Abstract

We demonstrate that the optical event horizon can provide an effective technique to actively control the propagation properties of a dark soliton with another weak probe wave. Careful power adjustment of the probe wave enables the black soliton converted into a gray one with varying grayness through the nonlinear interaction, corresponding to a nearly adiabatic variation of the soliton’s speed. The sign of the phase angle for the newly formed gray soliton at optical event horizon is significantly dependent on the frequency of the launched probe wave. Linear-stability analysis of dark solitons under the perturbation of a weak probe wave is performed to clarify the intrinsic mechanism of the nonlinear interaction. The probe wave manipulated collisional dynamics between both dark solitons are investigated as an analogue of the combined white-hole and black-hole horizons which provides some insights into exploring the transition between integrable and non-integrable systems.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  37. W. M. Cao and B. Y. Guo, “Fourier collocation method for solving nonlinear Klein-Gordon equation,” J. Comput. Phys. 108(2), 296–305 (1993).
    [Crossref]
  38. D. E. Pelinovsky and P. G. Kevrekidis, “Dark solitons in external potentials,” Z. Angew. Math. Phys. 59(4), 559–599 (2008).
    [Crossref]
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    [Crossref] [PubMed]

2018 (1)

2017 (4)

C. Milián, T. Marest, A. Kudlinski, and D. V. Skryabin, “Spectral wings of the fiber supercontinuum and the dark-bright soliton interaction,” Opt. Express 25(9), 10494–10499 (2017).
[Crossref] [PubMed]

M. Sciacca, C. F. Barenghi, and N. G. Parker, “Matter-wave dark solitons in boxlike traps,” Phys. Rev. A 95(1), 013628 (2017).
[Crossref]

Z. X. Deng, J. Liu, X. W. Huang, C. J. Zhao, and X. L. Wang, “Active control of adiabatic soliton fission by external dispersive wave at optical event horizon,” Opt. Express 25(2–3), 28556–28566 (2017).
[Crossref]

M. A. Gaafar, A. Y. Petrov, and M. Eich, “Free carrier front induced indirect photonic transitions: A new paradigm for frequency manipulation on chip,” ACS Photonics 4(11), 2751–2758 (2017).
[Crossref]

2016 (7)

2015 (7)

2014 (2)

K. E. Webb, M. Erkintalo, Y. Xu, N. G. Broderick, J. M. Dudley, G. Genty, and S. G. Murdoch, “Nonlinear optics of fibre event horizons,” Nat. Commun. 5(1), 4969 (2014).
[Crossref] [PubMed]

J. H. Nguyen, P. Dyke, D. Luo, B. A. Malomed, and R. G. Hulet, “Collisions of matter-wave solitons,” Nat. Phys. 10(12), 918 (2014).
[Crossref]

2013 (3)

A. Demircan, S. Amiranashvili, C. Brée, and G. Steinmeyer, “Compressible octave spanning supercontinuum generation by two-pulse collisions,” Phys. Rev. Lett. 110(23), 233901 (2013).
[Crossref] [PubMed]

A. V. Yulin, R. Driben, B. A. Malomed, and D. V. Skryabin, “Soliton interaction mediated by cascaded four wave mixing with dispersive waves,” Opt. Express 21(12), 14481–14486 (2013).
[Crossref] [PubMed]

S. Batz and U. Peschel, “Diametrically driven self-accelerating pulses in a photonic crystal fiber,” Phys. Rev. Lett. 110(19), 193901 (2013).
[Crossref] [PubMed]

2012 (1)

2011 (1)

A. Demircan, Sh. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett. 106(16), 163901 (2011).
[Crossref] [PubMed]

2010 (3)

D. V. Skryabin and A. V. Gorbach, “Colloquium: Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82(2), 1287–1299 (2010).
[Crossref]

S. Robertson and U. Leonhardt, “Frequency shifting at fiber-optical event horizons: the effect of Raman deceleration,” Phys. Rev. A 81(6), 063835 (2010).
[Crossref]

D. J. Frantzeskakis, “Dark solitons in atomic Bose-Einstein condensates: From theory to experiments,” J. Phys. A Math. Theor. 43(21), 213001 (2010).
[Crossref]

2009 (1)

2008 (2)

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319(5868), 1367–1370 (2008).
[Crossref] [PubMed]

D. E. Pelinovsky and P. G. Kevrekidis, “Dark solitons in external potentials,” Z. Angew. Math. Phys. 59(4), 559–599 (2008).
[Crossref]

2005 (1)

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(21), 213902 (2005).
[Crossref] [PubMed]

2002 (1)

