Abstract

We present experimental and numerical results demonstrating the existence of polarization instability of femtosecond solitons in small core photonic crystal fibers. The frequency of the solitons in our setup shifts rapidly with propagation along the dispersion curve due to the Raman effect. This process can cause initially stable solitons to become unstable, or vice versa depending on the parameters.

© 2006 Optical Society of America

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  1. J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J.C. Knight, W.J. Wadsworth, P.St.J. Russell, and G. Korn, "Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers," Phys. Rev. Lett. 88, 173901 (2002).
    [CrossRef] [PubMed]
  2. J. Dudley, X. Gu, L. Xu, M. Kimmel, E. Zeek, P. O’Shea, R. Trebino, S. Coen, and R. Windeler, "Crosscorrelation frequency resolved optical gating analysis of broadband continuum generation in photonic crystal fiber: simulations and experiments," Opt. Express 10, 1215-1221 (2002).
    [PubMed]
  3. L.F. Mollenauer, "Nonlinear optics in fibers," Science 302, 996-997 (2003).
    [CrossRef] [PubMed]
  4. D.V. Skryabin, F. Luan, J.C. Knight, and P.St.J. Russell, "Soliton self-frequency shift cancellation in photonic crystal fibers," Science 301, 1705-1708 (2003).
    [CrossRef] [PubMed]
  5. A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. Russell, "Interaction of an optical soliton with a dispersive wave," Phys. Rev. Lett. 95, 213902 (2005).
    [CrossRef] [PubMed]
  6. J.R. Salgueiro, Y.S. Kivshar, D.E. Pelinovsky, V. Simon, and H. Michinel, "Spatial vector solitons in nonlinear photonic crystal fibers," Studies in Appl. Math. 115, 157-171 (2005).
    [CrossRef]
  7. M. Hu, C. Wang, Y. Song, Y. Li, L. Chai, E. Serebryannikov, and A. Zheltikov, "Mode-selective mapping and control of vectorial nonlinear-optical processes in multimode photonic-crystal fibers," Opt. Express 14, 1189- 1198 (2006).
    [CrossRef] [PubMed]
  8. F. Biancalana and D.V. Skryabin, "Vector modulational instabilities in ultra-small core optical fibres," J. Opt. A 6, 301-306 (2004).
    [CrossRef]
  9. F. Lu, Q. Lin, W. H. Knox, and G. P. Agrawal, "Vector Soliton Fission," Phys. Rev. Lett. 93, 183901 (2004).
    [CrossRef] [PubMed]
  10. K. Blow, N. Doran, and D. Wood, "Polarization instabilities for solitons in birefringent fibers," Opt. Lett. 12, 202-204 (1987).
    [CrossRef] [PubMed]
  11. N. Akhmediev, A. Buryak, J. Soto-Crespo, and D. Andersen, "Phase-locked stationary soliton states in birefringent nonlinear optical fibers," J. Opt. Soc. Am. B 12, 434-439 (1995).
    [CrossRef]
  12. D. Hutchings and J. Arnold, "Polarization stability of solitons in birefringent optical fibers," J. Opt. Soc. Am. B 16, 513-518 (1999).
    [CrossRef]
  13. D. Mihalache, D. Mazilu, and L.-C. Crasovan, "Linear stability analysis of walking vector solitons," Phys. Rev. E 60, 007504 (1999).
    [CrossRef]
  14. Y. Barad and Y. Silberberg, "Polarization evolution and polarization instability of solitons in a birefringent optical fiber," Phys. Rev. Lett. 78, 003290 (1997).
    [CrossRef]
  15. R. Malendevich, L. Friedrich, G. Stegeman, J. Soto-Crespo, N. Akhmediev, and J. Aitchison, "Radiation-related polarization instability of Kerr spatial vector solitons," J. Opt. Soc. Am. B 19, 695-702 (2002).
    [CrossRef]
  16. J.C. Knight, J. Arriaga, T.A. Birks, A. Ortigosa-Blanch, W.J. Wadsworth, and P.S. Russell, "Anomalous dispersion in photonic crystal fiber," IEEE Photon. Technol. Lett. 12, 807-809 (2000).
    [CrossRef]
  17. X. Liu, C. Xu, W.H. Knox, J.K. Chandalia, B.J. Eggleton, S.G. Kosinski, and B.S. Windeler, "Soliton selffrequency shift in a short tapered air-silica microstructure fiber," Opt. Lett. 26, 358-360 (2001).
    [CrossRef]

2006 (1)

2005 (2)

