Abstract

We demonstrate that trapping of dispersive waves between two optical solitons takes place when resonant scattering of the waves on the solitons leads to nearly perfect reflections. The momentum transfer from the radiation to solitons results in their mutual attraction and a subsequent collision. The spectrum of the trapped radiation can either expand or shrink in the course of the propagation, which is controlled by arranging either collision or separation of the solitons.

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References

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  1. D.V. Skryabin and A.V. Gorbach, “Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys.82, 1287–1299 (2010).
    [CrossRef]
  2. J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys78, 1135–1184 (2006).
    [CrossRef]
  3. N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A51, 2602–2607 (1995).
    [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,” Science301, 1705–1708 (2003).
    [CrossRef] [PubMed]
  5. A. V. Yulin, D. V. Skryabin, and P. St. J. Russell, “Four-wave mixing of linear waves and solitons in fibers with higher-order dispersion,” Opt. Lett.29, 2411–2413 (2004).
    [CrossRef] [PubMed]
  6. D. V. Skryabin and A. V. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E72, 016619 (2005).
    [CrossRef]
  7. A. Demircan, S. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett.106, 163901 (2011).
    [CrossRef] [PubMed]
  8. A. Efimov, A. J. Taylor, F. G. Omenetto, A. V. Yulin, N. Y. Joly, F. Biancalana, D. V. Skryabin, J. C. Knight, and P. St. J. Russell, “Time-spectrally-resolved ultrafast nonlinear dynamics in small-core photonic crystal fibers: Experiment and modelling,” Opt. Express12, 6499–6507 (2004).
    [CrossRef]
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    [CrossRef] [PubMed]
  10. A. Efimov, A. J. Taylor, A. V. Yulin, D. V. Skryabin, and J. C. Knight, “Phase-sensitive scattering of a continuous wave on a soliton,” Opt. Lett.31, 1624 (2006).
    [CrossRef] [PubMed]
  11. B. A. Malomed, “Potential of interaction between two- and three-dimensional solitons,” Phys. Rev. E58, 7928–7933 (1998).
    [CrossRef]
  12. F. Luan, D. V. Skryabin, A. V. Yulin, and J. C. Knight, “Energy exchange between colliding solitons in photonic crystal fibers,” Opt. Express14, 9844–9853 (2006).
    [CrossRef] [PubMed]
  13. R Driben and B. A Malomed, “Suppression of crosstalk between solitons in a multi-channel split-step system,” Opt. Commun.197, 481–489 (2001)
    [CrossRef]
  14. G. Agrawal, Nonlinear Fiber Optics (Academic Press, New York, 2007).
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    [CrossRef] [PubMed]
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    [CrossRef]
  17. P. J. Hardman, P. D. Townsend, A. J. Poustie, and K. J. Blow, “Experimental investigation of resonant enhancement of the acoustic interaction of optical pulses in an optical fiber,” Opt. Lett.21, 393–395 (1996).
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    [CrossRef] [PubMed]
  19. R. Driben, F. Mitschke, and N. Zhavoronkov, “Cascaded interactions between Raman induced solitons and dispersive waves in photonic crystal fibers at the advanced stage of supercontinuum generation,” Opt. Express18, 25993–25998 (2010).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2012 (2)

A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, “Rogue events in the group velocity horizon,” Scientific Reports2, 850 (2012).
[CrossRef] [PubMed]

R. Driben and I. V. Babushkin, “Accelerated rogue waves generated by soliton fusion at the advanced stage of supercontinuum formation in photonic crystal fibers,” Opt. Lett.37, 5157–5159 (2012).
[CrossRef] [PubMed]

2011 (1)

A. Demircan, S. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett.106, 163901 (2011).
[CrossRef] [PubMed]

2010 (3)

2007 (1)

2006 (3)

2005 (2)

D. V. Skryabin and A. V. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E72, 016619 (2005).
[CrossRef]

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]

2004 (2)

A. Efimov, A. J. Taylor, F. G. Omenetto, A. V. Yulin, N. Y. Joly, F. Biancalana, D. V. Skryabin, J. C. Knight, and P. St. J. Russell, “Time-spectrally-resolved ultrafast nonlinear dynamics in small-core photonic crystal fibers: Experiment and modelling,” Opt. Express12, 6499–6507 (2004).
[CrossRef]

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

2003 (1)

D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science301, 1705–1708 (2003).
[CrossRef] [PubMed]

2001 (1)

R Driben and B. A Malomed, “Suppression of crosstalk between solitons in a multi-channel split-step system,” Opt. Commun.197, 481–489 (2001)
[CrossRef]

1998 (1)

B. A. Malomed, “Potential of interaction between two- and three-dimensional solitons,” Phys. Rev. E58, 7928–7933 (1998).
[CrossRef]

1996 (1)

1995 (2)

N. N. Akhmediev and A. V. Buryak, “Interactions of solitons with oscillating tails,” Opt. Commun.121, 109–114 (1995).
[CrossRef]

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A51, 2602–2607 (1995).
[CrossRef] [PubMed]

1994 (1)

Afanasjev, V. V.

