Abstract

We demonstrate that the relatively small power induced changes in the soliton wavenumber comparable with splitting of the effective indexes of the orthogonally polarized waveguide modes result in significant changes of the efficiency of the interaction between solitons and dispersive waves and can be used to control energy transfer between the soliton and newly generated waves and to delay or accelerate solitons.

© 2014 Optical Society of America

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References

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  1. D. V. Skryabin, A. V. Gorbach, “Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010).
    [CrossRef]
  2. D. V. Skryabin, A. V. Gorbach, “Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic-crystal fibres,” Nature-Photonics 1, 653–657 (2007).
    [CrossRef]
  3. A. C. Judge, O. Bang, C. Martijn de Sterke, “Theory of dispersive wave frequency shift via trapping by a soliton in an axially nonuniform optical fiber,” J. Opt. Soc. Am B 27, 2195–2202 (2010).
    [CrossRef]
  4. R. Driben, F. Mitschke, N. Zhavoronkov, “Cascaded interactions between Raman induced solitons and dispersive waves in photonic crystal fibers at the advanced stage of supercontinuum generation,” Opt. Express 18, 25993–25998 (2010).
    [CrossRef] [PubMed]
  5. A. Demircan, S. Amiranashvili, C. Brie, C. Mahnke, F. Mitschke, G. Steinmeyer, “Rogue events in the group velocity horizon,” Sci. Rep. 2, 850 (2012).
    [CrossRef] [PubMed]
  6. R. Driben, I. Babushkin, “Accelerated rogue waves generated by soliton fusion at the advanced stage of supercontinuum formation in photonic-crystal fibers,” Opt. Lett. 37, 5157 (2012).
    [CrossRef] [PubMed]
  7. R. Driben, B. A. Malomed, “Generation of tightly compressed solitons with a tunable frequency shift in Raman-free fibers,” Opt. Lett. 38, 3623 (2013).
    [CrossRef] [PubMed]
  8. R. Driben, B. A. Malomed, A. V. Yulin, D.V. Skryabin, “Newton’s cradles in optics: From to N-soliton fission to soliton chains,” Phys. Rev. A, 87(6), 063808 (2013).
    [CrossRef]
  9. A. V. Yulin, R. Driben, B. A. Malomed, D. V. Skryabin, “Soliton interaction mediated by cascaded four wave mixing with dispersive waves,” Opt. Express 21, 14481–14486 (2013).
    [CrossRef]
  10. R. Driben, A. V. Yulin, A. Efimov, B. A. Malomed, “Trapping of light in solitonic cavities and its role in the supercontinuum generation,” Opt. Express 21, 19091–19096 (2013).
    [CrossRef] [PubMed]
  11. A. Demircan, S. Amiranashvili, G. Steinmeyer, “Controlling Light by Light with an Optical Event Horizon,” Phys. Rev. Lett. 106, 163901 (2011).
    [CrossRef] [PubMed]
  12. A. Demircan, S. Amiranashvili, C. Bree, G. Steinmeyer, “Compressible Octave Spanning Supercontinuum Generation by Two-Pulse Collisions,” Phys. Rev. Lett. 110, 233901 (2013).
    [CrossRef]
  13. A. Demircan, S. Amiranashvili, C. Bree, U. Morgner, G. Steinmeyer, “Supercontinuum generation by multiple scatterings at a group velocity horizon,” Opt. Express, 22, (4), 3866–3879 (2014).
    [CrossRef] [PubMed]
  14. A. Efimov, A. V. Yulin, D. V. Skryabin, J. C. Knight, N. Joly, F. G. Omenetto, A. J. Taylor, P. Russell, “Interaction of an optical soliton with a dispersive wave,” Phys. Rev. Lett. 95, 213902 (2005).
    [CrossRef] [PubMed]
  15. A. Efimov, A. J. Taylor, A. V. Yulin, D. V. Skryabin, J. C. Knight, “Phase-sensitive scattering of a continuous wave on a soliton,” Opt. Lett. 31, 1624–1626 (2006).
    [CrossRef] [PubMed]
  16. A. V. Yulin, D. V. Skryabin, P. St. J. Russell, “Four-wave mixing of linear waves and solitons in fibers with higher-order dispersion,” Optics Lett. 29, 2411–2413 (2004).
    [CrossRef]
  17. D. V. Skryabin, A. V. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E 72, 016619 (2005).
    [CrossRef]
  18. F. Lu, Q. Lin, W. H. Knox, G. P. Agrawal, “Vector soliton fission,” Phys. Rev. Lett. 93, 183901 (2004).
    [CrossRef] [PubMed]
  19. W. Ding, A. V. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. J. Strain, M. Sorel, R. M. De la Rue, “Time and frequency domain measurements of solitons in subwavelength silicon waveguides using a cross-correlation technique,” Opt. Express 18, 26625–26630 (2010).
    [CrossRef] [PubMed]
  20. N. Belanger, A. Villeneuve, J. S. Aitchison, “Solitonlike pulses in self-defocusing AlGaAs waveguides,” J. Opt. Soc. Am. B 14, 3003–3012 (1997).
    [CrossRef]
  21. F. Luan, A.V. Yulin, J.C. Knight, D.V. Skryabin, “Polarization instability of solitons in photonic crystal fibers,” Opt. Express 14, 6550 (2006).
    [CrossRef] [PubMed]