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. Russell, "Interaction of an optical soliton with a dispersive wave," Phys. Rev. Lett. 95, 213902 (2005).
[CrossRef] [PubMed]

J.R. Salgueiro, Y.S. Kivshar, D.E. Pelinovsky, V. Simon, and H. Michinel, "Spatial vector solitons in nonlinear photonic crystal fibers," Studies in Appl. Math. 115, 157-171 (2005).
[CrossRef]

2004 (2)

F. Biancalana and D.V. Skryabin, "Vector modulational instabilities in ultra-small core optical fibres," J. Opt. A 6, 301-306 (2004).
[CrossRef]

F. Lu, Q. Lin, W. H. Knox, and G. P. Agrawal, "Vector Soliton Fission," Phys. Rev. Lett. 93, 183901 (2004).
[CrossRef] [PubMed]

2003 (2)

L.F. Mollenauer, "Nonlinear optics in fibers," Science 302, 996-997 (2003).
[CrossRef] [PubMed]

D.V. Skryabin, F. Luan, J.C. Knight, and P.St.J. Russell, "Soliton self-frequency shift cancellation in photonic crystal fibers," Science 301, 1705-1708 (2003).
[CrossRef] [PubMed]

2002 (3)

2001 (1)

2000 (1)

J.C. Knight, J. Arriaga, T.A. Birks, A. Ortigosa-Blanch, W.J. Wadsworth, and P.S. Russell, "Anomalous dispersion in photonic crystal fiber," IEEE Photon. Technol. Lett. 12, 807-809 (2000).
[CrossRef]

1999 (2)

D. Mihalache, D. Mazilu, and L.-C. Crasovan, "Linear stability analysis of walking vector solitons," Phys. Rev. E 60, 007504 (1999).
[CrossRef]

D. Hutchings and J. Arnold, "Polarization stability of solitons in birefringent optical fibers," J. Opt. Soc. Am. B 16, 513-518 (1999).
[CrossRef]

1997 (1)

Y. Barad and Y. Silberberg, "Polarization evolution and polarization instability of solitons in a birefringent optical fiber," Phys. Rev. Lett. 78, 003290 (1997).
[CrossRef]

1995 (1)

1987 (1)

Agrawal, G. P.

F. Lu, Q. Lin, W. H. Knox, and G. P. Agrawal, "Vector Soliton Fission," Phys. Rev. Lett. 93, 183901 (2004).
[CrossRef] [PubMed]

Aitchison, J.

Akhmediev, N.

Andersen, D.

Arnold, J.

Arriaga, J.

J.C. Knight, J. Arriaga, T.A. Birks, A. Ortigosa-Blanch, W.J. Wadsworth, and P.S. Russell, "Anomalous dispersion in photonic crystal fiber," IEEE Photon. Technol. Lett. 12, 807-809 (2000).
[CrossRef]

Barad, Y.

Y. Barad and Y. Silberberg, "Polarization evolution and polarization instability of solitons in a birefringent optical fiber," Phys. Rev. Lett. 78, 003290 (1997).
[CrossRef]

Biancalana, F.

F. Biancalana and D.V. Skryabin, "Vector modulational instabilities in ultra-small core optical fibres," J. Opt. A 6, 301-306 (2004).
[CrossRef]

Birks, T.A.

J.C. Knight, J. Arriaga, T.A. Birks, A. Ortigosa-Blanch, W.J. Wadsworth, and P.S. Russell, "Anomalous dispersion in photonic crystal fiber," IEEE Photon. Technol. Lett. 12, 807-809 (2000).
[CrossRef]

Blow, K.

Buryak, A.

Chai, L.

Chandalia, J.K.

Coen, S.

Crasovan, L.-C.

D. Mihalache, D. Mazilu, and L.-C. Crasovan, "Linear stability analysis of walking vector solitons," Phys. Rev. E 60, 007504 (1999).
[CrossRef]

Doran, N.

Dudley, J.

Efimov, A.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. Russell, "Interaction of an optical soliton with a dispersive wave," Phys. Rev. Lett. 95, 213902 (2005).
[CrossRef] [PubMed]

Eggleton, B.J.

Friedrich, L.

Griebner, U.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J.C. Knight, W.J. Wadsworth, P.St.J. Russell, and G. Korn, "Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers," Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

Gu, X.

Herrmann, J.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J.C. Knight, W.J. Wadsworth, P.St.J. Russell, and G. Korn, "Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers," Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

Hu, M.

Husakou, A.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J.C. Knight, W.J. Wadsworth, P.St.J. Russell, and G. Korn, "Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers," Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

Hutchings, D.

