Abstract

We investigate the resonant interaction of two optical pulses of the same group velocity with a pump pulse of different velocity in a weakly dispersive quadratic medium and report on the complementary rogue wave dynamics which are unique to such a parametric three-wave mixing. Analytic rogue wave solutions up to the second order are explicitly presented and their robustness is confirmed by numerical simulations, in spite of the onset of modulation instability activated by quantum noise.

© 2016 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref]
  4. C. Lecaplain, Ph. Grelu, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative rogue waves generated by chaotic pulse bunching in a mode-locked laser,” Phys. Rev. Lett. 108, 233901 (2012).
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  5. S. Birkholz, E. T. J. Nibbering, C. Bree, S. Skupin, A. Demircan, G. Genty, and G. Steinmeyer, “Spatiotemporal rogue events in optical multiple filamentation,” Phys. Rev. Lett. 111, 243903 (2013).
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  6. F. Selmi, S. Coulibaly, Z. Loghmari, I. Sagnes, G. Beaudoin, M. G. Clerc, and S. Barbay, “Spatiotemporal chaos induces extreme events in an extended microcavity laser,” Phys. Rev. Lett. 116, 013901 (2016).
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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  37. S. Toenger, T. Godin, C. Billet, F. Dias, M. Erkintalo, G. Genty, and J. M. Dudley, “Emergent rogue wave structures and statistics in spontaneous modulation instability,” Sci. Rep. 5, 10380 (2015).
    [Crossref] [PubMed]
  38. B. Frisquet, B. Kibler, Ph. Morin, F. Baronio, M. Conforti, G. Millot, and S. Wabnitz, “Optical dark rogue wave,” Sci. Rep. 6, 20785 (2016).
    [Crossref] [PubMed]
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    [Crossref]

2016 (2)

F. Selmi, S. Coulibaly, Z. Loghmari, I. Sagnes, G. Beaudoin, M. G. Clerc, and S. Barbay, “Spatiotemporal chaos induces extreme events in an extended microcavity laser,” Phys. Rev. Lett. 116, 013901 (2016).
[Crossref] [PubMed]

B. Frisquet, B. Kibler, Ph. Morin, F. Baronio, M. Conforti, G. Millot, and S. Wabnitz, “Optical dark rogue wave,” Sci. Rep. 6, 20785 (2016).
[Crossref] [PubMed]

2015 (4)

S. Chen, J. M. Soto-Crespo, and Ph. Grelu, “Watch-hand-like optical rogue waves in three-wave interactions,” Opt. Express 23(1), 349–359 (2015).
[Crossref] [PubMed]

F. Baronio, S. Chen, Ph. Grelu, S. Wabnitz, and M. Conforti, “Baseband modulation instability as the origin of rogue waves,” Phys. Rev. A. 91, 033804 (2015).
[Crossref]

S. Chen, F. Baronio, J. M. Soto-Crespo, Ph. Grelu, M. Conforti, and S. Wabnitz, “Optical rogue waves in parametric three-wave mixing and coherent stimulated scattering,” Phys. Rev. A. 92, 033847 (2015).
[Crossref]

S. Toenger, T. Godin, C. Billet, F. Dias, M. Erkintalo, G. Genty, and J. M. Dudley, “Emergent rogue wave structures and statistics in spontaneous modulation instability,” Sci. Rep. 5, 10380 (2015).
[Crossref] [PubMed]

2014 (7)

S. Wabnitz and B. Wetzel, “Instability and noise-induced thermalization of Fermi–Pasta–Ulam recurrence in the nonlinear Schrödinger equation,” Phys. Lett. A 378, 2750–2756 (2014).
[Crossref]

F. Baronio, M. Conforti, A. Degasperis, S. Lombardo, M. Onorato, and S. Wabnitz, “Vector rogue waves and baseband modulation instability in the defocusing regime,” Phys. Rev. Lett. 113, 034101 (2014).
[Crossref] [PubMed]

S. Chen, Ph. Grelu, and J. M. Soto-Crespo, “Dark- and bright-rogue-wave solutions for media with long-wave–short-wave resonance,” Phys. Rev. E. 89, 011201 (2014).
[Crossref]

S. Chen, J. M. Soto-Crespo, and Ph. Grelu, “Coexisting rogue waves within the (2+1)-component long-wave–short-wave resonance,” Phys. Rev. E 90, 033203 (2014).
[Crossref]

J. M. Dudley, F. Dias, M. Erkintalo, and G. Genty, “Instabilities, breathers and rogue waves in optics,” Nature Photon. 8, 755–764 (2014).
[Crossref]

A. Chabchoub, B. Kibler, J. M. Dudley, and N. Akhmediev, “Hydrodynamics of periodic breathers,” Phil. Trans. R. Soc. A. 372, 20140005 (2014).
[Crossref] [PubMed]

S. Chen and J. M. Soto-Crespo, and Ph. Grelu, “Dark three-sister rogue waves in normally dispersive optical fibers with random birefringence,” Opt. Express 22(22), 27632–27642 (2014).
[Crossref] [PubMed]

2013 (8)

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nature Photon. 7, 102–112 (2013).
[Crossref]

S. Birkholz, E. T. J. Nibbering, C. Bree, S. Skupin, A. Demircan, G. Genty, and G. Steinmeyer, “Spatiotemporal rogue events in optical multiple filamentation,” Phys. Rev. Lett. 111, 243903 (2013).
[Crossref]

M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, “Rogue waves and their generating mechanisms in different physical contexts,” Phys. Rep. 528, 47–89 (2013).
[Crossref]

N. Akhmediev, J. M. Dudley, D. R. Solli, and S. K. Turitsyn, “Recent progress in investigating optical rogue waves,” J. Opt. 15, 060201 (2013).
[Crossref]

F. Baronio, M. Conforti, A. Degasperis, and S. Lombardo, “Rogue waves emerging from the resonant interaction of three waves,” Phys. Rev. Lett. 111, 114101 (2013).
[Crossref] [PubMed]

A. Degasperis and S. Lombardo, “Rational solitons of wave resonant-interaction models,” Phys. Rev. E. 88, 052914 (2013).
[Crossref]

L.-C. Zhao and J. Liu, “Rogue-wave solutions of a three-component coupled nonlinear Schrödinger equation,” Phys. Rev. E 87, 013201 (2013).
[Crossref]

A. Chabchoub and N. Akhmediev, “Observation of rogue wave triplets in water waves,” Phys. Lett. A 377, 2590–2593 (2013).
[Crossref]

2012 (2)

F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, “Solutions of the vector nonlinear Schrödinger equations: Evidence for deterministic rogue waves,” Phys. Rev. Lett. 109, 044102 (2012).
[Crossref]

C. Lecaplain, Ph. Grelu, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative rogue waves generated by chaotic pulse bunching in a mode-locked laser,” Phys. Rev. Lett. 108, 233901 (2012).
[Crossref] [PubMed]

2011 (2)

A. Chabchoub, N. P. Hoffmann, and N. Akhmediev, “Rogue wave observation in a water wave tank,” Phys. Rev. Lett. 106, 204502 (2011).
[Crossref] [PubMed]