A. Muryshev, G. V. Shlyapnikov, W. Ertmer, K. Sengstock, and M. Lewenstein, “Dynamics of dark solitons in elongated Bose-Einstein condensates,” Phys. Rev. Lett. 89(11), 110401 (2002).
[Crossref] [PubMed]

2001 (1)

A. Mahalingam and K. Porsezian, “Propagation of dark solitons with higher-order effects in optical fibers,” Phys. Rev. E 64(4), 046608 (2001).
[Crossref] [PubMed]

1998 (1)

Y. S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Phys. Rep. 298(2/3), 81–197 (1998).
[Crossref]

1996 (1)

1993 (1)

W. M. Cao and B. Y. Guo, “Fourier collocation method for solving nonlinear Klein-Gordon equation,” J. Comput. Phys. 108(2), 296–305 (1993).
[Crossref]

1991 (1)

1987 (1)

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, and A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62(6), 374–379 (1987).
[Crossref]

1973 (1)

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion,” Appl. Phys. Lett. 23(4), 171–172 (1973).
[Crossref]

Afanasjev, V. V.

Amiranashvili, S.

S. Pickartz, U. Bandelow, and S. Amiranashvili, “Adiabatic theory of solitons fed by dispersive waves,” Phys. Rev. A 94(3), 033811 (2016).
[Crossref]

A. Demircan, S. Amiranashvili, C. Brée, and G. Steinmeyer, “Compressible octave spanning supercontinuum generation by two-pulse collisions,” Phys. Rev. Lett. 110(23), 233901 (2013).
[Crossref] [PubMed]

Amiranashvili, Sh.

A. Demircan, Sh. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett. 106(16), 163901 (2011).
[Crossref] [PubMed]

Arabí, C. M.

T. Marest, C. M. Arabí, M. Conforti, A. Mussot, C. Milián, D. V. Skryabin, and A. Kudlinski, “Grayness-dependent emission of dispersive waves from dark solitons in optical fibers,” Opt. Lett. 43(7), 1511–1514 (2018).
[Crossref] [PubMed]

C. M. Arabí, F. Bessin, A. Kudlinski, A. Mussot, D. Skryabin, and M. Conforti, “Efficiency of four-wave mixing between orthogonally polarized linear waves and solitons in a birefringent fiber,” Phys. Rev. A 94(6), 063847 (2016).
[Crossref]

Bache, M.

Bandelow, U.

S. Pickartz, U. Bandelow, and S. Amiranashvili, “Adiabatic theory of solitons fed by dispersive waves,” Phys. Rev. A 94(3), 033811 (2016).
[Crossref]

Barenghi, C. F.

M. Sciacca, C. F. Barenghi, and N. G. Parker, “Matter-wave dark solitons in boxlike traps,” Phys. Rev. A 95(1), 013628 (2017).
[Crossref]

Barthelemy, A.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, and A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62(6), 374–379 (1987).
[Crossref]

Batz, S.

S. Batz and U. Peschel, “Diametrically driven self-accelerating pulses in a photonic crystal fiber,” Phys. Rev. Lett. 110(19), 193901 (2013).
[Crossref] [PubMed]

Bendahmane, A.

S. F. Wang, A. Mussot, M. Conforti, A. Bendahmane, X. L. Zeng, and A. Kudlinski, “Optical event horizons from the collision of a soliton and its own dispersive wave,” Phys. Rev. A 92(2), 023837 (2015).
[Crossref]

A. Bendahmane, A. Mussot, M. Conforti, and A. Kudlinski, “Observation of the stepwise blue shift of a dispersive wave preceding its trapping by a soliton,” Opt. Express 23(13), 16595–16601 (2015).
[Crossref] [PubMed]

Bessin, F.

C. M. Arabí, F. Bessin, A. Kudlinski, A. Mussot, D. Skryabin, and M. Conforti, “Efficiency of four-wave mixing between orthogonally polarized linear waves and solitons in a birefringent fiber,” Phys. Rev. A 94(6), 063847 (2016).
[Crossref]

Brée, C.

A. Demircan, S. Amiranashvili, C. Brée, and G. Steinmeyer, “Compressible octave spanning supercontinuum generation by two-pulse collisions,” Phys. Rev. Lett. 110(23), 233901 (2013).
[Crossref] [PubMed]

Broderick, N. G.

K. E. Webb, M. Erkintalo, Y. Xu, N. G. Broderick, J. M. Dudley, G. Genty, and S. G. Murdoch, “Nonlinear optics of fibre event horizons,” Nat. Commun. 5(1), 4969 (2014).
[Crossref] [PubMed]

Cao, W. M.