Agrawal, G.

G. Agrawal, Nonlinear Fiber Optics (Academic Press, New York, 2007).

Akhmediev, N.

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A51, 2602–2607 (1995).
[CrossRef] [PubMed]

Akhmediev, N. N.

N. N. Akhmediev and A. V. Buryak, “Interactions of solitons with oscillating tails,” Opt. Commun.121, 109–114 (1995).
[CrossRef]

Amiranashvili, S.

A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, “Rogue events in the group velocity horizon,” Scientific Reports2, 850 (2012).
[CrossRef] [PubMed]

A. Demircan, S. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett.106, 163901 (2011).
[CrossRef] [PubMed]

Babushkin, I. V.

Biancalana, F.

A. Efimov, A. J. Taylor, F. G. Omenetto, A. V. Yulin, N. Y. Joly, F. Biancalana, D. V. Skryabin, J. C. Knight, and P. St. J. Russell, “Time-spectrally-resolved ultrafast nonlinear dynamics in small-core photonic crystal fibers: Experiment and modelling,” Opt. Express12, 6499–6507 (2004).
[CrossRef]

Blow, K. J.

Brée, C.

A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, “Rogue events in the group velocity horizon,” Scientific Reports2, 850 (2012).
[CrossRef] [PubMed]

Buryak, A. V.

N. N. Akhmediev and A. V. Buryak, “Interactions of solitons with oscillating tails,” Opt. Commun.121, 109–114 (1995).
[CrossRef]

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys78, 1135–1184 (2006).
[CrossRef]

Demircan, A.

A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, “Rogue events in the group velocity horizon,” Scientific Reports2, 850 (2012).
[CrossRef] [PubMed]

A. Demircan, S. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett.106, 163901 (2011).
[CrossRef] [PubMed]

Driben, R

R Driben and B. A Malomed, “Suppression of crosstalk between solitons in a multi-channel split-step system,” Opt. Commun.197, 481–489 (2001)
[CrossRef]

Driben, R.

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys78, 1135–1184 (2006).
[CrossRef]

Efimov, A.

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

A. Efimov, A. J. Taylor, F. G. Omenetto, A. V. Yulin, N. Y. Joly, F. Biancalana, D. V. Skryabin, J. C. Knight, and P. St. J. Russell, “Time-spectrally-resolved ultrafast nonlinear dynamics in small-core photonic crystal fibers: Experiment and modelling,” Opt. Express12, 6499–6507 (2004).
[CrossRef]

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys78, 1135–1184 (2006).
[CrossRef]

Gorbach, A.V.

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

Grudinin, A. B.

Hardman, P. J.

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]

Joly, N. Y.

A. Podlipensky, P. Szarniak, N. Y. Joly, C. G. Poulton, and P. St. J. Russell, “Bound soliton pairs in photonic crystal fiber,” Opt. Express15, 1653–1662 (2007)
[CrossRef] [PubMed]

A. Efimov, A. J. Taylor, F. G. Omenetto, A. V. Yulin, N. Y. Joly, F. Biancalana, D. V. Skryabin, J. C. Knight, and P. St. J. Russell, “Time-spectrally-resolved ultrafast nonlinear dynamics in small-core photonic crystal fibers: Experiment and modelling,” Opt. Express12, 6499–6507 (2004).
[CrossRef]

Karlsson, M.

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A51, 2602–2607 (1995).
[CrossRef] [PubMed]

Knight, J. C.

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

F. Luan, D. V. Skryabin, A. V. Yulin, and J. C. Knight, “Energy exchange between colliding solitons in photonic crystal fibers,” Opt. Express14, 9844–9853 (2006).
[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]

A. Efimov, A. J. Taylor, F. G. Omenetto, A. V. Yulin, N. Y. Joly, F. Biancalana, D. V. Skryabin, J. C. Knight, and P. St. J. Russell, “Time-spectrally-resolved ultrafast nonlinear dynamics in small-core photonic crystal fibers: Experiment and modelling,” Opt. Express12, 6499–6507 (2004).
[CrossRef]

D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science301, 1705–1708 (2003).
[CrossRef] [PubMed]

Loh, W. H.

Luan, F.