2014 (1)

2013 (5)

2012 (2)

A. Demircan, S. Amiranashvili, C. Brie, C. Mahnke, F. Mitschke, G. Steinmeyer, “Rogue events in the group velocity horizon,” Sci. Rep. 2, 850 (2012).
[CrossRef] [PubMed]

R. Driben, I. Babushkin, “Accelerated rogue waves generated by soliton fusion at the advanced stage of supercontinuum formation in photonic-crystal fibers,” Opt. Lett. 37, 5157 (2012).
[CrossRef] [PubMed]

2011 (1)

A. Demircan, S. Amiranashvili, G. Steinmeyer, “Controlling Light by Light with an Optical Event Horizon,” Phys. Rev. Lett. 106, 163901 (2011).
[CrossRef] [PubMed]

2010 (4)

2007 (1)

D. V. Skryabin, A. V. Gorbach, “Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic-crystal fibres,” Nature-Photonics 1, 653–657 (2007).
[CrossRef]

2006 (2)

2005 (2)

D. V. Skryabin, A. V. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E 72, 016619 (2005).
[CrossRef]

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

2004 (2)

F. Lu, Q. Lin, W. H. Knox, G. P. Agrawal, “Vector soliton fission,” Phys. Rev. Lett. 93, 183901 (2004).
[CrossRef] [PubMed]

A. V. Yulin, D. V. Skryabin, P. St. J. Russell, “Four-wave mixing of linear waves and solitons in fibers with higher-order dispersion,” Optics Lett. 29, 2411–2413 (2004).
[CrossRef]

1997 (1)

Agrawal, G. P.

F. Lu, Q. Lin, W. H. Knox, G. P. Agrawal, “Vector soliton fission,” Phys. Rev. Lett. 93, 183901 (2004).
[CrossRef] [PubMed]

Aitchison, J. S.

Amiranashvili, S.

A. Demircan, S. Amiranashvili, C. Bree, U. Morgner, G. Steinmeyer, “Supercontinuum generation by multiple scatterings at a group velocity horizon,” Opt. Express, 22, (4), 3866–3879 (2014).
[CrossRef] [PubMed]

A. Demircan, S. Amiranashvili, C. Bree, G. Steinmeyer, “Compressible Octave Spanning Supercontinuum Generation by Two-Pulse Collisions,” Phys. Rev. Lett. 110, 233901 (2013).
[CrossRef]

A. Demircan, S. Amiranashvili, C. Brie, C. Mahnke, F. Mitschke, G. Steinmeyer, “Rogue events in the group velocity horizon,” Sci. Rep. 2, 850 (2012).
[CrossRef] [PubMed]

A. Demircan, S. Amiranashvili, G. Steinmeyer, “Controlling Light by Light with an Optical Event Horizon,” Phys. Rev. Lett. 106, 163901 (2011).
[CrossRef] [PubMed]

Babushkin, I.

Bang, O.

A. C. Judge, O. Bang, C. Martijn de Sterke, “Theory of dispersive wave frequency shift via trapping by a soliton in an axially nonuniform optical fiber,” J. Opt. Soc. Am B 27, 2195–2202 (2010).
[CrossRef]

Belanger, N.

Bree, C.

A. Demircan, S. Amiranashvili, C. Bree, U. Morgner, G. Steinmeyer, “Supercontinuum generation by multiple scatterings at a group velocity horizon,” Opt. Express, 22, (4), 3866–3879 (2014).
[CrossRef] [PubMed]

A. Demircan, S. Amiranashvili, C. Bree, G. Steinmeyer, “Compressible Octave Spanning Supercontinuum Generation by Two-Pulse Collisions,” Phys. Rev. Lett. 110, 233901 (2013).
[CrossRef]

Brie, C.

