Abstract

Vector soliton propagation in circularly birefringent fibers was studied by perturbation analysis and numerically. The results show that in presence of both Raman self-frequency shift and group velocity difference between circularly polarized components the Raman cross–polarization term causes an energy transfer from the slower to the faster circular component of vector solitons. This effect leads to polarization stabilization of circularly polarized vector solitons.

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  1. L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picoseconds pulse narrowing and solitons in optical fiber,” Phys. Rev. Lett.45(13), 1095–1098 (1980).
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  8. S. T. Cundiff, B. C. Collings, and W. H. Knox, “Polarization locking in an isotropic, modelocked soliton Er/Yb fiber laser,” Opt. Express1(1), 12–21 (1997).
    [CrossRef] [PubMed]
  9. 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(11), 852–854 (1998).
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    [CrossRef]
  11. 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 an optical fiber,” Phys. Rev. Lett.82(20), 3988–3991 (1999).
    [CrossRef]
  12. B. C. Collings, S. T. Cundiff, N. N. Akhmediev, J. M. Soto-Crespo, K. Bergman, and W. H. Knox, “Polarization-locked temporal vector solitons in a fiber laser: experiment,” J. Opt. Soc. Am. B17(3), 354–365 (2000).
    [CrossRef]
  13. D. Y. Tang, H. Zhang, L. M. Zhao, and X. Wu, “Observation of high-order polarization-locked vector solitons in a fiber laser,” Phys. Rev. Lett.101(15), 153904 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  17. J. H. Wong, K. Wu, H. H. Liu, Ch. Ouyang, H. Wang, S. Aditya, P. Shum, S. Fu, E. J. R. Kelleher, A. Chernov, and E. D. Obraztsova, “Vector solitons in a laser passively mode-locked by single-wall carbon nanotubes,” Opt. Commun.284(7), 2007–2011 (2011).
    [CrossRef]
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    [CrossRef] [PubMed]
  21. M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform (Society for Industrial and Applied Mathematics, 1981.
  22. I. Mandelbaum, M. Bolshtyansky, T. F. Heinz, and A. R. H. Walker, “Method for measuring the Raman gain tensor in optical fibers,” J. Opt. Soc. Am. B23(4), 621–627 (2006).
    [CrossRef]
  23. J. Yang, “Classification of the solitary waves in coupled nonlinear Schrodinger equations,” Physica D108(1-2), 92–112 (1997).
    [CrossRef]

2012 (1)

2011 (2)

C. Mou, S. Sergeyev, A. Rozhin, and S. Turistyn, “All-fiber polarization locked vector soliton laser using carbon nanotubes,” Opt. Lett.36(19), 3831–3833 (2011).
[CrossRef] [PubMed]

J. H. Wong, K. Wu, H. H. Liu, Ch. Ouyang, H. Wang, S. Aditya, P. Shum, S. Fu, E. J. R. Kelleher, A. Chernov, and E. D. Obraztsova, “Vector solitons in a laser passively mode-locked by single-wall carbon nanotubes,” Opt. Commun.284(7), 2007–2011 (2011).
[CrossRef]

2008 (2)

D. Y. Tang, H. Zhang, L. M. Zhao, and X. Wu, “Observation of high-order polarization-locked vector solitons in a fiber laser,” Phys. Rev. Lett.101(15), 153904 (2008).
[CrossRef] [PubMed]

H. Zhang, D. Y. Tang, L. M. Zhao, and H. Y. Tam, “Induced solitons formed by cross-polarization coupling in a birefringent cavity fiber laser,” Opt. Lett.33(20), 2317–2319 (2008).
[CrossRef] [PubMed]

2006 (2)

2000 (2)

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 an optical fiber,” Phys. Rev. Lett.82(20), 3988–3991 (1999).
[CrossRef]

1998 (1)

1997 (2)

S. T. Cundiff, B. C. Collings, and W. H. Knox, “Polarization locking in an isotropic, modelocked soliton Er/Yb fiber laser,” Opt. Express1(1), 12–21 (1997).
[CrossRef] [PubMed]

J. Yang, “Classification of the solitary waves in coupled nonlinear Schrodinger equations,” Physica D108(1-2), 92–112 (1997).
[CrossRef]

1996 (1)

M. Midrio, S. Wabnitz, and P. Franco, “Perturbation theory for coupled nonlinear Schrödinger equations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics54(5), 5743–5751 (1996).
[CrossRef] [PubMed]

1995 (1)

1989 (1)

1988 (2)

1987 (1)

1980 (1)

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picoseconds pulse narrowing and solitons in optical fiber,” Phys. Rev. Lett.45(13), 1095–1098 (1980).
[CrossRef]

Aditya, S.

