-locking pulse dynamics in a fiber laser with a saturable Bragg reflector,” J. Opt. Soc. Am. B 14, 2681–2690 (1997).
[CrossRef]

Blow, K. J.

Buryak, A.

N. Akhmediev, A. Buryak, and J. M. Soto-Crespo, “Elliptically polarized solitons in birefringent optical fibers,” Opt. Commun. 112, 278–282 (1994).
[CrossRef]

Buryak, A. V.

Chen, Y.

Christodoulides, D. N.

Collings, B. C.

Cundiff, S.

Cundiff, S. T.

J. M. Soto-Crespo, N. N. Akhmediev, B. C. Collings, S. T. Cundiff, K. Bergman, and W. H. Knox, “Polarization-locked temporal vector solitons in a fiber laser: theory,” J. Opt. Soc. Am. B 17, 366–372 (2000).
[CrossRef]

S. T. Cundiff, B. C. Collings, N. N. Akhmediev, J. M. Soto-Crespo, K. Bergman, and W. H. Knox, “Observation of polarization-locked vector solitons in optical fiber,” Phys. Rev. Lett. 82, 3988–3991 (1999).
[CrossRef]

N. N. Akhmediev, J. M. Soto-Crespo, S. T. Cundiff, B. C. Collings, and W. H. Knox, “Phase locking and periodic evolution of solitons in passively mode-locked fiber lasers with a semiconductor saturable absorber,” Opt. Lett. 23, 852–854 (1998).
[CrossRef]

S. T. Cundiff, B. C. Collings, and W. H. Knox, “Polarization locking in an isotropic, mode-locked soliton Er/Yb fiber laser,” Opt. Express 1, 12–20 (1997); http://epubs.osa.org/opticsexpress.
[CrossRef] [PubMed]

B. C. Collings, K. Bergman, S. T. Cundiff, S. Tsuda, J. N. Kutz, M. Koch, and W. H. Knox, “Short cavity erbium/ytterbium fiber lasers mode-locked with a saturable Bragg reflector,” IEEE J. Sel. Top. Quantum Electron. 3, 1065–1075 (1997).
[CrossRef]

S. Tsuda, W. H. Knox, S. T. Cundiff, W. Y. Jan, and J. E. Cunningham, “Mode-locking ultrafast solid-state lasers with saturable Bragg reflectors,” IEEE J. Sel. Top. Quantum Electron. 2, 454–464 (1996).
[CrossRef]

Cunningham, J. E.

S. Tsuda, W. H. Knox, S. T. Cundiff, W. Y. Jan, and J. E. Cunningham, “Mode-locking ultrafast solid-state lasers with saturable Bragg reflectors,” IEEE J. Sel. Top. Quantum Electron. 2, 454–464 (1996).
[CrossRef]

Doran, N. J.

Evangelides Jr., S. G.

S. G. Evangelides, Jr., L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10, 28–35 (1992).
[CrossRef]

Gordon, J. P.

Hasegawa, A.

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear pulses in dispersive dielectric fiber. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

Holmes, P.

Islam, M. N.

Jan, W. Y.

S. Tsuda, W. H. Knox, S. T. Cundiff, W. Y. Jan, and J. E. Cunningham, “Mode-locking ultrafast solid-state lasers with saturable Bragg reflectors,” IEEE J. Sel. Top. Quantum Electron. 2, 454–464 (1996).
[CrossRef]

Joseph, R. I.

Kaminow, I. P.

I. P. Kaminow, “Polarization in optical fibers,” IEEE J. Quantum Electron. QE-17, 15–22 (1981).
[CrossRef]

Kang, J. U.

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, “Observation of Manakov spatial solitons in AlGaAs planar waveguides,” Phys. Rev. Lett. 76, 3699–3702 (1996).
[CrossRef] [PubMed]

Kelley, S. M. J.

S. M. J. Kelley, “Characteristic side-band instability of periodically amplified average soliton,” Electron. Lett. 28, 806–807 (1992).
[CrossRef]

Knox, W. H.

J. M. Soto-Crespo, N. N. Akhmediev, B. C. Collings, S. T. Cundiff, K. Bergman, and W. H. Knox, “Polarization-locked temporal vector solitons in a fiber laser: theory,” J. Opt. Soc. Am. B 17, 366–372 (2000).
[CrossRef]

S. T. Cundiff, B. C. Collings, N. N. Akhmediev, J. M. Soto-Crespo, K. Bergman, and W. H. Knox, “Observation of polarization-locked vector solitons in optical fiber,” Phys. Rev. Lett. 82, 3988–3991 (1999).
[CrossRef]

N. N. Akhmediev, J. M. Soto-Crespo, S. T. Cundiff, B. C. Collings, and W. H. Knox, “Phase locking and periodic evolution of solitons in passively mode-locked fiber lasers with a semiconductor saturable absorber,” Opt. Lett. 23, 852–854 (1998).
[CrossRef]

S. T. Cundiff, B. C. Collings, and W. H. Knox, “Polarization locking in an isotropic, mode-locked soliton Er/Yb fiber laser,” Opt. Express 1, 12–20 (1997); http://epubs.osa.org/opticsexpress.
[CrossRef] [PubMed]