Joly, N.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. Russell, "Interaction of an optical soliton with a dispersive wave," Phys. Rev. Lett. 95, 213902 (2005).
[CrossRef] [PubMed]

Kimmel, M.

Kivshar, Y.S.

J.R. Salgueiro, Y.S. Kivshar, D.E. Pelinovsky, V. Simon, and H. Michinel, "Spatial vector solitons in nonlinear photonic crystal fibers," Studies in Appl. Math. 115, 157-171 (2005).
[CrossRef]

Knight, J. C.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. Russell, "Interaction of an optical soliton with a dispersive wave," Phys. Rev. Lett. 95, 213902 (2005).
[CrossRef] [PubMed]

Knight, J.C.

D.V. Skryabin, F. Luan, J.C. Knight, and P.St.J. Russell, "Soliton self-frequency shift cancellation in photonic crystal fibers," Science 301, 1705-1708 (2003).
[CrossRef] [PubMed]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J.C. Knight, W.J. Wadsworth, P.St.J. Russell, and G. Korn, "Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers," Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

J.C. Knight, J. Arriaga, T.A. Birks, A. Ortigosa-Blanch, W.J. Wadsworth, and P.S. Russell, "Anomalous dispersion in photonic crystal fiber," IEEE Photon. Technol. Lett. 12, 807-809 (2000).
[CrossRef]

Knox, W. H.

F. Lu, Q. Lin, W. H. Knox, and G. P. Agrawal, "Vector Soliton Fission," Phys. Rev. Lett. 93, 183901 (2004).
[CrossRef] [PubMed]

Knox, W.H.

Korn, G.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J.C. Knight, W.J. Wadsworth, P.St.J. Russell, and G. Korn, "Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers," Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

Kosinski, S.G.

Li, Y.

Lin, Q.

F. Lu, Q. Lin, W. H. Knox, and G. P. Agrawal, "Vector Soliton Fission," Phys. Rev. Lett. 93, 183901 (2004).
[CrossRef] [PubMed]

Liu, X.

Lu, F.

F. Lu, Q. Lin, W. H. Knox, and G. P. Agrawal, "Vector Soliton Fission," Phys. Rev. Lett. 93, 183901 (2004).
[CrossRef] [PubMed]

Luan, F.

D.V. Skryabin, F. Luan, J.C. Knight, and P.St.J. Russell, "Soliton self-frequency shift cancellation in photonic crystal fibers," Science 301, 1705-1708 (2003).
[CrossRef] [PubMed]

Malendevich, R.

Mazilu, D.

D. Mihalache, D. Mazilu, and L.-C. Crasovan, "Linear stability analysis of walking vector solitons," Phys. Rev. E 60, 007504 (1999).
[CrossRef]

Michinel, H.

J.R. Salgueiro, Y.S. Kivshar, D.E. Pelinovsky, V. Simon, and H. Michinel, "Spatial vector solitons in nonlinear photonic crystal fibers," Studies in Appl. Math. 115, 157-171 (2005).
[CrossRef]

Mihalache, D.

D. Mihalache, D. Mazilu, and L.-C. Crasovan, "Linear stability analysis of walking vector solitons," Phys. Rev. E 60, 007504 (1999).
[CrossRef]

Mollenauer, L.F.

L.F. Mollenauer, "Nonlinear optics in fibers," Science 302, 996-997 (2003).
[CrossRef] [PubMed]

Nickel, D.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J.C. Knight, W.J. Wadsworth, P.St.J. Russell, and G. Korn, "Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers," Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

O’Shea, P.

Omenetto, F. G.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. Russell, "Interaction of an optical soliton with a dispersive wave," Phys. Rev. Lett. 95, 213902 (2005).
[CrossRef] [PubMed]

Ortigosa-Blanch, A.

J.C. Knight, J. Arriaga, T.A. Birks, A. Ortigosa-Blanch, W.J. Wadsworth, and P.S. Russell, "Anomalous dispersion in photonic crystal fiber," IEEE Photon. Technol. Lett. 12, 807-809 (2000).
[CrossRef]

Pelinovsky, D.E.

J.R. Salgueiro, Y.S. Kivshar, D.E. Pelinovsky, V. Simon, and H. Michinel, "Spatial vector solitons in nonlinear photonic crystal fibers," Studies in Appl. Math. 115, 157-171 (2005).
[CrossRef]

Russell, P.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. Russell, "Interaction of an optical soliton with a dispersive wave," Phys. Rev. Lett. 95, 213902 (2005).
[CrossRef] [PubMed]

Russell, P.S.