F. Luan, D. V. Skryabin, A. V. Yulin, and J. C. Knight, “Energy exchange between colliding solitons in photonic crystal fibers,” Opt. Express14, 9844–9853 (2006).
[CrossRef] [PubMed]

D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science301, 1705–1708 (2003).
[CrossRef] [PubMed]

Mahnke, C.

A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, “Rogue events in the group velocity horizon,” Scientific Reports2, 850 (2012).
[CrossRef] [PubMed]

Malomed, B. A

R Driben and B. A Malomed, “Suppression of crosstalk between solitons in a multi-channel split-step system,” Opt. Commun.197, 481–489 (2001)
[CrossRef]

Malomed, B. A.

B. A. Malomed, “Potential of interaction between two- and three-dimensional solitons,” Phys. Rev. E58, 7928–7933 (1998).
[CrossRef]

Mitschke, F.

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]

A. Efimov, A. J. Taylor, F. G. Omenetto, A. V. Yulin, N. Y. Joly, F. Biancalana, D. V. Skryabin, J. C. Knight, and P. St. J. Russell, “Time-spectrally-resolved ultrafast nonlinear dynamics in small-core photonic crystal fibers: Experiment and modelling,” Opt. Express12, 6499–6507 (2004).
[CrossRef]

Payne, D. N.

Podlipensky, A.

Poulton, C. G.

Poustie, A. J.

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. St. J.

A. Podlipensky, P. Szarniak, N. Y. Joly, C. G. Poulton, and P. St. J. Russell, “Bound soliton pairs in photonic crystal fiber,” Opt. Express15, 1653–1662 (2007)
[CrossRef] [PubMed]

A. Efimov, A. J. Taylor, F. G. Omenetto, A. V. Yulin, N. Y. Joly, F. Biancalana, D. V. Skryabin, J. C. Knight, and P. St. J. Russell, “Time-spectrally-resolved ultrafast nonlinear dynamics in small-core photonic crystal fibers: Experiment and modelling,” Opt. Express12, 6499–6507 (2004).
[CrossRef]

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

D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science301, 1705–1708 (2003).
[CrossRef] [PubMed]

Skryabin, D. V.

F. Luan, D. V. Skryabin, A. V. Yulin, and J. C. Knight, “Energy exchange between colliding solitons in photonic crystal fibers,” Opt. Express14, 9844–9853 (2006).
[CrossRef] [PubMed]

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

D. V. Skryabin and A. V. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E72, 016619 (2005).
[CrossRef]

A. Efimov, A. J. Taylor, F. G. Omenetto, A. V. Yulin, N. Y. Joly, F. Biancalana, D. V. Skryabin, J. C. Knight, and P. St. J. Russell, “Time-spectrally-resolved ultrafast nonlinear dynamics in small-core photonic crystal fibers: Experiment and modelling,” Opt. Express12, 6499–6507 (2004).
[CrossRef]

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

D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science301, 1705–1708 (2003).
[CrossRef] [PubMed]

Skryabin, D.V.

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

Steinmeyer, G.

A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, “Rogue events in the group velocity horizon,” Scientific Reports2, 850 (2012).
[CrossRef] [PubMed]

A. Demircan, S. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett.106, 163901 (2011).
[CrossRef] [PubMed]

Szarniak, P.

Taylor, A. J.

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

A. Efimov, A. J. Taylor, F. G. Omenetto, A. V. Yulin, N. Y. Joly, F. Biancalana, D. V. Skryabin, J. C. Knight, and P. St. J. Russell, “Time-spectrally-resolved ultrafast nonlinear dynamics in small-core photonic crystal fibers: Experiment and modelling,” Opt. Express12, 6499–6507 (2004).
[CrossRef]

Townsend, P. D.

Yulin, A. V.

F. Luan, D. V. Skryabin, A. V. Yulin, and J. C. Knight, “Energy exchange between colliding solitons in photonic crystal fibers,” Opt. Express14, 9844–9853 (2006).
[CrossRef] [PubMed]

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

D. V. Skryabin and A. V. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E72, 016619 (2005).
[CrossRef]

A. Efimov, A. J. Taylor, F. G. Omenetto, A. V. Yulin, N. Y. Joly, F. Biancalana, D. V. Skryabin, J. C. Knight, and P. St. J. Russell, “Time-spectrally-resolved ultrafast nonlinear dynamics in small-core photonic crystal fibers: Experiment and modelling,” Opt. Express12, 6499–6507 (2004).
[CrossRef]

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

Zhavoronkov, N.