W. M. Cao and B. Y. Guo, “Fourier collocation method for solving nonlinear Klein-Gordon equation,” J. Comput. Phys. 108(2), 296–305 (1993).
[Crossref]

Choudhary, A.

Conforti, M.

Demircan, A.

A. Demircan, S. Amiranashvili, C. Brée, and G. Steinmeyer, “Compressible octave spanning supercontinuum generation by two-pulse collisions,” Phys. Rev. Lett. 110(23), 233901 (2013).
[Crossref] [PubMed]

A. Demircan, Sh. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett. 106(16), 163901 (2011).
[Crossref] [PubMed]

Deng, Z.

Deng, Z. X.

Driben, R.

Dudley, J. M.

K. E. Webb, M. Erkintalo, Y. Xu, N. G. Broderick, J. M. Dudley, G. Genty, and S. G. Murdoch, “Nonlinear optics of fibre event horizons,” Nat. Commun. 5(1), 4969 (2014).
[Crossref] [PubMed]

Dyke, P.

J. H. Nguyen, P. Dyke, D. Luo, B. A. Malomed, and R. G. Hulet, “Collisions of matter-wave solitons,” Nat. Phys. 10(12), 918 (2014).
[Crossref]

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(21), 213902 (2005).
[Crossref] [PubMed]

Eich, M.

M. A. Gaafar, A. Y. Petrov, and M. Eich, “Free carrier front induced indirect photonic transitions: A new paradigm for frequency manipulation on chip,” ACS Photonics 4(11), 2751–2758 (2017).
[Crossref]

Emplit, P.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, and A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62(6), 374–379 (1987).
[Crossref]

Erkintalo, M.

K. E. Webb, M. Erkintalo, Y. Xu, N. G. Broderick, J. M. Dudley, G. Genty, and S. G. Murdoch, “Nonlinear optics of fibre event horizons,” Nat. Commun. 5(1), 4969 (2014).
[Crossref] [PubMed]

Ertmer, W.

A. Muryshev, G. V. Shlyapnikov, W. Ertmer, K. Sengstock, and M. Lewenstein, “Dynamics of dark solitons in elongated Bose-Einstein condensates,” Phys. Rev. Lett. 89(11), 110401 (2002).
[Crossref] [PubMed]

Ferrando, A.

Frantzeskakis, D. J.

D. J. Frantzeskakis, “Dark solitons in atomic Bose-Einstein condensates: From theory to experiments,” J. Phys. A Math. Theor. 43(21), 213001 (2010).
[Crossref]

Froehly, C.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, and A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62(6), 374–379 (1987).
[Crossref]

Fu, X.

Fu, X. Q.

Gaafar, M. A.

M. A. Gaafar, A. Y. Petrov, and M. Eich, “Free carrier front induced indirect photonic transitions: A new paradigm for frequency manipulation on chip,” ACS Photonics 4(11), 2751–2758 (2017).
[Crossref]

Genty, G.

K. E. Webb, M. Erkintalo, Y. Xu, N. G. Broderick, J. M. Dudley, G. Genty, and S. G. Murdoch, “Nonlinear optics of fibre event horizons,” Nat. Commun. 5(1), 4969 (2014).
[Crossref] [PubMed]

Gorbach, A. V.

D. V. Skryabin and A. V. Gorbach, “Colloquium: Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82(2), 1287–1299 (2010).
[Crossref]

Guo, B. Y.

W. M. Cao and B. Y. Guo, “Fourier collocation method for solving nonlinear Klein-Gordon equation,” J. Comput. Phys. 108(2), 296–305 (1993).
[Crossref]

Guo, H.

Hamaide, J. P.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, and A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62(6), 374–379 (1987).
[Crossref]

Hasegawa, A.

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion,” Appl. Phys. Lett. 23(4), 171–172 (1973).
[Crossref]

Hill, S.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319(5868), 1367–1370 (2008).
[Crossref] [PubMed]

Huang, X. W.

Hulet, R. G.

J. H. Nguyen, P. Dyke, D. Luo, B. A. Malomed, and R. G. Hulet, “Collisions of matter-wave solitons,” Nat. Phys. 10(12), 918 (2014).
[Crossref]

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(21), 213902 (2005).
[Crossref] [PubMed]

Kamalakis, T.

Kanakis, P.

Kelleher, E. J. R.

R. I. Woodward and E. J. R. Kelleher, “Dark solitons in laser radiation build-up dynamics,” Phys Rev E 93(3), 032221 (2016).
[Crossref] [PubMed]

Kevrekidis, P. G.

D. E. Pelinovsky and P. G. Kevrekidis, “Dark solitons in external potentials,” Z. Angew. Math. Phys. 59(4), 559–599 (2008).
[Crossref]

Kivshar, Y. S.