A. Ankiewicz, D. J. Kedziora, and N. Akhmediev, “Rogue wave triplets,” Phys. Lett. A 375, 2782–2785 (2011).
[Crossref]

2010 (2)

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fibre optics,” Nature Phys. 6, 790–795 (2010).
[Crossref]

F. Baronio, M. Conforti, C. De Angelis, A. Degasperis, M. Andreana, V. Couderc, and A. Barthélémy, “Velocity-locked solitary waves in quadratic media,” Phys. Rev. Lett. 104, 113902 (2010).
[Crossref] [PubMed]

2009 (2)

A. Abdolvand, A. Nazarkin, A. V. Chugreev, C. F. Kaminski, P. St, and J. Russell, “Solitary pulse generation by backward Raman scattering in H2-filled photonic crystal fibers,” Phys. Rev. Lett. 103, 183902 (2009).
[Crossref]

N. Akhmediev, A. Ankiewicz, and M. Taki, “Waves that appear from nowhere and disappear without a trace,” Phys. Lett. A. 373, 675–678 (2009).
[Crossref]

2008 (1)

2007 (2)

2006 (2)

M. Onorato, A. R. Osborne, and M. Serio, “Modulational instability in crossing sea states: A possible mechanism for the formation of freak waves,” Phys. Rev. Lett. 96, 014503 (2006).
[Crossref] [PubMed]

M. Conforti, F. Baronio, A. Degasperis, and S. Wabnitz, “Inelastic scattering and interactions of three-wave parametric solitons,” Phys. Rev. E. 74, 065602 (2006).
[Crossref]

2001 (1)

A. Picozzi and M. Haelterman, “Parametric three-wave soliton generated from incoherent light,” Phys. Rev. Lett. 86, 2010–2013 (2001).
[Crossref] [PubMed]

1999 (1)

V. M. Malkin, G. Shvets, and N. J. Fisch, “Fast compression of laser beams to highly overcritical powers,” Phys. Rev. Lett. 82, 4448–4451 (1999).
[Crossref]

1996 (1)

1991 (2)

P. St, J. Russell, D. Culverhouse, and F. Farahi, “Theory of forward stimulated Brillouin scattering in dual-mode single-core fibers,” IEEE J. Quantum Electron. 27, 836–842 (1991).
[Crossref]

E. Picholle, C. Montes, C. Leycuras, O. Legrand, and J. Botineau, “Observation of dissipative superluminous solitons in a Brillouin fiber ring laser,” Phys. Rev. Lett. 66, 1454–1457 (1991).
[Crossref] [PubMed]

1979 (1)

D. J. Kaup, A. Reiman, and A. Bers, “Space-time evolution of nonlinear three-wave interactions. I. Interaction in a homogeneous medium,” Rev. Mod. Phys. 51, 275–309 (1979).
[Crossref]

Abdolvand, A.

A. Abdolvand, A. Nazarkin, A. V. Chugreev, C. F. Kaminski, P. St, and J. Russell, “Solitary pulse generation by backward Raman scattering in H2-filled photonic crystal fibers,” Phys. Rev. Lett. 103, 183902 (2009).
[Crossref]

Akhmediev, N.

A. Chabchoub, B. Kibler, J. M. Dudley, and N. Akhmediev, “Hydrodynamics of periodic breathers,” Phil. Trans. R. Soc. A. 372, 20140005 (2014).
[Crossref] [PubMed]

N. Akhmediev, J. M. Dudley, D. R. Solli, and S. K. Turitsyn, “Recent progress in investigating optical rogue waves,” J. Opt. 15, 060201 (2013).
[Crossref]

A. Chabchoub and N. Akhmediev, “Observation of rogue wave triplets in water waves,” Phys. Lett. A 377, 2590–2593 (2013).
[Crossref]

C. Lecaplain, Ph. Grelu, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative rogue waves generated by chaotic pulse bunching in a mode-locked laser,” Phys. Rev. Lett. 108, 233901 (2012).
[Crossref] [PubMed]

A. Chabchoub, N. P. Hoffmann, and N. Akhmediev, “Rogue wave observation in a water wave tank,” Phys. Rev. Lett. 106, 204502 (2011).
[Crossref] [PubMed]

A. Ankiewicz, D. J. Kedziora, and N. Akhmediev, “Rogue wave triplets,” Phys. Lett. A 375, 2782–2785 (2011).
[Crossref]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fibre optics,” Nature Phys. 6, 790–795 (2010).
[Crossref]

N. Akhmediev, A. Ankiewicz, and M. Taki, “Waves that appear from nowhere and disappear without a trace,” Phys. Lett. A. 373, 675–678 (2009).
[Crossref]

Andreana, M.

F. Baronio, M. Conforti, C. De Angelis, A. Degasperis, M. Andreana, V. Couderc, and A. Barthélémy, “Velocity-locked solitary waves in quadratic media,” Phys. Rev. Lett. 104, 113902 (2010).
[Crossref] [PubMed]

Ankiewicz, A.

A. Ankiewicz, D. J. Kedziora, and N. Akhmediev, “Rogue wave triplets,” Phys. Lett. A 375, 2782–2785 (2011).
[Crossref]

N. Akhmediev, A. Ankiewicz, and M. Taki, “Waves that appear from nowhere and disappear without a trace,” Phys. Lett. A. 373, 675–678 (2009).
[Crossref]

Arecchi, F. T.

M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, “Rogue waves and their generating mechanisms in different physical contexts,” Phys. Rep. 528, 47–89 (2013).
[Crossref]

Barbay, S.

F. Selmi, S. Coulibaly, Z. Loghmari, I. Sagnes, G. Beaudoin, M. G. Clerc, and S. Barbay, “Spatiotemporal chaos induces extreme events in an extended microcavity laser,” Phys. Rev. Lett. 116, 013901 (2016).
[Crossref] [PubMed]

Baronio, F.

B. Frisquet, B. Kibler, Ph. Morin, F. Baronio, M. Conforti, G. Millot, and S. Wabnitz, “Optical dark rogue wave,” Sci. Rep. 6, 20785 (2016).
[Crossref] [PubMed]

S. Chen, F. Baronio, J. M. Soto-Crespo, Ph. Grelu, M. Conforti, and S. Wabnitz, “Optical rogue waves in parametric three-wave mixing and coherent stimulated scattering,” Phys. Rev. A. 92, 033847 (2015).
[Crossref]

F. Baronio, S. Chen, Ph. Grelu, S. Wabnitz, and M. Conforti, “Baseband modulation instability as the origin of rogue waves,” Phys. Rev. A. 91, 033804 (2015).
[Crossref]

F. Baronio, M. Conforti, A. Degasperis, S. Lombardo, M. Onorato, and S. Wabnitz, “Vector rogue waves and baseband modulation instability in the defocusing regime,” Phys. Rev. Lett. 113, 034101 (2014).
[Crossref] [PubMed]

F. Baronio, M. Conforti, A. Degasperis, and S. Lombardo, “Rogue waves emerging from the resonant interaction of three waves,” Phys. Rev. Lett. 111, 114101 (2013).
[Crossref] [PubMed]

F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, “Solutions of the vector nonlinear Schrödinger equations: Evidence for deterministic rogue waves,” Phys. Rev. Lett. 109, 044102 (2012).
[Crossref]

F. Baronio, M. Conforti, C. De Angelis, A. Degasperis, M. Andreana, V. Couderc, and A. Barthélémy, “Velocity-locked solitary waves in quadratic media,” Phys. Rev. Lett. 104, 113902 (2010).
[Crossref] [PubMed]

M. Conforti, F. Baronio, A. Degasperis, and S. Wabnitz, “Parametric frequency conversion of short optical pulses controlled by a CW background,” Opt. Express 15(19), 12246–12251 (2007).
[Crossref] [PubMed]

M. Conforti, F. Baronio, A. Degasperis, and S. Wabnitz, “Inelastic scattering and interactions of three-wave parametric solitons,” Phys. Rev. E. 74, 065602 (2006).
[Crossref]

Barthélémy, A.