B. C. Collings, K. Bergman, S. T. Cundiff, S. Tsuda, J. N. Kutz, M. Koch, and W. H. Knox, “Short cavity erbium/ytterbium fiber lasers mode-locked with a saturable Bragg reflector,” IEEE J. Sel. Top. Quantum Electron. 3, 1065–1075 (1997).
[CrossRef]

J. N. Kutz, B. C. Collings, K. Bergman, S. Tsuda, S. Cundiff, W. H. Knox, P. Holmes, and M. I. Weinstein, “Mode-locking pulse dynamics in a fiber laser with a saturable Bragg reflector,” J. Opt. Soc. Am. B 14, 2681–2690 (1997).
[CrossRef]

S. Tsuda, W. H. Knox, S. T. Cundiff, W. Y. Jan, and J. E. Cunningham, “Mode-locking ultrafast solid-state lasers with saturable Bragg reflectors,” IEEE J. Sel. Top. Quantum Electron. 2, 454–464 (1996).
[CrossRef]

Koch, M.

B. C. Collings, K. Bergman, S. T. Cundiff, S. Tsuda, J. N. Kutz, M. Koch, and W. H. Knox, “Short cavity erbium/ytterbium fiber lasers mode-locked with a saturable Bragg reflector,” IEEE J. Sel. Top. Quantum Electron. 3, 1065–1075 (1997).
[CrossRef]

Kutz, J. N.

B. C. Collings, K. Bergman, S. T. Cundiff, S. Tsuda, J. N. Kutz, M. Koch, and W. H. Knox, “Short cavity erbium/ytterbium fiber lasers mode-locked with a saturable Bragg reflector,” IEEE J. Sel. Top. Quantum Electron. 3, 1065–1075 (1997).
[CrossRef]

J. N. Kutz, B. C. Collings, K. Bergman, S. Tsuda, S. Cundiff, W. H. Knox, P. Holmes, and M. I. Weinstein, “Mode-locking pulse dynamics in a fiber laser with a saturable Bragg reflector,” J. Opt. Soc. Am. B 14, 2681–2690 (1997).
[CrossRef]

Lefevre, H. C.

H. C. Lefevre, “Single-mode fiber fractional wave devices and polarization controllers,” Electron. Lett. 16, 778–780 (1980).
[CrossRef]

Manakov, S. V.

S. V. Manakov, “On the theory of two-dimensional self-focusing of electromagnetic waves,” Sov. Phys. JETP 38, 248–253 (1974).

Menyuk, C. R.

Mollenauer, L. F.

S. G. Evangelides, Jr., L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10, 28–35 (1992).
[CrossRef]

L. F. Mollenauer, K. Smith, J. P. Gordon, and C. R. Menyuk, “Resistance of solitons to the effects of polarization dispersion in optical fibers,” Opt. Lett. 14, 1219–1221 (1989).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

Poole, C. D.

M. N. Islam, C. D. Poole, and J. P. Gordon, “Soliton trapping in birefringent optical fibers,” Opt. Lett. 14, 1011–1013 (1989).
[CrossRef] [PubMed]

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, “Polarization dispersion and principal states in a 147-km undersea lightwave cable,” J. Lightwave Technol. 6, 1185–1190 (1988).
[CrossRef]

Schulte, H. J.

C. D. Poole, N. S. Bergano, R. E. Wagner, and H. J. Schulte, “Polarization dispersion and principal states in a 147-km undersea lightwave cable,” J. Lightwave Technol. 6, 1185–1190 (1988).
[CrossRef]

Silberberg, Y.

Y. Barad and Y. Silberberg, “Polarization evolution and polarization instability of solitons in a birefringent optical fiber,” Phys. Rev. Lett. 78, 3290–3293 (1997).
[CrossRef]

Sipe, J. E.

M. V. Tratnik and J. E. Sipe, “Bound solitary waves in a birefringent optical fiber,” Phys. Rev. A 38, 2011–2017 (1988).
[CrossRef] [PubMed]

Smith, K.

Soto-Crespo, J. M.

J. M. Soto-Crespo, N. N. Akhmediev, B. C. Collings, S. T. Cundiff, K. Bergman, and W. H. Knox, “Polarization-locked temporal vector solitons in a fiber laser: theory,” J. Opt. Soc. Am. B 17, 366–372 (2000).
[CrossRef]

S. T. Cundiff, B. C. Collings, N. N. Akhmediev, J. M. Soto-Crespo, K. Bergman, and W. H. Knox, “Observation of polarization-locked vector solitons in optical fiber,” Phys. Rev. Lett. 82, 3988–3991 (1999).
[CrossRef]

N. N. Akhmediev, J. M. Soto-Crespo, S. T. Cundiff, B. C. Collings, and W. H. Knox, “Phase locking and periodic evolution of solitons in passively mode-locked fiber lasers with a semiconductor saturable absorber,” Opt. Lett. 23, 852–854 (1998).
[CrossRef]