Y. S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Phys. Rep. 298(2/3), 81–197 (1998).
[Crossref]

V. V. Afanasjev, C. R. Menyuk, and Y. S. Kivshar, “Effect of third-order dispersion on dark solitons,” Opt. Lett. 21(24), 1975–1977 (1996).
[Crossref] [PubMed]

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(21), 213902 (2005).
[Crossref] [PubMed]

König, F.

A. Choudhary and F. König, “Efficient frequency shifting of dispersive waves at solitons,” Opt. Express 20(5), 5538–5546 (2012).
[Crossref] [PubMed]

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319(5868), 1367–1370 (2008).
[Crossref] [PubMed]

Kudlinski, A.

T. Marest, C. M. Arabí, M. Conforti, A. Mussot, C. Milián, D. V. Skryabin, and A. Kudlinski, “Grayness-dependent emission of dispersive waves from dark solitons in optical fibers,” Opt. Lett. 43(7), 1511–1514 (2018).
[Crossref] [PubMed]

C. Milián, T. Marest, A. Kudlinski, and D. V. Skryabin, “Spectral wings of the fiber supercontinuum and the dark-bright soliton interaction,” Opt. Express 25(9), 10494–10499 (2017).
[Crossref] [PubMed]

T. Marest, C. Mas Arabí, M. Conforti, A. Mussot, C. Milián, D. V. Skryabin, and A. Kudlinski, “Emission of dispersive waves from a train of dark solitons in optical fibers,” Opt. Lett. 41(11), 2454–2457 (2016).
[Crossref] [PubMed]

C. M. Arabí, F. Bessin, A. Kudlinski, A. Mussot, D. Skryabin, and M. Conforti, “Efficiency of four-wave mixing between orthogonally polarized linear waves and solitons in a birefringent fiber,” Phys. Rev. A 94(6), 063847 (2016).
[Crossref]

S. F. Wang, A. Mussot, M. Conforti, A. Bendahmane, X. L. Zeng, and A. Kudlinski, “Optical event horizons from the collision of a soliton and its own dispersive wave,” Phys. Rev. A 92(2), 023837 (2015).
[Crossref]

A. Bendahmane, A. Mussot, M. Conforti, and A. Kudlinski, “Observation of the stepwise blue shift of a dispersive wave preceding its trapping by a soliton,” Opt. Express 23(13), 16595–16601 (2015).
[Crossref] [PubMed]

S. F. Wang, A. Mussot, M. Conforti, X. L. Zeng, and A. Kudlinski, “Bouncing of a dispersive wave in a solitonic cage,” Opt. Lett. 40(14), 3320–3323 (2015).
[Crossref] [PubMed]

Kuklewicz, C.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319(5868), 1367–1370 (2008).
[Crossref] [PubMed]

Leonhardt, U.

S. Robertson and U. Leonhardt, “Frequency shifting at fiber-optical event horizons: the effect of Raman deceleration,” Phys. Rev. A 81(6), 063835 (2010).
[Crossref]

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319(5868), 1367–1370 (2008).
[Crossref] [PubMed]

Lewenstein, M.

A. Muryshev, G. V. Shlyapnikov, W. Ertmer, K. Sengstock, and M. Lewenstein, “Dynamics of dark solitons in elongated Bose-Einstein condensates,” Phys. Rev. Lett. 89(11), 110401 (2002).
[Crossref] [PubMed]

Liu, J.

Liu, X.

Luo, D.

J. H. Nguyen, P. Dyke, D. Luo, B. A. Malomed, and R. G. Hulet, “Collisions of matter-wave solitons,” Nat. Phys. 10(12), 918 (2014).
[Crossref]

Luther-Davies, B.

Y. S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Phys. Rep. 298(2/3), 81–197 (1998).
[Crossref]

Mahalingam, A.

A. Mahalingam and K. Porsezian, “Propagation of dark solitons with higher-order effects in optical fibers,” Phys. Rev. E 64(4), 046608 (2001).
[Crossref] [PubMed]

Malomed, B. A.

Marest, T.

Mas Arabí, C.

Menyuk, C. R.

Milián, C.

Murdoch, S. G.

K. E. Webb, M. Erkintalo, Y. Xu, N. G. Broderick, J. M. Dudley, G. Genty, and S. G. Murdoch, “Nonlinear optics of fibre event horizons,” Nat. Commun. 5(1), 4969 (2014).
[Crossref] [PubMed]

Muryshev, A.