F. Baronio, M. Conforti, C. De Angelis, A. Degasperis, M. Andreana, V. Couderc, and A. Barthélémy, “Velocity-locked solitary waves in quadratic media,” Phys. Rev. Lett. 104, 113902 (2010).
[Crossref] [PubMed]

Beaudoin, G.

F. Selmi, S. Coulibaly, Z. Loghmari, I. Sagnes, G. Beaudoin, M. G. Clerc, and S. Barbay, “Spatiotemporal chaos induces extreme events in an extended microcavity laser,” Phys. Rev. Lett. 116, 013901 (2016).
[Crossref] [PubMed]

Bers, A.

D. J. Kaup, A. Reiman, and A. Bers, “Space-time evolution of nonlinear three-wave interactions. I. Interaction in a homogeneous medium,” Rev. Mod. Phys. 51, 275–309 (1979).
[Crossref]

Billet, C.

S. Toenger, T. Godin, C. Billet, F. Dias, M. Erkintalo, G. Genty, and J. M. Dudley, “Emergent rogue wave structures and statistics in spontaneous modulation instability,” Sci. Rep. 5, 10380 (2015).
[Crossref] [PubMed]

Birkholz, S.

S. Birkholz, E. T. J. Nibbering, C. Bree, S. Skupin, A. Demircan, G. Genty, and G. Steinmeyer, “Spatiotemporal rogue events in optical multiple filamentation,” Phys. Rev. Lett. 111, 243903 (2013).
[Crossref]

Bortolozzo, U.

M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, “Rogue waves and their generating mechanisms in different physical contexts,” Phys. Rep. 528, 47–89 (2013).
[Crossref]

Botineau, J.

E. Picholle, C. Montes, C. Leycuras, O. Legrand, and J. Botineau, “Observation of dissipative superluminous solitons in a Brillouin fiber ring laser,” Phys. Rev. Lett. 66, 1454–1457 (1991).
[Crossref] [PubMed]

Bree, C.

S. Birkholz, E. T. J. Nibbering, C. Bree, S. Skupin, A. Demircan, G. Genty, and G. Steinmeyer, “Spatiotemporal rogue events in optical multiple filamentation,” Phys. Rev. Lett. 111, 243903 (2013).
[Crossref]

Chabchoub, A.

A. Chabchoub, B. Kibler, J. M. Dudley, and N. Akhmediev, “Hydrodynamics of periodic breathers,” Phil. Trans. R. Soc. A. 372, 20140005 (2014).
[Crossref] [PubMed]

A. Chabchoub and N. Akhmediev, “Observation of rogue wave triplets in water waves,” Phys. Lett. A 377, 2590–2593 (2013).
[Crossref]

A. Chabchoub, N. P. Hoffmann, and N. Akhmediev, “Rogue wave observation in a water wave tank,” Phys. Rev. Lett. 106, 204502 (2011).
[Crossref] [PubMed]

Chen, S.

F. Baronio, S. Chen, Ph. Grelu, S. Wabnitz, and M. Conforti, “Baseband modulation instability as the origin of rogue waves,” Phys. Rev. A. 91, 033804 (2015).
[Crossref]

S. Chen, F. Baronio, J. M. Soto-Crespo, Ph. Grelu, M. Conforti, and S. Wabnitz, “Optical rogue waves in parametric three-wave mixing and coherent stimulated scattering,” Phys. Rev. A. 92, 033847 (2015).
[Crossref]

S. Chen, J. M. Soto-Crespo, and Ph. Grelu, “Watch-hand-like optical rogue waves in three-wave interactions,” Opt. Express 23(1), 349–359 (2015).
[Crossref] [PubMed]

S. Chen and J. M. Soto-Crespo, and Ph. Grelu, “Dark three-sister rogue waves in normally dispersive optical fibers with random birefringence,” Opt. Express 22(22), 27632–27642 (2014).
[Crossref] [PubMed]

S. Chen, J. M. Soto-Crespo, and Ph. Grelu, “Coexisting rogue waves within the (2+1)-component long-wave–short-wave resonance,” Phys. Rev. E 90, 033203 (2014).
[Crossref]

S. Chen, Ph. Grelu, and J. M. Soto-Crespo, “Dark- and bright-rogue-wave solutions for media with long-wave–short-wave resonance,” Phys. Rev. E. 89, 011201 (2014).
[Crossref]

Chugreev, A. V.

A. Abdolvand, A. Nazarkin, A. V. Chugreev, C. F. Kaminski, P. St, and J. Russell, “Solitary pulse generation by backward Raman scattering in H2-filled photonic crystal fibers,” Phys. Rev. Lett. 103, 183902 (2009).
[Crossref]

Clerc, M. G.

F. Selmi, S. Coulibaly, Z. Loghmari, I. Sagnes, G. Beaudoin, M. G. Clerc, and S. Barbay, “Spatiotemporal chaos induces extreme events in an extended microcavity laser,” Phys. Rev. Lett. 116, 013901 (2016).
[Crossref] [PubMed]

Conforti, M.

B. Frisquet, B. Kibler, Ph. Morin, F. Baronio, M. Conforti, G. Millot, and S. Wabnitz, “Optical dark rogue wave,” Sci. Rep. 6, 20785 (2016).
[Crossref] [PubMed]

F. Baronio, S. Chen, Ph. Grelu, S. Wabnitz, and M. Conforti, “Baseband modulation instability as the origin of rogue waves,” Phys. Rev. A. 91, 033804 (2015).
[Crossref]

S. Chen, F. Baronio, J. M. Soto-Crespo, Ph. Grelu, M. Conforti, and S. Wabnitz, “Optical rogue waves in parametric three-wave mixing and coherent stimulated scattering,” Phys. Rev. A. 92, 033847 (2015).
[Crossref]

F. Baronio, M. Conforti, A. Degasperis, S. Lombardo, M. Onorato, and S. Wabnitz, “Vector rogue waves and baseband modulation instability in the defocusing regime,” Phys. Rev. Lett. 113, 034101 (2014).
[Crossref] [PubMed]

F. Baronio, M. Conforti, A. Degasperis, and S. Lombardo, “Rogue waves emerging from the resonant interaction of three waves,” Phys. Rev. Lett. 111, 114101 (2013).
[Crossref] [PubMed]

F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, “Solutions of the vector nonlinear Schrödinger equations: Evidence for deterministic rogue waves,” Phys. Rev. Lett. 109, 044102 (2012).
[Crossref]

F. Baronio, M. Conforti, C. De Angelis, A. Degasperis, M. Andreana, V. Couderc, and A. Barthélémy, “Velocity-locked solitary waves in quadratic media,” Phys. Rev. Lett. 104, 113902 (2010).
[Crossref] [PubMed]

M. Conforti, F. Baronio, A. Degasperis, and S. Wabnitz, “Parametric frequency conversion of short optical pulses controlled by a CW background,” Opt. Express 15(19), 12246–12251 (2007).
[Crossref] [PubMed]

M. Conforti, F. Baronio, A. Degasperis, and S. Wabnitz, “Inelastic scattering and interactions of three-wave parametric solitons,” Phys. Rev. E. 74, 065602 (2006).
[Crossref]

Couderc, V.