A. Demircan, S. Amiranashvili, C. Brie, C. Mahnke, F. Mitschke, G. Steinmeyer, “Rogue events in the group velocity horizon,” Sci. Rep. 2, 850 (2012).
[CrossRef] [PubMed]

De la Rue, R. M.

Demircan, A.

A. Demircan, S. Amiranashvili, C. Bree, U. Morgner, G. Steinmeyer, “Supercontinuum generation by multiple scatterings at a group velocity horizon,” Opt. Express, 22, (4), 3866–3879 (2014).
[CrossRef] [PubMed]

A. Demircan, S. Amiranashvili, C. Bree, G. Steinmeyer, “Compressible Octave Spanning Supercontinuum Generation by Two-Pulse Collisions,” Phys. Rev. Lett. 110, 233901 (2013).
[CrossRef]

A. Demircan, S. Amiranashvili, C. Brie, C. Mahnke, F. Mitschke, G. Steinmeyer, “Rogue events in the group velocity horizon,” Sci. Rep. 2, 850 (2012).
[CrossRef] [PubMed]

A. Demircan, S. Amiranashvili, G. Steinmeyer, “Controlling Light by Light with an Optical Event Horizon,” Phys. Rev. Lett. 106, 163901 (2011).
[CrossRef] [PubMed]

Ding, W.

Driben, R.

Efimov, A.

Gorbach, A. V.

W. Ding, A. V. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. J. Strain, M. Sorel, R. M. De la Rue, “Time and frequency domain measurements of solitons in subwavelength silicon waveguides using a cross-correlation technique,” Opt. Express 18, 26625–26630 (2010).
[CrossRef] [PubMed]

D. V. Skryabin, A. V. Gorbach, “Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010).
[CrossRef]

D. V. Skryabin, A. V. Gorbach, “Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic-crystal fibres,” Nature-Photonics 1, 653–657 (2007).
[CrossRef]

Joly, N.

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

Judge, A. C.

A. C. Judge, O. Bang, C. Martijn de Sterke, “Theory of dispersive wave frequency shift via trapping by a soliton in an axially nonuniform optical fiber,” J. Opt. Soc. Am B 27, 2195–2202 (2010).
[CrossRef]

Knight, J. C.

Knight, J.C.

Knox, W. H.

F. Lu, Q. Lin, W. H. Knox, G. P. Agrawal, “Vector soliton fission,” Phys. Rev. Lett. 93, 183901 (2004).
[CrossRef] [PubMed]

Lin, Q.

F. Lu, Q. Lin, W. H. Knox, G. P. Agrawal, “Vector soliton fission,” Phys. Rev. Lett. 93, 183901 (2004).
[CrossRef] [PubMed]

Lu, F.

F. Lu, Q. Lin, W. H. Knox, G. P. Agrawal, “Vector soliton fission,” Phys. Rev. Lett. 93, 183901 (2004).
[CrossRef] [PubMed]

Luan, F.

Mahnke, C.

A. Demircan, S. Amiranashvili, C. Brie, C. Mahnke, F. Mitschke, G. Steinmeyer, “Rogue events in the group velocity horizon,” Sci. Rep. 2, 850 (2012).
[CrossRef] [PubMed]

Malomed, B. A.

Martijn de Sterke, C.

A. C. Judge, O. Bang, C. Martijn de Sterke, “Theory of dispersive wave frequency shift via trapping by a soliton in an axially nonuniform optical fiber,” J. Opt. Soc. Am B 27, 2195–2202 (2010).
[CrossRef]

Mitschke, F.

Morgner, U.

Omenetto, F. G.

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

Russell, P.

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

Russell, P. St. J.

A. V. Yulin, D. V. Skryabin, P. St. J. Russell, “Four-wave mixing of linear waves and solitons in fibers with higher-order dispersion,” Optics Lett. 29, 2411–2413 (2004).
[CrossRef]

Skryabin, D. V.