J.C. Knight, J. Arriaga, T.A. Birks, A. Ortigosa-Blanch, W.J. Wadsworth, and P.S. Russell, "Anomalous dispersion in photonic crystal fiber," IEEE Photon. Technol. Lett. 12, 807-809 (2000).
[CrossRef]

Russell, P.St.J.

D.V. Skryabin, F. Luan, J.C. Knight, and P.St.J. Russell, "Soliton self-frequency shift cancellation in photonic crystal fibers," Science 301, 1705-1708 (2003).
[CrossRef] [PubMed]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J.C. Knight, W.J. Wadsworth, P.St.J. Russell, and G. Korn, "Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers," Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

Salgueiro, J.R.

J.R. Salgueiro, Y.S. Kivshar, D.E. Pelinovsky, V. Simon, and H. Michinel, "Spatial vector solitons in nonlinear photonic crystal fibers," Studies in Appl. Math. 115, 157-171 (2005).
[CrossRef]

Serebryannikov, E.

Silberberg, Y.

Y. Barad and Y. Silberberg, "Polarization evolution and polarization instability of solitons in a birefringent optical fiber," Phys. Rev. Lett. 78, 003290 (1997).
[CrossRef]

Simon, V.

J.R. Salgueiro, Y.S. Kivshar, D.E. Pelinovsky, V. Simon, and H. Michinel, "Spatial vector solitons in nonlinear photonic crystal fibers," Studies in Appl. Math. 115, 157-171 (2005).
[CrossRef]

Skryabin, D. V.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. Russell, "Interaction of an optical soliton with a dispersive wave," Phys. Rev. Lett. 95, 213902 (2005).
[CrossRef] [PubMed]

Skryabin, D.V.

F. Biancalana and D.V. Skryabin, "Vector modulational instabilities in ultra-small core optical fibres," J. Opt. A 6, 301-306 (2004).
[CrossRef]

D.V. Skryabin, F. Luan, J.C. Knight, and P.St.J. Russell, "Soliton self-frequency shift cancellation in photonic crystal fibers," Science 301, 1705-1708 (2003).
[CrossRef] [PubMed]

Song, Y.

Soto-Crespo, J.

Stegeman, G.

Taylor, A. J.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. Russell, "Interaction of an optical soliton with a dispersive wave," Phys. Rev. Lett. 95, 213902 (2005).
[CrossRef] [PubMed]

Trebino, R.

Wadsworth, W.J.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J.C. Knight, W.J. Wadsworth, P.St.J. Russell, and G. Korn, "Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers," Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

J.C. Knight, J. Arriaga, T.A. Birks, A. Ortigosa-Blanch, W.J. Wadsworth, and P.S. Russell, "Anomalous dispersion in photonic crystal fiber," IEEE Photon. Technol. Lett. 12, 807-809 (2000).
[CrossRef]

Wang, C.

Windeler, B.S.

Windeler, R.

Wood, D.

Xu, C.

Xu, L.

Yulin, A. V.

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. Russell, "Interaction of an optical soliton with a dispersive wave," Phys. Rev. Lett. 95, 213902 (2005).
[CrossRef] [PubMed]

Zeek, E.

Zhavoronkov, N.

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J.C. Knight, W.J. Wadsworth, P.St.J. Russell, and G. Korn, "Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers," Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

Zheltikov, A.

IEEE Photon. Technol. Lett. (1)

J.C. Knight, J. Arriaga, T.A. Birks, A. Ortigosa-Blanch, W.J. Wadsworth, and P.S. Russell, "Anomalous dispersion in photonic crystal fiber," IEEE Photon. Technol. Lett. 12, 807-809 (2000).
[CrossRef]

J. Opt. A (1)

F. Biancalana and D.V. Skryabin, "Vector modulational instabilities in ultra-small core optical fibres," J. Opt. A 6, 301-306 (2004).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. E (1)

D. Mihalache, D. Mazilu, and L.-C. Crasovan, "Linear stability analysis of walking vector solitons," Phys. Rev. E 60, 007504 (1999).
[CrossRef]

Phys. Rev. Lett. (4)

Y. Barad and Y. Silberberg, "Polarization evolution and polarization instability of solitons in a birefringent optical fiber," Phys. Rev. Lett. 78, 003290 (1997).
[CrossRef]

F. Lu, Q. Lin, W. H. Knox, and G. P. Agrawal, "Vector Soliton Fission," Phys. Rev. Lett. 93, 183901 (2004).
[CrossRef] [PubMed]