F. Baronio, M. Conforti, C. De Angelis, A. Degasperis, M. Andreana, V. Couderc, and A. Barthélémy, “Velocity-locked solitary waves in quadratic media,” Phys. Rev. Lett. 104, 113902 (2010).
[Crossref] [PubMed]

Coulibaly, S.

F. Selmi, S. Coulibaly, Z. Loghmari, I. Sagnes, G. Beaudoin, M. G. Clerc, and S. Barbay, “Spatiotemporal chaos induces extreme events in an extended microcavity laser,” Phys. Rev. Lett. 116, 013901 (2016).
[Crossref] [PubMed]

Culverhouse, D.

P. St, J. Russell, D. Culverhouse, and F. Farahi, “Theory of forward stimulated Brillouin scattering in dual-mode single-core fibers,” IEEE J. Quantum Electron. 27, 836–842 (1991).
[Crossref]

De Angelis, C.

F. Baronio, M. Conforti, C. De Angelis, A. Degasperis, M. Andreana, V. Couderc, and A. Barthélémy, “Velocity-locked solitary waves in quadratic media,” Phys. Rev. Lett. 104, 113902 (2010).
[Crossref] [PubMed]

Degasperis, A.

F. Baronio, M. Conforti, A. Degasperis, S. Lombardo, M. Onorato, and S. Wabnitz, “Vector rogue waves and baseband modulation instability in the defocusing regime,” Phys. Rev. Lett. 113, 034101 (2014).
[Crossref] [PubMed]

F. Baronio, M. Conforti, A. Degasperis, and S. Lombardo, “Rogue waves emerging from the resonant interaction of three waves,” Phys. Rev. Lett. 111, 114101 (2013).
[Crossref] [PubMed]

A. Degasperis and S. Lombardo, “Rational solitons of wave resonant-interaction models,” Phys. Rev. E. 88, 052914 (2013).
[Crossref]

F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, “Solutions of the vector nonlinear Schrödinger equations: Evidence for deterministic rogue waves,” Phys. Rev. Lett. 109, 044102 (2012).
[Crossref]

F. Baronio, M. Conforti, C. De Angelis, A. Degasperis, M. Andreana, V. Couderc, and A. Barthélémy, “Velocity-locked solitary waves in quadratic media,” Phys. Rev. Lett. 104, 113902 (2010).
[Crossref] [PubMed]

M. Conforti, F. Baronio, A. Degasperis, and S. Wabnitz, “Parametric frequency conversion of short optical pulses controlled by a CW background,” Opt. Express 15(19), 12246–12251 (2007).
[Crossref] [PubMed]

M. Conforti, F. Baronio, A. Degasperis, and S. Wabnitz, “Inelastic scattering and interactions of three-wave parametric solitons,” Phys. Rev. E. 74, 065602 (2006).
[Crossref]

Demircan, A.

S. Birkholz, E. T. J. Nibbering, C. Bree, S. Skupin, A. Demircan, G. Genty, and G. Steinmeyer, “Spatiotemporal rogue events in optical multiple filamentation,” Phys. Rev. Lett. 111, 243903 (2013).
[Crossref]

Dias, F.

S. Toenger, T. Godin, C. Billet, F. Dias, M. Erkintalo, G. Genty, and J. M. Dudley, “Emergent rogue wave structures and statistics in spontaneous modulation instability,” Sci. Rep. 5, 10380 (2015).
[Crossref] [PubMed]

J. M. Dudley, F. Dias, M. Erkintalo, and G. Genty, “Instabilities, breathers and rogue waves in optics,” Nature Photon. 8, 755–764 (2014).
[Crossref]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fibre optics,” Nature Phys. 6, 790–795 (2010).
[Crossref]

Dudley, J. M.

S. Toenger, T. Godin, C. Billet, F. Dias, M. Erkintalo, G. Genty, and J. M. Dudley, “Emergent rogue wave structures and statistics in spontaneous modulation instability,” Sci. Rep. 5, 10380 (2015).
[Crossref] [PubMed]

J. M. Dudley, F. Dias, M. Erkintalo, and G. Genty, “Instabilities, breathers and rogue waves in optics,” Nature Photon. 8, 755–764 (2014).
[Crossref]

A. Chabchoub, B. Kibler, J. M. Dudley, and N. Akhmediev, “Hydrodynamics of periodic breathers,” Phil. Trans. R. Soc. A. 372, 20140005 (2014).
[Crossref] [PubMed]

N. Akhmediev, J. M. Dudley, D. R. Solli, and S. K. Turitsyn, “Recent progress in investigating optical rogue waves,” J. Opt. 15, 060201 (2013).
[Crossref]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fibre optics,” Nature Phys. 6, 790–795 (2010).
[Crossref]

J. M. Dudley, G. Genty, and B. J. Eggleton, “Harnessing and control of optical rogue waves in supercontinuum generation,” Opt. Express 16(6), 3644–3651 (2008).
[Crossref] [PubMed]

Eggleton, B. J.

Erkintalo, M.

S. Toenger, T. Godin, C. Billet, F. Dias, M. Erkintalo, G. Genty, and J. M. Dudley, “Emergent rogue wave structures and statistics in spontaneous modulation instability,” Sci. Rep. 5, 10380 (2015).
[Crossref] [PubMed]

J. M. Dudley, F. Dias, M. Erkintalo, and G. Genty, “Instabilities, breathers and rogue waves in optics,” Nature Photon. 8, 755–764 (2014).
[Crossref]

Farahi, F.

P. St, J. Russell, D. Culverhouse, and F. Farahi, “Theory of forward stimulated Brillouin scattering in dual-mode single-core fibers,” IEEE J. Quantum Electron. 27, 836–842 (1991).
[Crossref]

Fatome, J.

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fibre optics,” Nature Phys. 6, 790–795 (2010).
[Crossref]

Finot, C.

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fibre optics,” Nature Phys. 6, 790–795 (2010).
[Crossref]

Fisch, N. J.

V. M. Malkin, G. Shvets, and N. J. Fisch, “Fast compression of laser beams to highly overcritical powers,” Phys. Rev. Lett. 82, 4448–4451 (1999).
[Crossref]

Frisquet, B.