A. V. Yulin, R. Driben, B. A. Malomed, D. V. Skryabin, “Soliton interaction mediated by cascaded four wave mixing with dispersive waves,” Opt. Express 21, 14481–14486 (2013).
[CrossRef]

D. V. Skryabin, A. V. Gorbach, “Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010).
[CrossRef]

W. Ding, A. V. Gorbach, W. J. Wadsworth, J. C. Knight, D. V. Skryabin, M. J. Strain, M. Sorel, R. M. De la Rue, “Time and frequency domain measurements of solitons in subwavelength silicon waveguides using a cross-correlation technique,” Opt. Express 18, 26625–26630 (2010).
[CrossRef] [PubMed]

D. V. Skryabin, A. V. Gorbach, “Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic-crystal fibres,” Nature-Photonics 1, 653–657 (2007).
[CrossRef]

A. Efimov, A. J. Taylor, A. V. Yulin, D. V. Skryabin, J. C. Knight, “Phase-sensitive scattering of a continuous wave on a soliton,” Opt. Lett. 31, 1624–1626 (2006).
[CrossRef] [PubMed]

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

D. V. Skryabin, A. V. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E 72, 016619 (2005).
[CrossRef]

A. V. Yulin, D. V. Skryabin, P. St. J. Russell, “Four-wave mixing of linear waves and solitons in fibers with higher-order dispersion,” Optics Lett. 29, 2411–2413 (2004).
[CrossRef]

Skryabin, D.V.

R. Driben, B. A. Malomed, A. V. Yulin, D.V. Skryabin, “Newton’s cradles in optics: From to N-soliton fission to soliton chains,” Phys. Rev. A, 87(6), 063808 (2013).
[CrossRef]

F. Luan, A.V. Yulin, J.C. Knight, D.V. Skryabin, “Polarization instability of solitons in photonic crystal fibers,” Opt. Express 14, 6550 (2006).
[CrossRef] [PubMed]

Sorel, M.

Steinmeyer, G.

A. Demircan, S. Amiranashvili, C. Bree, U. Morgner, G. Steinmeyer, “Supercontinuum generation by multiple scatterings at a group velocity horizon,” Opt. Express, 22, (4), 3866–3879 (2014).
[CrossRef] [PubMed]

A. Demircan, S. Amiranashvili, C. Bree, G. Steinmeyer, “Compressible Octave Spanning Supercontinuum Generation by Two-Pulse Collisions,” Phys. Rev. Lett. 110, 233901 (2013).
[CrossRef]

A. Demircan, S. Amiranashvili, C. Brie, C. Mahnke, F. Mitschke, G. Steinmeyer, “Rogue events in the group velocity horizon,” Sci. Rep. 2, 850 (2012).
[CrossRef] [PubMed]

A. Demircan, S. Amiranashvili, G. Steinmeyer, “Controlling Light by Light with an Optical Event Horizon,” Phys. Rev. Lett. 106, 163901 (2011).
[CrossRef] [PubMed]

Strain, M. J.

Taylor, A. J.

A. Efimov, A. J. Taylor, A. V. Yulin, D. V. Skryabin, J. C. Knight, “Phase-sensitive scattering of a continuous wave on a soliton,” Opt. Lett. 31, 1624–1626 (2006).
[CrossRef] [PubMed]

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

Villeneuve, A.

Wadsworth, W. J.

Yulin, A. V.

A. V. Yulin, R. Driben, B. A. Malomed, D. V. Skryabin, “Soliton interaction mediated by cascaded four wave mixing with dispersive waves,” Opt. Express 21, 14481–14486 (2013).
[CrossRef]

R. Driben, B. A. Malomed, A. V. Yulin, D.V. Skryabin, “Newton’s cradles in optics: From to N-soliton fission to soliton chains,” Phys. Rev. A, 87(6), 063808 (2013).
[CrossRef]

R. Driben, A. V. Yulin, A. Efimov, B. A. Malomed, “Trapping of light in solitonic cavities and its role in the supercontinuum generation,” Opt. Express 21, 19091–19096 (2013).
[CrossRef] [PubMed]

A. Efimov, A. J. Taylor, A. V. Yulin, D. V. Skryabin, J. C. Knight, “Phase-sensitive scattering of a continuous wave on a soliton,” Opt. Lett. 31, 1624–1626 (2006).
[CrossRef] [PubMed]

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

D. V. Skryabin, A. V. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E 72, 016619 (2005).
[CrossRef]

A. V. Yulin, D. V. Skryabin, P. St. J. Russell, “Four-wave mixing of linear waves and solitons in fibers with higher-order dispersion,” Optics Lett. 29, 2411–2413 (2004).
[CrossRef]

Yulin, A.V.

Zhavoronkov, N.