Opt. Commun. (2)

R Driben and B. A Malomed, “Suppression of crosstalk between solitons in a multi-channel split-step system,” Opt. Commun.197, 481–489 (2001)
[CrossRef]

N. N. Akhmediev and A. V. Buryak, “Interactions of solitons with oscillating tails,” Opt. Commun.121, 109–114 (1995).
[CrossRef]

Opt. Express (5)

Opt. Lett. (5)

Phys. Rev. A (1)

N. Akhmediev and M. Karlsson, “Cherenkov radiation emitted by solitons in optical fibers,” Phys. Rev. A51, 2602–2607 (1995).
[CrossRef] [PubMed]

Phys. Rev. E (2)

D. V. Skryabin and A. V. Yulin, “Theory of generation of new frequencies by mixing of solitons and dispersive waves in optical fibers,” Phys. Rev. E72, 016619 (2005).
[CrossRef]

B. A. Malomed, “Potential of interaction between two- and three-dimensional solitons,” Phys. Rev. E58, 7928–7933 (1998).
[CrossRef]

Phys. Rev. Lett. (2)

A. Demircan, S. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett.106, 163901 (2011).
[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]

Rev. Mod. Phys (1)

J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys78, 1135–1184 (2006).
[CrossRef]

Rev. Mod. Phys. (1)

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

Science (1)

D. V. Skryabin, F. Luan, J. C. Knight, and P. St. J. Russell, “Soliton self-frequency shift cancellation in photonic crystal fibers,” Science301, 1705–1708 (2003).
[CrossRef] [PubMed]

Scientific Reports (1)

A. Demircan, S. Amiranashvili, C. Brée, C. Mahnke, F. Mitschke, and G. Steinmeyer, “Rogue events in the group velocity horizon,” Scientific Reports2, 850 (2012).
[CrossRef] [PubMed]

Other (1)

G. Agrawal, Nonlinear Fiber Optics (Academic Press, New York, 2007).

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Figures (5)

Fig. 1
Fig. 1

(a) The dispersion diagram and resonances between the reflected and incident waves predicted by roots of Eq. (4), with δ = 0 corresponding to the soliton frequency. (b,c) The single event of the scattering of a dispersive pulse on the soliton for the incident pulse with frequency δr (b) and δi (c), respectively. Here, β3 = −0.015, the soliton input is A = 2 q sech ( 2 q ( t t s ) ), q = 18, ts = 10. The input for the dispersive pulse is A = I sech ( ( t t 0 ) 8 / w 8 ) e i δ r , i t, with t0 = 12, and I = 0.4w = 5 in (b) and I = 0.5, w = 12 in (c).

Fig. 2
Fig. 2

(a) The soliton collision caused by the effective attraction due to multiple scattering of dispersive waves. Initial solitons have zero frequencies and q = 12.5, the dispersive pulse is A = I sech ( t / w ) e i δ t, I = 0.25, δ = −28. (b) The change of the dispersive-pulse’s spectrum following the collision shown in (a). (c) The collision distance (zc) vs. the initial amplitude of the dispersive pulse ( I). For comparison, the best fit to dependence z c ~ 1 / I (see the text) is shown in (c) too.

Fig. 3
Fig. 3

The attraction and collision induced by the random wave field trapped between the solitons. (a) The intensity evolution in the (z, t)-plane for the solitons with zero frequency and q = 8. (b,c) Initial (z = 0) and intermediate (z = 15) time-frequency diagrams showing the solitons and dispersive waves. Density plots in (b,c) show XFROG function calculated as | + A exp ( ( t τ ) 2 / w r 2 ) exp ( i δ t ) d t | with wr = 2. The parameters are β3 = −0.025, θ = 0.18, τ1 = 0.061, and τ2 = 0.16, cf. Ref. [1].

Fig. 4
Fig. 4

The narrowing of the radiation spectrum trapped between two separating solitons. The initial solitons are taken with q = 12.5 and frequencies δ = 1.5, δ = 0. (a) The dispersion diagram showing the scattering cascade. (b,c) The evolution in the temporal and frequency domains. In this case, β3 = −0.01.

Fig. 5
Fig. 5

The same as in Fig. 4, but for expansion of the radiation spectrum trapped between two separating solitons. The initial solitons are taken with q = 18 and frequencies δ = −0.3, δ = 0.3.

Equations (4)

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i z A + 1 2 t 2 A i β 3 6 t 3 A + ( 1 θ ) | A | 2 A + A + R ( t ) | A ( t t ) | 2 d t = 0 ,
R = θ τ 1 2 + τ 2 2 τ 1 τ 2 2 Θ ( t ) exp ( t τ 2 ) sin ( t τ 1 ) .
k ( δ r ) = k s ( δ r ) [ k s ( δ i ) k ( δ i ) ] ,
z δ s ( δ i δ r ) I | k i | / Q s .

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