B. Frisquet, B. Kibler, Ph. Morin, F. Baronio, M. Conforti, G. Millot, and S. Wabnitz, “Optical dark rogue wave,” Sci. Rep. 6, 20785 (2016).
[Crossref] [PubMed]

Genty, G.

S. Toenger, T. Godin, C. Billet, F. Dias, M. Erkintalo, G. Genty, and J. M. Dudley, “Emergent rogue wave structures and statistics in spontaneous modulation instability,” Sci. Rep. 5, 10380 (2015).
[Crossref] [PubMed]

J. M. Dudley, F. Dias, M. Erkintalo, and G. Genty, “Instabilities, breathers and rogue waves in optics,” Nature Photon. 8, 755–764 (2014).
[Crossref]

S. Birkholz, E. T. J. Nibbering, C. Bree, S. Skupin, A. Demircan, G. Genty, and G. Steinmeyer, “Spatiotemporal rogue events in optical multiple filamentation,” Phys. Rev. Lett. 111, 243903 (2013).
[Crossref]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fibre optics,” Nature Phys. 6, 790–795 (2010).
[Crossref]

J. M. Dudley, G. Genty, and B. J. Eggleton, “Harnessing and control of optical rogue waves in supercontinuum generation,” Opt. Express 16(6), 3644–3651 (2008).
[Crossref] [PubMed]

Goda, K.

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nature Photon. 7, 102–112 (2013).
[Crossref]

Godin, T.

S. Toenger, T. Godin, C. Billet, F. Dias, M. Erkintalo, G. Genty, and J. M. Dudley, “Emergent rogue wave structures and statistics in spontaneous modulation instability,” Sci. Rep. 5, 10380 (2015).
[Crossref] [PubMed]

Grelu, Ph.

F. Baronio, S. Chen, Ph. Grelu, S. Wabnitz, and M. Conforti, “Baseband modulation instability as the origin of rogue waves,” Phys. Rev. A. 91, 033804 (2015).
[Crossref]

S. Chen, F. Baronio, J. M. Soto-Crespo, Ph. Grelu, M. Conforti, and S. Wabnitz, “Optical rogue waves in parametric three-wave mixing and coherent stimulated scattering,” Phys. Rev. A. 92, 033847 (2015).
[Crossref]

S. Chen, J. M. Soto-Crespo, and Ph. Grelu, “Watch-hand-like optical rogue waves in three-wave interactions,” Opt. Express 23(1), 349–359 (2015).
[Crossref] [PubMed]

S. Chen, Ph. Grelu, and J. M. Soto-Crespo, “Dark- and bright-rogue-wave solutions for media with long-wave–short-wave resonance,” Phys. Rev. E. 89, 011201 (2014).
[Crossref]

S. Chen, J. M. Soto-Crespo, and Ph. Grelu, “Coexisting rogue waves within the (2+1)-component long-wave–short-wave resonance,” Phys. Rev. E 90, 033203 (2014).
[Crossref]

C. Lecaplain, Ph. Grelu, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative rogue waves generated by chaotic pulse bunching in a mode-locked laser,” Phys. Rev. Lett. 108, 233901 (2012).
[Crossref] [PubMed]

Haelterman, M.

A. Picozzi and M. Haelterman, “Parametric three-wave soliton generated from incoherent light,” Phys. Rev. Lett. 86, 2010–2013 (2001).
[Crossref] [PubMed]

Hoffmann, N. P.

A. Chabchoub, N. P. Hoffmann, and N. Akhmediev, “Rogue wave observation in a water wave tank,” Phys. Rev. Lett. 106, 204502 (2011).
[Crossref] [PubMed]

Ibragimov, E.

Jalali, B.

K. Goda and B. Jalali, “Dispersive Fourier transformation for fast continuous single-shot measurements,” Nature Photon. 7, 102–112 (2013).
[Crossref]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature (London) 450, 1054–1057 (2007).
[Crossref]

Kaminski, C. F.

A. Abdolvand, A. Nazarkin, A. V. Chugreev, C. F. Kaminski, P. St, and J. Russell, “Solitary pulse generation by backward Raman scattering in H2-filled photonic crystal fibers,” Phys. Rev. Lett. 103, 183902 (2009).
[Crossref]

Kaup, D. J.

D. J. Kaup, A. Reiman, and A. Bers, “Space-time evolution of nonlinear three-wave interactions. I. Interaction in a homogeneous medium,” Rev. Mod. Phys. 51, 275–309 (1979).
[Crossref]

Kedziora, D. J.

A. Ankiewicz, D. J. Kedziora, and N. Akhmediev, “Rogue wave triplets,” Phys. Lett. A 375, 2782–2785 (2011).
[Crossref]

Kibler, B.

B. Frisquet, B. Kibler, Ph. Morin, F. Baronio, M. Conforti, G. Millot, and S. Wabnitz, “Optical dark rogue wave,” Sci. Rep. 6, 20785 (2016).
[Crossref] [PubMed]

A. Chabchoub, B. Kibler, J. M. Dudley, and N. Akhmediev, “Hydrodynamics of periodic breathers,” Phil. Trans. R. Soc. A. 372, 20140005 (2014).
[Crossref] [PubMed]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fibre optics,” Nature Phys. 6, 790–795 (2010).
[Crossref]

Koonath, P.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature (London) 450, 1054–1057 (2007).
[Crossref]

Lecaplain, C.

C. Lecaplain, Ph. Grelu, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative rogue waves generated by chaotic pulse bunching in a mode-locked laser,” Phys. Rev. Lett. 108, 233901 (2012).
[Crossref] [PubMed]

Legrand, O.

E. Picholle, C. Montes, C. Leycuras, O. Legrand, and J. Botineau, “Observation of dissipative superluminous solitons in a Brillouin fiber ring laser,” Phys. Rev. Lett. 66, 1454–1457 (1991).
[Crossref] [PubMed]

Leycuras, C.

E. Picholle, C. Montes, C. Leycuras, O. Legrand, and J. Botineau, “Observation of dissipative superluminous solitons in a Brillouin fiber ring laser,” Phys. Rev. Lett. 66, 1454–1457 (1991).
[Crossref] [PubMed]

Liu, J.

L.-C. Zhao and J. Liu, “Rogue-wave solutions of a three-component coupled nonlinear Schrödinger equation,” Phys. Rev. E 87, 013201 (2013).
[Crossref]

Loghmari, Z.

F. Selmi, S. Coulibaly, Z. Loghmari, I. Sagnes, G. Beaudoin, M. G. Clerc, and S. Barbay, “Spatiotemporal chaos induces extreme events in an extended microcavity laser,” Phys. Rev. Lett. 116, 013901 (2016).
[Crossref] [PubMed]

Lombardo, S.

F. Baronio, M. Conforti, A. Degasperis, S. Lombardo, M. Onorato, and S. Wabnitz, “Vector rogue waves and baseband modulation instability in the defocusing regime,” Phys. Rev. Lett. 113, 034101 (2014).
[Crossref] [PubMed]

A. Degasperis and S. Lombardo, “Rational solitons of wave resonant-interaction models,” Phys. Rev. E. 88, 052914 (2013).
[Crossref]

F. Baronio, M. Conforti, A. Degasperis, and S. Lombardo, “Rogue waves emerging from the resonant interaction of three waves,” Phys. Rev. Lett. 111, 114101 (2013).
[Crossref] [PubMed]

Malkin, V. M.