J. H. Wong, K. Wu, H. H. Liu, Ch. Ouyang, H. Wang, S. Aditya, P. Shum, S. Fu, E. J. R. Kelleher, A. Chernov, and E. D. Obraztsova, “Vector solitons in a laser passively mode-locked by single-wall carbon nanotubes,” Opt. Commun.284(7), 2007–2011 (2011).
[CrossRef]

Akhmediev, N. N.

Andersen, D. R.

Bergman, K.

Bolshtyansky, M.

Buryak, A. V.

Chernov, A.

J. H. Wong, K. Wu, H. H. Liu, Ch. Ouyang, H. Wang, S. Aditya, P. Shum, S. Fu, E. J. R. Kelleher, A. Chernov, and E. D. Obraztsova, “Vector solitons in a laser passively mode-locked by single-wall carbon nanotubes,” Opt. Commun.284(7), 2007–2011 (2011).
[CrossRef]

Christodoulides, D. N.

Collings, B. C.

Cundiff, S. T.

Franco, P.

M. Midrio, S. Wabnitz, and P. Franco, “Perturbation theory for coupled nonlinear Schrödinger equations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics54(5), 5743–5751 (1996).
[CrossRef] [PubMed]

Fu, S.

J. H. Wong, K. Wu, H. H. Liu, Ch. Ouyang, H. Wang, S. Aditya, P. Shum, S. Fu, E. J. R. Kelleher, A. Chernov, and E. D. Obraztsova, “Vector solitons in a laser passively mode-locked by single-wall carbon nanotubes,” Opt. Commun.284(7), 2007–2011 (2011).
[CrossRef]

Gordon, J. P.

M. N. Islam, C. D. Poole, and J. P. Gordon, “Soliton trapping in birefringent optical fibers,” Opt. Lett.14(18), 1011–1013 (1989).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picoseconds pulse narrowing and solitons in optical fiber,” Phys. Rev. Lett.45(13), 1095–1098 (1980).
[CrossRef]

Gumenyuk, R.

Heinz, T. F.

Islam, M. N.

Joseph, R. I.

Kelleher, E. J. R.

J. H. Wong, K. Wu, H. H. Liu, Ch. Ouyang, H. Wang, S. Aditya, P. Shum, S. Fu, E. J. R. Kelleher, A. Chernov, and E. D. Obraztsova, “Vector solitons in a laser passively mode-locked by single-wall carbon nanotubes,” Opt. Commun.284(7), 2007–2011 (2011).
[CrossRef]

Kikuchi, K.

Knox, W. H.

Liu, H. H.

J. H. Wong, K. Wu, H. H. Liu, Ch. Ouyang, H. Wang, S. Aditya, P. Shum, S. Fu, E. J. R. Kelleher, A. Chernov, and E. D. Obraztsova, “Vector solitons in a laser passively mode-locked by single-wall carbon nanotubes,” Opt. Commun.284(7), 2007–2011 (2011).
[CrossRef]

Mandelbaum, I.

Menyuk, C. R.

Midrio, M.

M. Midrio, S. Wabnitz, and P. Franco, “Perturbation theory for coupled nonlinear Schrödinger equations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics54(5), 5743–5751 (1996).
[CrossRef] [PubMed]

Mollenauer, L. F.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picoseconds pulse narrowing and solitons in optical fiber,” Phys. Rev. Lett.45(13), 1095–1098 (1980).
[CrossRef]

Mou, C.

Obraztsova, E. D.

J. H. Wong, K. Wu, H. H. Liu, Ch. Ouyang, H. Wang, S. Aditya, P. Shum, S. Fu, E. J. R. Kelleher, A. Chernov, and E. D. Obraztsova, “Vector solitons in a laser passively mode-locked by single-wall carbon nanotubes,” Opt. Commun.284(7), 2007–2011 (2011).
[CrossRef]

Okhotnikov, O. G.

Ouyang, Ch.