J. Opt. Soc. Am B (1)

A. C. Judge, O. Bang, C. Martijn de Sterke, “Theory of dispersive wave frequency shift via trapping by a soliton in an axially nonuniform optical fiber,” J. Opt. Soc. Am B 27, 2195–2202 (2010).
[CrossRef]

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

Nature-Photonics (1)

D. V. Skryabin, A. V. Gorbach, “Light trapping in gravity-like potentials and expansion of supercontinuum spectra in photonic-crystal fibres,” Nature-Photonics 1, 653–657 (2007).
[CrossRef]

Opt. Express (6)

Opt. Lett. (3)

Optics Lett. (1)

A. V. Yulin, D. V. Skryabin, P. St. J. Russell, “Four-wave mixing of linear waves and solitons in fibers with higher-order dispersion,” Optics Lett. 29, 2411–2413 (2004).
[CrossRef]

Phys. Rev. A (1)

R. Driben, B. A. Malomed, A. V. Yulin, D.V. Skryabin, “Newton’s cradles in optics: From to N-soliton fission to soliton chains,” Phys. Rev. A, 87(6), 063808 (2013).
[CrossRef]

Phys. Rev. E (1)

D. V. Skryabin, A. V. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E 72, 016619 (2005).
[CrossRef]

Phys. Rev. Lett. (4)

F. Lu, Q. Lin, W. H. Knox, G. P. Agrawal, “Vector soliton fission,” Phys. Rev. Lett. 93, 183901 (2004).
[CrossRef] [PubMed]

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

A. Demircan, S. Amiranashvili, G. Steinmeyer, “Controlling Light by Light with an Optical Event Horizon,” Phys. Rev. Lett. 106, 163901 (2011).
[CrossRef] [PubMed]

A. Demircan, S. Amiranashvili, C. Bree, G. Steinmeyer, “Compressible Octave Spanning Supercontinuum Generation by Two-Pulse Collisions,” Phys. Rev. Lett. 110, 233901 (2013).
[CrossRef]

Rev. Mod. Phys. (1)

D. V. Skryabin, A. V. Gorbach, “Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82, 1287–1299 (2010).
[CrossRef]

Sci. Rep. (1)

A. Demircan, S. Amiranashvili, C. Brie, C. Mahnke, F. Mitschke, G. Steinmeyer, “Rogue events in the group velocity horizon,” Sci. Rep. 2, 850 (2012).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

(a)–(c) show the output spectrum (a), graphical representation of the phase matching conditions (b) and evolution of the y-component of the field (c). The incident DW has ωi = 5 and B = 0.0333, the soliton parameter q = 6. Crossings of the parabola in (b) with the green and red horizontal lines correspond to the phase insensitive and phase sensitive resonances, respectively. (d)–(f) and (g)–(i) are the same as (a)–(c), but for ωi = 5, q = 3, B = 0.0333 and ωi = 3, q = 3, B = 0.0333, respectively. Dotted horizontal lines indicate the soliton wavenumber. Here and in all the other figures: β0 = 2, β1 = 1.5 and β2 = −0.2.

Fig. 2
Fig. 2

(a) Resonance frequencies for the phase sensitive process as a function of the soliton parameter q. Analytical solutions are given by the solid lines, the black dots show the frequencies obtained from numerical simulations. (b) The amplification coefficient K defined as a ratio of the photon numbers in the transmitted waves at frequency ωi to the photon number in the incident wave; ωi = 3. (c) Domains on the left from the parabolas give the values of β0 and β1 where the phase sensitive conditions can be satisfied for the suitable resonance frequencies (see Fig. 2(a)). The red-orange color indicates the region of the polarization instability of the soliton solutions for q = 5.

Fig. 3
Fig. 3

Evolution of the total intensity |Ax|2 (a–c) and |Ay|2 (d–f) resulting from the soliton collision with a DW: (a,d) B = 0.14, ωi = 3, q = 3.5; (b,e) B = 0.14, ωi = 3, q = 4.35; (c,f) B = 0.14, ωi = 3, q = 5.

Fig. 4
Fig. 4

(a) Changes in the soliton group velocity after interaction with the DW having ωi = 3 as a function of the soliton parameter q. The red dashed line indicates qcr when the phase sensitive resonances appear. (b) Changes in the soliton group velocity after interaction with the DW as a function of the DW frequency ωi. The paramerers of the solitons are q = 4 and q = 6, the amplitude of the incident wave is B = 0.5.

Equations (3)

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[ i z + D ^ x , y ] A x , y + [ | A x , y | 2 + 2 3 | A y , x | 2 ] A x , y + 1 3 A y , x 2 A x , y * = 0 ,
β ( ω ) = β ( ω i )
β ( ω ) = 2 q β ( ω i )

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