V. M. Malkin, G. Shvets, and N. J. Fisch, “Fast compression of laser beams to highly overcritical powers,” Phys. Rev. Lett. 82, 4448–4451 (1999).
[Crossref]

Millot, G.

B. Frisquet, B. Kibler, Ph. Morin, F. Baronio, M. Conforti, G. Millot, and S. Wabnitz, “Optical dark rogue wave,” Sci. Rep. 6, 20785 (2016).
[Crossref] [PubMed]

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fibre optics,” Nature Phys. 6, 790–795 (2010).
[Crossref]

Montes, C.

E. Picholle, C. Montes, C. Leycuras, O. Legrand, and J. Botineau, “Observation of dissipative superluminous solitons in a Brillouin fiber ring laser,” Phys. Rev. Lett. 66, 1454–1457 (1991).
[Crossref] [PubMed]

Montina, A.

M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, “Rogue waves and their generating mechanisms in different physical contexts,” Phys. Rep. 528, 47–89 (2013).
[Crossref]

Morin, Ph.

B. Frisquet, B. Kibler, Ph. Morin, F. Baronio, M. Conforti, G. Millot, and S. Wabnitz, “Optical dark rogue wave,” Sci. Rep. 6, 20785 (2016).
[Crossref] [PubMed]

Nazarkin, A.

A. Abdolvand, A. Nazarkin, A. V. Chugreev, C. F. Kaminski, P. St, and J. Russell, “Solitary pulse generation by backward Raman scattering in H2-filled photonic crystal fibers,” Phys. Rev. Lett. 103, 183902 (2009).
[Crossref]

Nibbering, E. T. J.

S. Birkholz, E. T. J. Nibbering, C. Bree, S. Skupin, A. Demircan, G. Genty, and G. Steinmeyer, “Spatiotemporal rogue events in optical multiple filamentation,” Phys. Rev. Lett. 111, 243903 (2013).
[Crossref]

Onorato, M.

F. Baronio, M. Conforti, A. Degasperis, S. Lombardo, M. Onorato, and S. Wabnitz, “Vector rogue waves and baseband modulation instability in the defocusing regime,” Phys. Rev. Lett. 113, 034101 (2014).
[Crossref] [PubMed]

M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, “Rogue waves and their generating mechanisms in different physical contexts,” Phys. Rep. 528, 47–89 (2013).
[Crossref]

M. Onorato, A. R. Osborne, and M. Serio, “Modulational instability in crossing sea states: A possible mechanism for the formation of freak waves,” Phys. Rev. Lett. 96, 014503 (2006).
[Crossref] [PubMed]

Osborne, A. R.

M. Onorato, A. R. Osborne, and M. Serio, “Modulational instability in crossing sea states: A possible mechanism for the formation of freak waves,” Phys. Rev. Lett. 96, 014503 (2006).
[Crossref] [PubMed]

Picholle, E.

E. Picholle, C. Montes, C. Leycuras, O. Legrand, and J. Botineau, “Observation of dissipative superluminous solitons in a Brillouin fiber ring laser,” Phys. Rev. Lett. 66, 1454–1457 (1991).
[Crossref] [PubMed]

Picozzi, A.

A. Picozzi and M. Haelterman, “Parametric three-wave soliton generated from incoherent light,” Phys. Rev. Lett. 86, 2010–2013 (2001).
[Crossref] [PubMed]

Reiman, A.

D. J. Kaup, A. Reiman, and A. Bers, “Space-time evolution of nonlinear three-wave interactions. I. Interaction in a homogeneous medium,” Rev. Mod. Phys. 51, 275–309 (1979).
[Crossref]

Residori, S.

M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, “Rogue waves and their generating mechanisms in different physical contexts,” Phys. Rep. 528, 47–89 (2013).
[Crossref]

Ropers, C.

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature (London) 450, 1054–1057 (2007).
[Crossref]

Russell, J.

A. Abdolvand, A. Nazarkin, A. V. Chugreev, C. F. Kaminski, P. St, and J. Russell, “Solitary pulse generation by backward Raman scattering in H2-filled photonic crystal fibers,” Phys. Rev. Lett. 103, 183902 (2009).
[Crossref]

P. St, J. Russell, D. Culverhouse, and F. Farahi, “Theory of forward stimulated Brillouin scattering in dual-mode single-core fibers,” IEEE J. Quantum Electron. 27, 836–842 (1991).
[Crossref]

Sagnes, I.

F. Selmi, S. Coulibaly, Z. Loghmari, I. Sagnes, G. Beaudoin, M. G. Clerc, and S. Barbay, “Spatiotemporal chaos induces extreme events in an extended microcavity laser,” Phys. Rev. Lett. 116, 013901 (2016).
[Crossref] [PubMed]

Selmi, F.

F. Selmi, S. Coulibaly, Z. Loghmari, I. Sagnes, G. Beaudoin, M. G. Clerc, and S. Barbay, “Spatiotemporal chaos induces extreme events in an extended microcavity laser,” Phys. Rev. Lett. 116, 013901 (2016).
[Crossref] [PubMed]

Serio, M.

M. Onorato, A. R. Osborne, and M. Serio, “Modulational instability in crossing sea states: A possible mechanism for the formation of freak waves,” Phys. Rev. Lett. 96, 014503 (2006).
[Crossref] [PubMed]

Shvets, G.

V. M. Malkin, G. Shvets, and N. J. Fisch, “Fast compression of laser beams to highly overcritical powers,” Phys. Rev. Lett. 82, 4448–4451 (1999).
[Crossref]

Skupin, S.

S. Birkholz, E. T. J. Nibbering, C. Bree, S. Skupin, A. Demircan, G. Genty, and G. Steinmeyer, “Spatiotemporal rogue events in optical multiple filamentation,” Phys. Rev. Lett. 111, 243903 (2013).
[Crossref]

Solli, D. R.

N. Akhmediev, J. M. Dudley, D. R. Solli, and S. K. Turitsyn, “Recent progress in investigating optical rogue waves,” J. Opt. 15, 060201 (2013).
[Crossref]

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature (London) 450, 1054–1057 (2007).
[Crossref]

Soto-Crespo, J. M.