J. H. Wong, K. Wu, H. H. Liu, Ch. Ouyang, H. Wang, S. Aditya, P. Shum, S. Fu, E. J. R. Kelleher, A. Chernov, and E. D. Obraztsova, “Vector solitons in a laser passively mode-locked by single-wall carbon nanotubes,” Opt. Commun.284(7), 2007–2011 (2011).
[CrossRef]

Poole, C. D.

Rozhin, A.

Sergeyev, S.

Shum, P.

J. H. Wong, K. Wu, H. H. Liu, Ch. Ouyang, H. Wang, S. Aditya, P. Shum, S. Fu, E. J. R. Kelleher, A. Chernov, and E. D. Obraztsova, “Vector solitons in a laser passively mode-locked by single-wall carbon nanotubes,” Opt. Commun.284(7), 2007–2011 (2011).
[CrossRef]

Soto-Crespo, J. M.

Stolen, R. H.

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picoseconds pulse narrowing and solitons in optical fiber,” Phys. Rev. Lett.45(13), 1095–1098 (1980).
[CrossRef]

Tam, H. Y.

Tanemura, T.

Tang, D. Y.

D. Y. Tang, H. Zhang, L. M. Zhao, and X. Wu, “Observation of high-order polarization-locked vector solitons in a fiber laser,” Phys. Rev. Lett.101(15), 153904 (2008).
[CrossRef] [PubMed]

H. Zhang, D. Y. Tang, L. M. Zhao, and H. Y. Tam, “Induced solitons formed by cross-polarization coupling in a birefringent cavity fiber laser,” Opt. Lett.33(20), 2317–2319 (2008).
[CrossRef] [PubMed]

Turistyn, S.

Wabnitz, S.

M. Midrio, S. Wabnitz, and P. Franco, “Perturbation theory for coupled nonlinear Schrödinger equations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics54(5), 5743–5751 (1996).
[CrossRef] [PubMed]

Walker, A. R. H.

Wang, H.

J. H. Wong, K. Wu, H. H. Liu, Ch. Ouyang, H. Wang, S. Aditya, P. Shum, S. Fu, E. J. R. Kelleher, A. Chernov, and E. D. Obraztsova, “Vector solitons in a laser passively mode-locked by single-wall carbon nanotubes,” Opt. Commun.284(7), 2007–2011 (2011).
[CrossRef]

Wong, J. H.

J. H. Wong, K. Wu, H. H. Liu, Ch. Ouyang, H. Wang, S. Aditya, P. Shum, S. Fu, E. J. R. Kelleher, A. Chernov, and E. D. Obraztsova, “Vector solitons in a laser passively mode-locked by single-wall carbon nanotubes,” Opt. Commun.284(7), 2007–2011 (2011).
[CrossRef]

Wu, K.

J. H. Wong, K. Wu, H. H. Liu, Ch. Ouyang, H. Wang, S. Aditya, P. Shum, S. Fu, E. J. R. Kelleher, A. Chernov, and E. D. Obraztsova, “Vector solitons in a laser passively mode-locked by single-wall carbon nanotubes,” Opt. Commun.284(7), 2007–2011 (2011).
[CrossRef]

Wu, X.

D. Y. Tang, H. Zhang, L. M. Zhao, and X. Wu, “Observation of high-order polarization-locked vector solitons in a fiber laser,” Phys. Rev. Lett.101(15), 153904 (2008).
[CrossRef] [PubMed]

Yang, J.

J. Yang, “Classification of the solitary waves in coupled nonlinear Schrodinger equations,” Physica D108(1-2), 92–112 (1997).
[CrossRef]

Zhang, H.

D. Y. Tang, H. Zhang, L. M. Zhao, and X. Wu, “Observation of high-order polarization-locked vector solitons in a fiber laser,” Phys. Rev. Lett.101(15), 153904 (2008).
[CrossRef] [PubMed]

H. Zhang, D. Y. Tang, L. M. Zhao, and H. Y. Tam, “Induced solitons formed by cross-polarization coupling in a birefringent cavity fiber laser,” Opt. Lett.33(20), 2317–2319 (2008).
[CrossRef] [PubMed]

Zhao, L. M.