J. Herrmann, U. Griebner, N. Zhavoronkov, A. Husakou, D. Nickel, J.C. Knight, W.J. Wadsworth, P.St.J. Russell, and G. Korn, "Experimental evidence for supercontinuum generation by fission of higher-order solitons in photonic fibers," Phys. Rev. Lett. 88, 173901 (2002).
[CrossRef] [PubMed]

A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, and P. Russell, "Interaction of an optical soliton with a dispersive wave," Phys. Rev. Lett. 95, 213902 (2005).
[CrossRef] [PubMed]

Science (2)

L.F. Mollenauer, "Nonlinear optics in fibers," Science 302, 996-997 (2003).
[CrossRef] [PubMed]

D.V. Skryabin, F. Luan, J.C. Knight, and P.St.J. Russell, "Soliton self-frequency shift cancellation in photonic crystal fibers," Science 301, 1705-1708 (2003).
[CrossRef] [PubMed]

Studies in Appl. Math. (1)

J.R. Salgueiro, Y.S. Kivshar, D.E. Pelinovsky, V. Simon, and H. Michinel, "Spatial vector solitons in nonlinear photonic crystal fibers," Studies in Appl. Math. 115, 157-171 (2005).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

The experimental setup. 86MHz, 200fs pulses from a Ti:Sapphire laser pass through an attenuator which consists of a half-waveplate and a polarising beam-splitter (PB), then through another half-waveplate to align with the axis of the PCF before coupling into the PCF. The output end of the PCF is mounted onto a rotational stage (RS) to align its axis with the output polarising beam-splitter, enabling independent and simultaneous analysis of the two polarization channels.

Fig. 2.
Fig. 2.

(a) Group index of the orthogonally polarized modes. Dashed line and open circles correspond to the fast axis and the full line and full circles to the slow axis. Circles mark the experimental measurements, while the lines correspond to the group index used in numerical modelling. (b) Group velocity dispersion (GVD) calculated from the group index. Dashed/full line corresponds to the fast/slow axis.

Fig. 3.
Fig. 3.

In this experiment, the input pulse energy was fixed at about 30pJ. The electric vector was rotated through 90 degrees in steps of 4 degrees using the waveplate. At each step, the output spectrum was independently measured for each polarization state. The left (right) plot shows how the spectrum from f-axis (s-axis) evolved during this process. The group velocity dispersion is anomalous to the left of the vertical lines in (a) and (b) and normal to the right.

Fig. 4.
Fig. 4.

In this experiment, we fixed the waveplate in front of the PCF and kept the input pulse polarized along the f-axis of the fiber. Then we increased the pulse energy from 3.5pJ to 40pJ in 25 steps. At each step, output spectra for each of the two polarizations were recorded. The left (right) plot shows how the measured spectrum from the f-axis (s-axis) changes during this process. A significant amount of power is coupled from the fast axis into the slow axis under specific conditions. The group velocity dispersion is anomalous to the left of the vertical lines in (a) and (b) and normal to the right.

Fig. 5.
Fig. 5.

Plot showing region of PI of the soliton for q=20/L 2. Maximum instability growth rate corresponds to the dark red color and the dark blue background indicates no instability. White lines show several possible ways that the local dispersion parameters experienced by a soliton could change along the fiber length as the soliton was shifted by the Raman effect. Line 1 corresponds to the soliton dynamics shown in Figs. 6,7. Bold lines mark the trajectories when PI was observed in modeling and the dashed ones correspond to the cases when PI did not develop.

Fig. 6.
Fig. 6.

Transmission spectra of the two polarizations numerically calculated using Eqs. (1). Propagation distance is 2m. Good consistency with experimental measurements in Fig. 4 is evident.

Fig. 7.
Fig. 7.

Polarization instability in the (z, t)-plane, see text for details. Distance, time and intensity are shown in dimensionless units. Physical propagation distance is 40cm. One unit of time is 200fs.

Equations (2)

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[ i z + D x , y ( i t ) ] A x , y + γ [ A x , y 2 + 2 3 A y , x 2 ] A x , y + γ 3 A y , x 2 A x , y * + γ A x , y dt R ( t ) I ( t t , z ) = 0 .
{ i z + [ β y ( 0 ) β x ( 0 ) ] + [ β y ( 1 ) β x ( 1 ) ] i t 1 2 β y ( 2 ) t 2 } A y + 2 γ 3 A x 2 A y + γ 3 A x 2 A y * = 0 .

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