S. Chen, F. Baronio, J. M. Soto-Crespo, Ph. Grelu, M. Conforti, and S. Wabnitz, “Optical rogue waves in parametric three-wave mixing and coherent stimulated scattering,” Phys. Rev. A. 92, 033847 (2015).
[Crossref]

S. Chen, J. M. Soto-Crespo, and Ph. Grelu, “Watch-hand-like optical rogue waves in three-wave interactions,” Opt. Express 23(1), 349–359 (2015).
[Crossref] [PubMed]

S. Chen and J. M. Soto-Crespo, and Ph. Grelu, “Dark three-sister rogue waves in normally dispersive optical fibers with random birefringence,” Opt. Express 22(22), 27632–27642 (2014).
[Crossref] [PubMed]

S. Chen, Ph. Grelu, and J. M. Soto-Crespo, “Dark- and bright-rogue-wave solutions for media with long-wave–short-wave resonance,” Phys. Rev. E. 89, 011201 (2014).
[Crossref]

S. Chen, J. M. Soto-Crespo, and Ph. Grelu, “Coexisting rogue waves within the (2+1)-component long-wave–short-wave resonance,” Phys. Rev. E 90, 033203 (2014).
[Crossref]

C. Lecaplain, Ph. Grelu, J. M. Soto-Crespo, and N. Akhmediev, “Dissipative rogue waves generated by chaotic pulse bunching in a mode-locked laser,” Phys. Rev. Lett. 108, 233901 (2012).
[Crossref] [PubMed]

St, P.

A. Abdolvand, A. Nazarkin, A. V. Chugreev, C. F. Kaminski, P. St, and J. Russell, “Solitary pulse generation by backward Raman scattering in H2-filled photonic crystal fibers,” Phys. Rev. Lett. 103, 183902 (2009).
[Crossref]

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S. Toenger, T. Godin, C. Billet, F. Dias, M. Erkintalo, G. Genty, and J. M. Dudley, “Emergent rogue wave structures and statistics in spontaneous modulation instability,” Sci. Rep. 5, 10380 (2015).
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N. Akhmediev, J. M. Dudley, D. R. Solli, and S. K. Turitsyn, “Recent progress in investigating optical rogue waves,” J. Opt. 15, 060201 (2013).
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Wabnitz, S.

B. Frisquet, B. Kibler, Ph. Morin, F. Baronio, M. Conforti, G. Millot, and S. Wabnitz, “Optical dark rogue wave,” Sci. Rep. 6, 20785 (2016).
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S. Chen, F. Baronio, J. M. Soto-Crespo, Ph. Grelu, M. Conforti, and S. Wabnitz, “Optical rogue waves in parametric three-wave mixing and coherent stimulated scattering,” Phys. Rev. A. 92, 033847 (2015).
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F. Baronio, S. Chen, Ph. Grelu, S. Wabnitz, and M. Conforti, “Baseband modulation instability as the origin of rogue waves,” Phys. Rev. A. 91, 033804 (2015).
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F. Baronio, M. Conforti, A. Degasperis, S. Lombardo, M. Onorato, and S. Wabnitz, “Vector rogue waves and baseband modulation instability in the defocusing regime,” Phys. Rev. Lett. 113, 034101 (2014).
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F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, “Solutions of the vector nonlinear Schrödinger equations: Evidence for deterministic rogue waves,” Phys. Rev. Lett. 109, 044102 (2012).
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M. Conforti, F. Baronio, A. Degasperis, and S. Wabnitz, “Inelastic scattering and interactions of three-wave parametric solitons,” Phys. Rev. E. 74, 065602 (2006).
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S. Wabnitz and B. Wetzel, “Instability and noise-induced thermalization of Fermi–Pasta–Ulam recurrence in the nonlinear Schrödinger equation,” Phys. Lett. A 378, 2750–2756 (2014).
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L.-C. Zhao and J. Liu, “Rogue-wave solutions of a three-component coupled nonlinear Schrödinger equation,” Phys. Rev. E 87, 013201 (2013).
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P. St, J. Russell, D. Culverhouse, and F. Farahi, “Theory of forward stimulated Brillouin scattering in dual-mode single-core fibers,” IEEE J. Quantum Electron. 27, 836–842 (1991).
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J. Opt. (1)

N. Akhmediev, J. M. Dudley, D. R. Solli, and S. K. Turitsyn, “Recent progress in investigating optical rogue waves,” J. Opt. 15, 060201 (2013).
[Crossref]

Nature (London) (1)

D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, “Optical rogue waves,” Nature (London) 450, 1054–1057 (2007).
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Nature Photon. (2)

J. M. Dudley, F. Dias, M. Erkintalo, and G. Genty, “Instabilities, breathers and rogue waves in optics,” Nature Photon. 8, 755–764 (2014).
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Nature Phys. (1)

B. Kibler, J. Fatome, C. Finot, G. Millot, F. Dias, G. Genty, N. Akhmediev, and J. M. Dudley, “The Peregrine soliton in nonlinear fibre optics,” Nature Phys. 6, 790–795 (2010).
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Opt. Express (4)

Opt. Lett. (1)

Phil. Trans. R. Soc. A. (1)

A. Chabchoub, B. Kibler, J. M. Dudley, and N. Akhmediev, “Hydrodynamics of periodic breathers,” Phil. Trans. R. Soc. A. 372, 20140005 (2014).
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Phys. Lett. A (3)

A. Ankiewicz, D. J. Kedziora, and N. Akhmediev, “Rogue wave triplets,” Phys. Lett. A 375, 2782–2785 (2011).
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S. Wabnitz and B. Wetzel, “Instability and noise-induced thermalization of Fermi–Pasta–Ulam recurrence in the nonlinear Schrödinger equation,” Phys. Lett. A 378, 2750–2756 (2014).
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Phys. Lett. A. (1)

N. Akhmediev, A. Ankiewicz, and M. Taki, “Waves that appear from nowhere and disappear without a trace,” Phys. Lett. A. 373, 675–678 (2009).
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Phys. Rep. (1)

M. Onorato, S. Residori, U. Bortolozzo, A. Montina, and F. T. Arecchi, “Rogue waves and their generating mechanisms in different physical contexts,” Phys. Rep. 528, 47–89 (2013).
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Phys. Rev. A. (2)

S. Chen, F. Baronio, J. M. Soto-Crespo, Ph. Grelu, M. Conforti, and S. Wabnitz, “Optical rogue waves in parametric three-wave mixing and coherent stimulated scattering,” Phys. Rev. A. 92, 033847 (2015).
[Crossref]

F. Baronio, S. Chen, Ph. Grelu, S. Wabnitz, and M. Conforti, “Baseband modulation instability as the origin of rogue waves,” Phys. Rev. A. 91, 033804 (2015).
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Phys. Rev. E (2)

S. Chen, J. M. Soto-Crespo, and Ph. Grelu, “Coexisting rogue waves within the (2+1)-component long-wave–short-wave resonance,” Phys. Rev. E 90, 033203 (2014).
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L.-C. Zhao and J. Liu, “Rogue-wave solutions of a three-component coupled nonlinear Schrödinger equation,” Phys. Rev. E 87, 013201 (2013).
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A. Degasperis and S. Lombardo, “Rational solitons of wave resonant-interaction models,” Phys. Rev. E. 88, 052914 (2013).
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S. Chen, Ph. Grelu, and J. M. Soto-Crespo, “Dark- and bright-rogue-wave solutions for media with long-wave–short-wave resonance,” Phys. Rev. E. 89, 011201 (2014).
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M. Conforti, F. Baronio, A. Degasperis, and S. Wabnitz, “Inelastic scattering and interactions of three-wave parametric solitons,” Phys. Rev. E. 74, 065602 (2006).
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S. Birkholz, E. T. J. Nibbering, C. Bree, S. Skupin, A. Demircan, G. Genty, and G. Steinmeyer, “Spatiotemporal rogue events in optical multiple filamentation,” Phys. Rev. Lett. 111, 243903 (2013).
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F. Baronio, M. Conforti, A. Degasperis, S. Lombardo, M. Onorato, and S. Wabnitz, “Vector rogue waves and baseband modulation instability in the defocusing regime,” Phys. Rev. Lett. 113, 034101 (2014).
[Crossref] [PubMed]