A. Muryshev, G. V. Shlyapnikov, W. Ertmer, K. Sengstock, and M. Lewenstein, “Dynamics of dark solitons in elongated Bose-Einstein condensates,” Phys. Rev. Lett. 89(11), 110401 (2002).
[Crossref] [PubMed]

Mussot, A.

Nguyen, J. H.

J. H. Nguyen, P. Dyke, D. Luo, B. A. Malomed, and R. G. Hulet, “Collisions of matter-wave solitons,” Nat. Phys. 10(12), 918 (2014).
[Crossref]

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(21), 213902 (2005).
[Crossref] [PubMed]

Oreshnikov, I.

Parker, N. G.

M. Sciacca, C. F. Barenghi, and N. G. Parker, “Matter-wave dark solitons in boxlike traps,” Phys. Rev. A 95(1), 013628 (2017).
[Crossref]

Pelinovsky, D. E.

D. E. Pelinovsky and P. G. Kevrekidis, “Dark solitons in external potentials,” Z. Angew. Math. Phys. 59(4), 559–599 (2008).
[Crossref]

Peschel, U.

S. Batz and U. Peschel, “Diametrically driven self-accelerating pulses in a photonic crystal fiber,” Phys. Rev. Lett. 110(19), 193901 (2013).
[Crossref] [PubMed]

Petrov, A. Y.

M. A. Gaafar, A. Y. Petrov, and M. Eich, “Free carrier front induced indirect photonic transitions: A new paradigm for frequency manipulation on chip,” ACS Photonics 4(11), 2751–2758 (2017).
[Crossref]

Philbin, T. G.

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319(5868), 1367–1370 (2008).
[Crossref] [PubMed]

Pickartz, S.

S. Pickartz, U. Bandelow, and S. Amiranashvili, “Adiabatic theory of solitons fed by dispersive waves,” Phys. Rev. A 94(3), 033811 (2016).
[Crossref]

Porsezian, K.

A. Mahalingam and K. Porsezian, “Propagation of dark solitons with higher-order effects in optical fibers,” Phys. Rev. E 64(4), 046608 (2001).
[Crossref] [PubMed]

Reynaud, F.

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, and A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62(6), 374–379 (1987).
[Crossref]

Robertson, S.

S. Robertson and U. Leonhardt, “Frequency shifting at fiber-optical event horizons: the effect of Raman deceleration,” Phys. Rev. A 81(6), 063835 (2010).
[Crossref]

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319(5868), 1367–1370 (2008).
[Crossref] [PubMed]

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(21), 213902 (2005).
[Crossref] [PubMed]

Sciacca, M.

M. Sciacca, C. F. Barenghi, and N. G. Parker, “Matter-wave dark solitons in boxlike traps,” Phys. Rev. A 95(1), 013628 (2017).
[Crossref]

Sengstock, K.

A. Muryshev, G. V. Shlyapnikov, W. Ertmer, K. Sengstock, and M. Lewenstein, “Dynamics of dark solitons in elongated Bose-Einstein condensates,” Phys. Rev. Lett. 89(11), 110401 (2002).
[Crossref] [PubMed]

Shi, X. H.

Shlyapnikov, G. V.

A. Muryshev, G. V. Shlyapnikov, W. Ertmer, K. Sengstock, and M. Lewenstein, “Dynamics of dark solitons in elongated Bose-Einstein condensates,” Phys. Rev. Lett. 89(11), 110401 (2002).
[Crossref] [PubMed]

Skryabin, D.

C. M. Arabí, F. Bessin, A. Kudlinski, A. Mussot, D. Skryabin, and M. Conforti, “Efficiency of four-wave mixing between orthogonally polarized linear waves and solitons in a birefringent fiber,” Phys. Rev. A 94(6), 063847 (2016).
[Crossref]

Skryabin, D. V.

Steinmeyer, G.

A. Demircan, S. Amiranashvili, C. Brée, and G. Steinmeyer, “Compressible octave spanning supercontinuum generation by two-pulse collisions,” Phys. Rev. Lett. 110(23), 233901 (2013).
[Crossref] [PubMed]

A. Demircan, Sh. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett. 106(16), 163901 (2011).
[Crossref] [PubMed]

Tan, C.

Tappert, F.

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion,” Appl. Phys. Lett. 23(4), 171–172 (1973).
[Crossref]

Tartara, L.

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(21), 213902 (2005).
[Crossref] [PubMed]

Thurston, R. N.

Wang, S. F.

S. F. Wang, A. Mussot, M. Conforti, X. L. Zeng, and A. Kudlinski, “Bouncing of a dispersive wave in a solitonic cage,” Opt. Lett. 40(14), 3320–3323 (2015).
[Crossref] [PubMed]

S. F. Wang, A. Mussot, M. Conforti, A. Bendahmane, X. L. Zeng, and A. Kudlinski, “Optical event horizons from the collision of a soliton and its own dispersive wave,” Phys. Rev. A 92(2), 023837 (2015).
[Crossref]

Wang, X. L.