N. N. Akhmediev, A. V. Buryak, J. M. Soto-Crespo, and D. R. Andersen, “Phase-locked stationary soliton states in birefringent nonlinear optical fibers,” J. Opt. Soc. Am. B 12, 434–439 (1995).
[CrossRef]

J. M. Soto-Crespo, N. Akhmediev, and A. Ankiewicz, “Stationary solitonlike pulses in biefringent optical fiber,” Phys. Rev. E 51, 3547–3555 (1995).
[CrossRef]

N. Akhmediev and J. M. Soto-Crespo, “Dynamics of solitonlike pulse propagation in birefringent optical fibers,” Phys. Rev. E 49, 5742–5754 (1994).
[CrossRef]

N. Akhmediev, A. Buryak, and J. M. Soto-Crespo, “Elliptically polarized solitons in birefringent optical fibers,” Opt. Commun. 112, 278–282 (1994).
[CrossRef]

Stegeman, G. I.

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, “Observation of Manakov spatial solitons in AlGaAs planar waveguides,” Phys. Rev. Lett. 76, 3699–3702 (1996).
[CrossRef] [PubMed]

Stolen, R. H.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picosecond narrowing and solitons in optical fibers,” Phys. Rev. Lett. 45, 1095–1098 (1980).
[CrossRef]

Tappert, F.

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear pulses in dispersive dielectric fiber. I. Anomalous dispersion,” Appl. Phys. Lett. 23, 142–144 (1973).
[CrossRef]

Tratnik, M. V.

M. V. Tratnik and J. E. Sipe, “Bound solitary waves in a birefringent optical fiber,” Phys. Rev. A 38, 2011–2017 (1988).
[CrossRef] [PubMed]

Tsuda, S.

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[CrossRef]

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Figures (11)

Fig. 1
Fig. 1

Schematic of the fiber laser cavity and output diagnostics. FPC, fiber polarization controller; PSA, polarization-state analyzer; WDM, wavelength division multiplexer; RFSA, radio-frequency spectrum analyzer; OC, output coupler.

Fig. 2
Fig. 2

Polarization-independent optical spectrum of the PLVS (curve) and sech2(ν) function fit (circles) versus frequency, ν, plotted on both log (a) and linear (b) scales.

Fig. 3
Fig. 3

(a) Schematic of polarization-independent output pulse train of frequency 1/τc. b) Schematic of the polarization states of the pulses of (a). (c) Schematic of the pulse train of (a) when passed through a linear polarizer aligned along a 45-deg angle or parallel with the polarization state of the leftmost pulse. The period of the intensity modulation of the pulse train is 9τc or 1/Δ. (d) Schematic of the frequency spectrum of (c) consisting of a component at the repetition frequency of the pulse train (1/τc) with sidebands of separation Δ.

Fig. 4
Fig. 4

Plot of PEF versus θ1 and θ2 for (a) high and (b) low pulse energies. The color gradient represents the PEF magnitude (normalized by 1/2τc) with black and white indicating regions of locked linearly and elliptically polarized output, respectively.

Fig. 5
Fig. 5

(a) Intensity difference between the components for both handednesses (normalized by the total intensity) and (b) relative optical phases versus total round-trip cavity retardance, β.

Fig. 6
Fig. 6

Maximum round-trip birefringence, β, where a PLVS is observed versus pulse energy. The solid curve is proportional to the square of the pulse energy.

Fig. 7
Fig. 7

Measured optical spectral widths of component along the fast axis (circle) and slow axis (square) versus total cavity retardance.

Fig. 8
Fig. 8

PEF versus θ1 (circles, θ1 increasing; triangles, θ1 decreasing; θ2 held constant) illustrating hysteresis at the boundary of the PLVS locking region. Elliptical polarization locking (PLVS) is represented as PEF0 as the data sets are vertically offset in the PLVS region for clarity.

Fig. 9
Fig. 9

Schematic of the amplitudes of the two components (dashed and solid curves) and relative phase between components illustrating the interplay and the oscillation between amplitude and relative phase perturbations as a function of propagation distance.

Fig. 10
Fig. 10

(a) Measured azimuthal angle of the slow axis (curve) and the linearly polarized locked output (circles). (b) Measured birefringence, β, versus θ2 (θ1 held constant).

Fig. 11
Fig. 11

Plot of the linearly polarized locking region versus intracavity pulse energy and round-trip birefringence, β.

Equations (13)

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i uz+iδ ut+γu+122ut2
+(|u|2+A|v|2)u+Bv2u*=0,
i vz-iδ vt-γv+122vt2
+(|v|2+A|u|2)v+Bu2v*=0,
u(τ,z)=U0 sech(τ-δz)exp(iγz),v(τ,z)=0,
u(τ,z)=0,v(τ,z)=V0 sech(τ+δz)exp(iγz).
|V|2-|U|2=(γ/g),
z0=πτ022|β2|,
E1(z)=E0 exp(iγz),
E2(z)=E0 exp(-iγ z).
E(z)=cos θE1(z)+sin θE2(z).
I(z)=|E(z)|2=E02[(cos θ)2+(sin θ)2+2 cos θ sin θ cos(2γz)],
I(z)=E02[1+2 cos θ sin θ cos(2γz)].

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