H. Zhang, D. Y. Tang, L. M. Zhao, and H. Y. Tam, “Induced solitons formed by cross-polarization coupling in a birefringent cavity fiber laser,” Opt. Lett.33(20), 2317–2319 (2008).
[CrossRef] [PubMed]

D. Y. Tang, H. Zhang, L. M. Zhao, and X. Wu, “Observation of high-order polarization-locked vector solitons in a fiber laser,” Phys. Rev. Lett.101(15), 153904 (2008).
[CrossRef] [PubMed]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. B (6)

Opt. Commun. (1)

J. H. Wong, K. Wu, H. H. Liu, Ch. Ouyang, H. Wang, S. Aditya, P. Shum, S. Fu, E. J. R. Kelleher, A. Chernov, and E. D. Obraztsova, “Vector solitons in a laser passively mode-locked by single-wall carbon nanotubes,” Opt. Commun.284(7), 2007–2011 (2011).
[CrossRef]

Opt. Express (1)

Opt. Lett. (6)

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

M. Midrio, S. Wabnitz, and P. Franco, “Perturbation theory for coupled nonlinear Schrödinger equations,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics54(5), 5743–5751 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

D. Y. Tang, H. Zhang, L. M. Zhao, and X. Wu, “Observation of high-order polarization-locked vector solitons in a fiber laser,” Phys. Rev. Lett.101(15), 153904 (2008).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, and J. P. Gordon, “Experimental observation of picoseconds pulse narrowing and solitons in optical fiber,” Phys. Rev. Lett.45(13), 1095–1098 (1980).
[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 an optical fiber,” Phys. Rev. Lett.82(20), 3988–3991 (1999).
[CrossRef]

Physica D (1)

J. Yang, “Classification of the solitary waves in coupled nonlinear Schrodinger equations,” Physica D108(1-2), 92–112 (1997).
[CrossRef]

Other (3)

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2001).

M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform (Society for Industrial and Applied Mathematics, 1981.

Ch. Tsao, Optical fiber waveguide analysis (Oxford University Press, New York, 1999).

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Figures (3)

Fig. 1
Fig. 1

Ratio between powers of the left- and right-circularly polarized components. Red and blue lines correspond to the fast and slow left circularly polarized component; solid lines – numerical, dashed lines – calculated using Eq. (13).

Fig. 2
Fig. 2

An asymptotic approximation of the soliton polarization to the circular; the blue line - numerical, the red line - Eq. (13).

Fig. 3
Fig. 3

Ratio between numerical and theoretical slopes of the dependence θ(z).

Equations (13)

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i z C + +i β 1 t C + β 2 2 t 2 C + = 2 3 γ( | C + | 2 +μ | C | 2 ) C + +γ T R [ 1+α 2 t ( | C + | 2 + | C | 2 ) C + +(1α) t (Re( C + C * )) C ],
i z C i β 1 t C β 2 2 t 2 C = 2 3 γ( | C | 2 +μ | C + | 2 ) C +γ T R [ 1+α 2 t ( | C + | 2 + | C | 2 ) C +(1α) t (Re( C + C * )) C + ].
i Z U+ 1 2 T 2 U+( | U | 2 + | V | 2 )U=i R U ,
i Z V+ 1 2 T 2 V+( | U | 2 + | V | 2 )V=i R V .
R U = i[ 1 3 ( | U | 2 | V | 2 )U+ T R | β 2 | 1/2 ( 1 2 T ( | U | 2 + | V | 2 )U+ T (Re(UV*exp(2iβT)))Vexp(2iβT)) ],
R V = i[ 1 3 ( | V | 2 | U | 2 )V+ T R | β 2 | 1/2 ( 1 2 T ( | U | 2 + | V | 2 )V+ T (Re(UV*exp(2iβT)))Vexp(2iβT)) ].
U=2νcos( θ )sech[ 2v( Tξ ) ]exp[ i2k( Tξ )+i δ U ],
V=2νsin(θ)sech[ 2v( Tξ ) ]exp[ i2k( Tξ )+i δ V ].
dθ(Z) dZ = 1 4ν Re [cos(θ) R V exp(i2κ(Tξ)i δ V )sin(θ) R U exp(i2κ(Tξ)i δ U )] cosh 1 (x) dx
| C + |~Acos(θ)sech[A | β 2 | 1/2 (t t 0 )],
| C |~Asin(θ)sech[A | β 2 | 1/2 (t t 0 )],
dθ(z) dz = 2(1α) 3 γ A 2 T R β 1 | β 2 | sin(θ)cos(θ).
| C (z) | | C + (z) | =tan(θ(z))=tan(θ(0))exp( 2(1α) 3 γ A 2 T R β 1 | β 2 | z ).

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