Webb, K. E.

K. E. Webb, M. Erkintalo, Y. Xu, N. G. Broderick, J. M. Dudley, G. Genty, and S. G. Murdoch, “Nonlinear optics of fibre event horizons,” Nat. Commun. 5(1), 4969 (2014).
[Crossref] [PubMed]

Weiner, A. M.

Wen, S.

Woodward, R. I.

R. I. Woodward and E. J. R. Kelleher, “Dark solitons in laser radiation build-up dynamics,” Phys Rev E 93(3), 032221 (2016).
[Crossref] [PubMed]

Xu, Y.

K. E. Webb, M. Erkintalo, Y. Xu, N. G. Broderick, J. M. Dudley, G. Genty, and S. G. Murdoch, “Nonlinear optics of fibre event horizons,” Nat. Commun. 5(1), 4969 (2014).
[Crossref] [PubMed]

Yulin, A. V.

Zeng, X. L.

S. F. Wang, A. Mussot, M. Conforti, A. Bendahmane, X. L. Zeng, and A. Kudlinski, “Optical event horizons from the collision of a soliton and its own dispersive wave,” Phys. Rev. A 92(2), 023837 (2015).
[Crossref]

S. F. Wang, A. Mussot, M. Conforti, X. L. Zeng, and A. Kudlinski, “Bouncing of a dispersive wave in a solitonic cage,” Opt. Lett. 40(14), 3320–3323 (2015).
[Crossref] [PubMed]

Zhao, C.

Zhao, C. J.

Zhou, B.

ACS Photonics (1)

M. A. Gaafar, A. Y. Petrov, and M. Eich, “Free carrier front induced indirect photonic transitions: A new paradigm for frequency manipulation on chip,” ACS Photonics 4(11), 2751–2758 (2017).
[Crossref]

Appl. Phys. Lett. (1)

A. Hasegawa and F. Tappert, “Transmission of stationary nonlinear optical pulses in dispersive dielectric fibers. II. Normal dispersion,” Appl. Phys. Lett. 23(4), 171–172 (1973).
[Crossref]

J. Comput. Phys. (1)

W. M. Cao and B. Y. Guo, “Fourier collocation method for solving nonlinear Klein-Gordon equation,” J. Comput. Phys. 108(2), 296–305 (1993).
[Crossref]

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

J. Phys. A Math. Theor. (1)

D. J. Frantzeskakis, “Dark solitons in atomic Bose-Einstein condensates: From theory to experiments,” J. Phys. A Math. Theor. 43(21), 213001 (2010).
[Crossref]

Nat. Commun. (1)

K. E. Webb, M. Erkintalo, Y. Xu, N. G. Broderick, J. M. Dudley, G. Genty, and S. G. Murdoch, “Nonlinear optics of fibre event horizons,” Nat. Commun. 5(1), 4969 (2014).
[Crossref] [PubMed]

Nat. Phys. (1)

J. H. Nguyen, P. Dyke, D. Luo, B. A. Malomed, and R. G. Hulet, “Collisions of matter-wave solitons,” Nat. Phys. 10(12), 918 (2014).
[Crossref]

Opt. Commun. (1)

P. Emplit, J. P. Hamaide, F. Reynaud, C. Froehly, and A. Barthelemy, “Picosecond steps and dark pulses through nonlinear single mode fibers,” Opt. Commun. 62(6), 374–379 (1987).
[Crossref]

Opt. Express (6)

Opt. Lett. (9)

I. Oreshnikov, R. Driben, and A. V. Yulin, “Weak and strong interactions between dark solitons and dispersive waves,” Opt. Lett. 40(21), 4871–4874 (2015).
[Crossref] [PubMed]

I. Oreshnikov, R. Driben, and A. V. Yulin, “Interaction of high-order solitons with external dispersive waves,” Opt. Lett. 40(23), 5554–5557 (2015).
[Crossref] [PubMed]

S. F. Wang, A. Mussot, M. Conforti, X. L. Zeng, and A. Kudlinski, “Bouncing of a dispersive wave in a solitonic cage,” Opt. Lett. 40(14), 3320–3323 (2015).
[Crossref] [PubMed]

P. Kanakis and T. Kamalakis, “Enabling transistor-like action in photonic crystal waveguides using optical event horizons,” Opt. Lett. 41(7), 1372–1375 (2016).
[Crossref] [PubMed]