F. Baronio, A. Degasperis, M. Conforti, and S. Wabnitz, “Solutions of the vector nonlinear Schrödinger equations: Evidence for deterministic rogue waves,” Phys. Rev. Lett. 109, 044102 (2012).
[Crossref]

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S. Toenger, T. Godin, C. Billet, F. Dias, M. Erkintalo, G. Genty, and J. M. Dudley, “Emergent rogue wave structures and statistics in spontaneous modulation instability,” Sci. Rep. 5, 10380 (2015).
[Crossref] [PubMed]

B. Frisquet, B. Kibler, Ph. Morin, F. Baronio, M. Conforti, G. Millot, and S. Wabnitz, “Optical dark rogue wave,” Sci. Rep. 6, 20785 (2016).
[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1 Fundamental optical rogue waves formed at a1 = 1, a 2 = a 3 = 3, δ = 1, and V = 4. (A)–(C) surface plots; (a)–(c) the corresponding contour distributions.
Fig. 2
Fig. 2 Rogue wave triplets formed under the same initial plane-wave parameters as in Fig. 1, but with extra structural parameters given by γ1 = 7, γ2 = 1, and γ3 = γ4 = 0. (A)–(C) surface plots; (a)–(c) the corresponding contour distributions.
Fig. 3
Fig. 3 Second-order optical rogue waves formed at a1 = a2 = a3 = 1, and δ = 1, for given structural parameters γ1 = 0.5, γ2 = 1, and γ3 = γ4 = 0. (a)–(c) V = 2; (d)–(f) V = 4. (a), (b), (d), and (e) show a butterfly-type pattern, while (c) and (f) show a bright structure.
Fig. 4
Fig. 4 Map of the MI gain versus Ω and δ for a1 = 1 and a 2 = 3 : (a) V = 2; (b) V = 4. (c) illustrates profiles of the growth rate γ versus Ω in (b) for several given values of δ. The same green cross in (b) and (c) indicates the maximum of the growth rate for given δ = 1, which occurs at a modulation frequency of about 1.23.
Fig. 5
Fig. 5 Simulation results intended for the fundamental rogue waves using the same initial plane-wave parameters as in Fig. 1. Left column: unperturbed; Right column: perturbed by a white noise of the intensity ε = 10−8.

Equations (17)

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u 1 t + V u 1 x = u 2 * u 3 * , u 2 t + V u 2 x = u 1 * u 3 * , u 3 t + V 3 u 3 x = u 1 * u 2 * ,
u 10 ( x , t ) = a 1 exp [ i ( k 1 x ω 1 t ) ] , u 20 ( x , t ) = a 2 exp [ i ( k 2 x ω 2 t ) ] , u 30 ( x , t ) = i a 3 exp [ i ( k 1 k 2 ) x i ( ω 1 ω 2 ) t ] ,
a 3 = a 1 a 2 δ , k 1 = ω 1 V + a 2 2 δ V , k 2 = ω 2 V + a 1 2 δ V ,
u 1 [ 1 ] = u 10 { 1 + 2 i δ V [ δ 2 V t ( δ 2 + A ) x ] δ 2 A V 2 / a 1 2 [ δ 2 V t ( δ 2 + B ) x ] 2 + 4 δ 2 a 3 2 x 2 + A 2 V 2 / ( 4 a 3 2 ) } , u 2 [ 1 ] = u 20 { 1 + 2 i δ V [ δ 2 V t ( δ 2 A ) x ] δ 2 A V 2 / a 2 2 [ δ 2 V t ( δ 2 + B ) x ] 2 + 4 δ 2 a 3 2 x 2 + A 2 V 2 / ( 4 a 3 2 ) } , u 3 [ 1 ] = u 30 { 1 4 i δ 3 V ( V t x ) + A 2 V 2 / a 3 2 [ δ 2 V t ( δ 2 + B ) x ] 2 + 4 δ 2 a 3 2 x 2 + A 2 V 2 / ( 4 a 3 2 ) } .
u 1 [ 2 ] = u 10 { 1 4 i a 2 R 1 * [ M 4 ( | R 2 | 2 M 2 * M 1 ) + R 0 ( | R 1 | 2 M 2 + | R 2 | 2 M 2 * ) ] δ ( M 1 2 + | R 1 R 2 M 2 | 2 ) } , u 2 [ 2 ] = u 20 { 1 4 i a 1 R 2 [ M 3 * ( | R 1 | 2 M 2 + M 1 ) + R 0 * ( | R 1 | 2 M 2 + | R 2 | 2 M 2 * ) ] δ ( M 1 2 + | R 1 R 2 M 2 | 2 ) } , u 3 [ 2 ] = u 30 { 1 4 i R 1 R 2 * [ | R 1 | 2 ( 2 + M 2 * ) + | R 2 | 2 ( 2 M 2 ) ] M 1 2 + | R 1 R 2 M 2 | 2 } ,
R 0 = γ 1 + γ 2 ξ , R j = a j α j ( γ 1 + γ 2 θ j ) , ( here and below j = 1 , 2 ) ,
S 0 = i γ 1 ξ φ + γ 2 [ q ξ 4 i a 3 x / ( δ V ) ] + γ 3 i γ 4 ξ ,
S j = α j S 0 + i γ 1 ϕ 2 [ θ j A / ( 2 δ 2 a 3 ) ] + γ 2 ( ϕ 2 ϑ j i q ) γ 4 α j ( γ 1 + γ 2 θ j ) ,
ξ = t [ 1 V ( 1 + B δ 2 ) + 2 i a 3 δ V ] x ,
α j = δ 2 A [ B 2 i δ a 3 ( 1 ) j A ] , θ j = ξ i α j ,
ϑ j = [ θ j 3 A / ( 2 δ 2 a 3 ) ] ( 2 + i α j ξ ) α j i 3 α j 2 ,
ϕ = 2 δ 2 a 3 A 2 A 2 2 B 2 + 4 i δ B a 3 , φ = i ϕ 2 A 2 δ 2 a 3 + 2 i a 3 ( δ 2 A ) 3 A ,
q = i ξ φ + ϕ 2 3 ξ 2 A 2 ϕ 2 4 δ 4 a 3 2 1 2 ,
M 1 = | R 1 | 2 + | R 2 | 2 > 0 , M 2 = S 2 S 1 ,
M 3 = S 1 R 0 S 0 2 R 0 , M 4 = S 2 R 0 S 0 2 R 0 .
| u 1 | 2 + | u 2 | 2 = a 1 2 + a 2 2 = A ,
Ω 2 μ 2 4 μ a 1 2 μ V [ μ A δ ( μ V ) δ ] 2 = 0.

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