C. Milián, D. V. Skryabin, and A. Ferrando, “Continuum generation by dark solitons,” Opt. Lett. 34(14), 2096–2098 (2009).
[Crossref] [PubMed]

T. Marest, C. Mas Arabí, M. Conforti, A. Mussot, C. Milián, D. V. Skryabin, and A. Kudlinski, “Emission of dispersive waves from a train of dark solitons in optical fibers,” Opt. Lett. 41(11), 2454–2457 (2016).
[Crossref] [PubMed]

T. Marest, C. M. Arabí, M. Conforti, A. Mussot, C. Milián, D. V. Skryabin, and A. Kudlinski, “Grayness-dependent emission of dispersive waves from dark solitons in optical fibers,” Opt. Lett. 43(7), 1511–1514 (2018).
[Crossref] [PubMed]

V. V. Afanasjev, C. R. Menyuk, and Y. S. Kivshar, “Effect of third-order dispersion on dark solitons,” Opt. Lett. 21(24), 1975–1977 (1996).
[Crossref] [PubMed]

X. Liu, B. Zhou, H. Guo, and M. Bache, “Mid-IR femtosecond frequency conversion by soliton-probe collision in phase-mismatched quadratic nonlinear crystals,” Opt. Lett. 40(16), 3798–3801 (2015).
[Crossref] [PubMed]

Phys Rev E (1)

R. I. Woodward and E. J. R. Kelleher, “Dark solitons in laser radiation build-up dynamics,” Phys Rev E 93(3), 032221 (2016).
[Crossref] [PubMed]

Phys. Rep. (1)

Y. S. Kivshar and B. Luther-Davies, “Dark optical solitons: physics and applications,” Phys. Rep. 298(2/3), 81–197 (1998).
[Crossref]

Phys. Rev. A (5)

S. Robertson and U. Leonhardt, “Frequency shifting at fiber-optical event horizons: the effect of Raman deceleration,” Phys. Rev. A 81(6), 063835 (2010).
[Crossref]

M. Sciacca, C. F. Barenghi, and N. G. Parker, “Matter-wave dark solitons in boxlike traps,” Phys. Rev. A 95(1), 013628 (2017).
[Crossref]

C. M. Arabí, F. Bessin, A. Kudlinski, A. Mussot, D. Skryabin, and M. Conforti, “Efficiency of four-wave mixing between orthogonally polarized linear waves and solitons in a birefringent fiber,” Phys. Rev. A 94(6), 063847 (2016).
[Crossref]

S. Pickartz, U. Bandelow, and S. Amiranashvili, “Adiabatic theory of solitons fed by dispersive waves,” Phys. Rev. A 94(3), 033811 (2016).
[Crossref]

S. F. Wang, A. Mussot, M. Conforti, A. Bendahmane, X. L. Zeng, and A. Kudlinski, “Optical event horizons from the collision of a soliton and its own dispersive wave,” Phys. Rev. A 92(2), 023837 (2015).
[Crossref]

Phys. Rev. E (1)

A. Mahalingam and K. Porsezian, “Propagation of dark solitons with higher-order effects in optical fibers,” Phys. Rev. E 64(4), 046608 (2001).
[Crossref] [PubMed]

Phys. Rev. Lett. (5)

A. Muryshev, G. V. Shlyapnikov, W. Ertmer, K. Sengstock, and M. Lewenstein, “Dynamics of dark solitons in elongated Bose-Einstein condensates,” Phys. Rev. Lett. 89(11), 110401 (2002).
[Crossref] [PubMed]

S. Batz and U. Peschel, “Diametrically driven self-accelerating pulses in a photonic crystal fiber,” Phys. Rev. Lett. 110(19), 193901 (2013).
[Crossref] [PubMed]

A. Demircan, Sh. Amiranashvili, and G. Steinmeyer, “Controlling light by light with an optical event horizon,” Phys. Rev. Lett. 106(16), 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(21), 213902 (2005).
[Crossref] [PubMed]

A. Demircan, S. Amiranashvili, C. Brée, and G. Steinmeyer, “Compressible octave spanning supercontinuum generation by two-pulse collisions,” Phys. Rev. Lett. 110(23), 233901 (2013).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

D. V. Skryabin and A. V. Gorbach, “Colloquium: Looking at a soliton through the prism of optical supercontinuum,” Rev. Mod. Phys. 82(2), 1287–1299 (2010).
[Crossref]

Science (1)

T. G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König, and U. Leonhardt, “Fiber-optical analog of the event horizon,” Science 319(5868), 1367–1370 (2008).
[Crossref] [PubMed]

Z. Angew. Math. Phys. (1)

D. E. Pelinovsky and P. G. Kevrekidis, “Dark solitons in external potentials,” Z. Angew. Math. Phys. 59(4), 559–599 (2008).
[Crossref]

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Figures (7)

Fig. 1
Fig. 1 Definition of a dark soliton, showing the relative intensity (a) and phase (b) of a black soliton (G = 1) and two gray solitons (G = 0.8 and 0.5). G denotes the soliton grayness. The remaining parameters are fixed to T 0 =0, A 0 =1.
Fig. 2
Fig. 2 Wavenumber and corresponding retarded-frame group-velocity as a function of angular frequency, illustrating how phase-matched probe-idler pairs experience group-velocities with opposite signs relative to soliton. In the soliton-probe wave interaction process, both the frequencies of the probe and idler waves are swapped. In the retarded reference frame, optical waves with frequencies falling in the green (orange)-shaded area propagate more slowly (quickly) than the dark soliton. DW: dispersive wave generated by the phase-matched resonant excitation.
Fig. 3
Fig. 3 Numerical results of the manipulated propagation of a dark soliton (186 W) using probe waves with different initial frequencies with a same peak power of 2 W (Left panels: probe wave with frequency located in the green-shaded area; right panels: frequency of probe wave in the yellow-shaded area). Red dotted lines in (a, b) indicate the reference lines for the horizon-induced temporal displacement of the dark soliton. Red and blue curves in (c, d) represent the resulting output dark soliton profiles before and after the collision between the dark soliton and the probe wave, respectively.
Fig. 4
Fig. 4 Output dark pulse profiles for the analogue of white-hole horizon as the peak power of the probe wave is varied, showing that both the soliton decay and the time shift between the dark solitons before and after their interaction with the probe wave can be controlled by adjusting the peak power of the probe wave.
Fig. 5
Fig. 5 (a) Corresponding spectral plane ( κ r , κ i )of the eigenvalues. It shows a pair of imaginary eigenvalues demonstrating the dynamical instability of the dark soliton solution. (b) the imaginary part of the eigenvalue κ i as a function ofε. Solid red curve represents the analytical prediction while blue circles correspond to the numerical results.
Fig. 6
Fig. 6 (a) Density maps of the temporal evolution of interaction between two dark solitons and dual-probe waves in an optical fiber. The collision between both dark solitons will occur due to an acceleration or deceleration of them induced by the probe wave at optical event horizon; (b) magnified collision region; (c) illustration on how the dark solitons pass through each other, involving undergoing a time shift but maintaining their direction (different colours are used to define each soliton).
Fig. 7
Fig. 7 Position of dark soliton-soliton collision and the collision-induced time shifting for both solitons as a function of the peak power of the probe wave. The red-filled circle lines correspond to the collision position of both dark solitons while the temporal shift of solitons induced by twin-soliton collision is shown by the blue-filled circle lines.

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

A(z,T) z =iD(i T )A(z,T)+iγ|A(z,T) | 2 A(z,T).
A(T)= A ds (T)+ A p (T),
A p (T)= P p exp[ ( T t 1 T 1 ) 2 ]exp(iΔωT)
A ds (T)= A 0 { cosϕtanh[ A 0 cosϕ(T T 0 )]+isinϕ }
A ds (T)= A 0 tanh[ A 0 (T T 0 )],
τ=T A 0 ,ξ=z/ L D ,U(ξ,τ)=A(z,T)/ A 0 ,
i U ξ 1 2 2 U τ 2 +|U | 2 U=εV(τ)U,
V(τ)R( D r / L fiber )| A p (τ) | 2 ,
U(ξ,τ)= e iξ [ ν s (τ)+δ(b(τ) e iκξ + c ¯ (τ) e i κ ¯ ξ )],
Lψ=κψ,
L=( 1 2 τ 2 +εV(τ)1+2 ν s 2 ν s 2 ν s 2 1 2 τ 2 εV(τ)+12 ν s 2 ),ψ=( b c )
M (s)= + V τ [ 1tan h 2 (τs) ]dτ
λ 2 + ε 4 M ( s 0 )( 1 λ 2 )=O( ε 2 ),
M ( s 0 )=2 + V τ tanh(τ s 0 )sec h 2 (τ s 0 )dτ
A(0,T)= P p { exp[ ( T+ t 1 T 1 ) 2 ]exp(iΔ ω 1 T)+exp[ ( T t 1 T 1 ) 2 ]exp(iΔ ω 2 T) }+ A ds2 (T)
A ds2 (T)= u 0 tanh[ u 0 (T+ t 2 )],
A ds2 (T)= u 0 tanh[ u 0 (T t 2 )],

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