Abstract

We investigate the resonant interaction of three optical pulses of different group velocity in quadratic media and report on the novel watch-hand-like super rogue wave patterns. In addition to having a giant wall-like hump, each rogue-wave hand involves a peak amplitude more than five times its background height. We attribute such peculiar structures to the nonlinear superposition of six Peregrine-type solitons. The robustness has been confirmed by numerical simulations. This stability along with the non-overlapping distribution property may facilitate the experimental diagnostics and observation of these super rogue waves.

© 2015 Optical Society of America

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References

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    [Crossref]
  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]
  3. J. M. Dudley, G. Genty, and B. J. Eggleton, “Harnessing and control of optical rogue waves in supercontinuum generation,” Opt. Express 16, 3644–3651 (2008).
    [Crossref] [PubMed]
  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).
  5. S. Birkholz, E. T. J. Nibbering, C. Brée, S. Skupin, A. Demircan, G. Genty, and G. Steinmeyer, “Spatiotemporal rogue events in optical multiple filamentation,” Phys. Rev. Lett. 111, 243903 (2013).
  6. 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]
  7. 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]
  8. A. Chabchoub, N. P. Hoffmann, and N. Akhmediev, “Rogue wave observation in a water wave tank,” Phys. Rev. Lett. 106, 204502 (2011).
  9. 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).
  10. A. Degasperis and S. Lombardo, “Rational solitons of wave resonant-interaction models,” Phys. Rev. E 88, 052914 (2013).
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    [Crossref]
  12. 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]
  13. 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).
  14. A. Ankiewicz, D. J. Kedziora, and N. Akhmediev, “Rogue wave triplets,” Phys. Lett. A 375, 2782–2785 (2011).
    [Crossref]
  15. D. J. Kedziora, A. Ankiewicz, and N. Akhmediev, “Classifying the hierarchy of nonlinear-Schrödinger-equation rogue-wave solutions,” Phys. Rev. E 88, 013207 (2013).
    [Crossref]
  16. A. Chabchoub, N. Hoffmann, M. Onorato, and N. Akhmediev, “Super rogue waves: Observation of a higher-order breather in water waves,” Phys. Rev. X 2, 011015 (2012).
  17. S. Chen, J. M. Soto-Crespo, and Ph. Grelu, “Dark three-sister rogue waves in normally dispersive optical fibers with random birefringence,” Opt. Express 22, 27632–27642 (2014).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  21. A. Picozzi and M. Haelterman, “Parametric three-wave soliton generated from incoherent light,” Phys. Rev. Lett. 86, 2010–2013 (2001).
  22. 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).
  23. V. E. Zakharov and S. V. Manakov, “Resonant interaction of wave packets in nonlinear media,” Jept. Lett. 18, 243–245 (1973).
  24. A. Buryak, P. Di Trapani, D. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
    [Crossref]
  25. A. Degasperis, M. Conforti, F. Baronio, and S. Wabnitz, “Stable control of pulse speed in parametric three-wave solitons,” Phys. Rev. Lett. 97, 093901 (2006).
  26. 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).
  27. M. Conforti, F. Baronio, and A. Degasperis, “Modulational instability of dark solitons in three wave resonant interaction,” Physica D 240, 1362–1369 (2011).
    [Crossref]
  28. V. E. Zakharov and E. I. Schulman, “To the integrability of the system of two coupled nonlinear Schrödinger equations,” Physica D 4, 270–274 (1982).
    [Crossref]

2014 (3)

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).

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

2013 (5)

D. J. Kedziora, A. Ankiewicz, and N. Akhmediev, “Classifying the hierarchy of nonlinear-Schrödinger-equation rogue-wave solutions,” Phys. Rev. E 88, 013207 (2013).
[Crossref]

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

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]

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

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]

2012 (3)

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).

A. Chabchoub, N. Hoffmann, M. Onorato, and N. Akhmediev, “Super rogue waves: Observation of a higher-order breather in water waves,” Phys. Rev. X 2, 011015 (2012).

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).

2011 (3)

M. Conforti, F. Baronio, and A. Degasperis, “Modulational instability of dark solitons in three wave resonant interaction,” Physica D 240, 1362–1369 (2011).
[Crossref]

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

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

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).

2009 (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).
[Crossref]

2008 (1)

2007 (2)

2006 (1)

A. Degasperis, M. Conforti, F. Baronio, and S. Wabnitz, “Stable control of pulse speed in parametric three-wave solitons,” Phys. Rev. Lett. 97, 093901 (2006).

2002 (1)

A. Buryak, P. Di Trapani, D. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[Crossref]

2001 (1)

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

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).

1996 (1)

1982 (1)

V. E. Zakharov and E. I. Schulman, “To the integrability of the system of two coupled nonlinear Schrödinger equations,” Physica D 4, 270–274 (1982).
[Crossref]

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]

1973 (1)

V. E. Zakharov and S. V. Manakov, “Resonant interaction of wave packets in nonlinear media,” Jept. Lett. 18, 243–245 (1973).

Akhmediev, N.

D. J. Kedziora, A. Ankiewicz, and N. Akhmediev, “Classifying the hierarchy of nonlinear-Schrödinger-equation rogue-wave solutions,” Phys. Rev. E 88, 013207 (2013).
[Crossref]

A. Chabchoub, N. Hoffmann, M. Onorato, and N. Akhmediev, “Super rogue waves: Observation of a higher-order breather in water waves,” Phys. Rev. X 2, 011015 (2012).

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).

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

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).

Ankiewicz, A.

D. J. Kedziora, A. Ankiewicz, and N. Akhmediev, “Classifying the hierarchy of nonlinear-Schrödinger-equation rogue-wave solutions,” Phys. Rev. E 88, 013207 (2013).
[Crossref]

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]

Baronio, F.

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]

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).

M. Conforti, F. Baronio, and A. Degasperis, “Modulational instability of dark solitons in three wave resonant interaction,” Physica D 240, 1362–1369 (2011).
[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).

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

A. Degasperis, M. Conforti, F. Baronio, and S. Wabnitz, “Stable control of pulse speed in parametric three-wave solitons,” Phys. Rev. Lett. 97, 093901 (2006).

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).

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]

Birkholz, S.

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

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]

Brée, C.

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

Buryak, A.

A. Buryak, P. Di Trapani, D. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[Crossref]

Chabchoub, A.

A. Chabchoub, N. Hoffmann, M. Onorato, and N. Akhmediev, “Super rogue waves: Observation of a higher-order breather in water waves,” Phys. Rev. X 2, 011015 (2012).

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

Chen, S.

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).

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

Conforti, M.

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]

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).

M. Conforti, F. Baronio, and A. Degasperis, “Modulational instability of dark solitons in three wave resonant interaction,” Physica D 240, 1362–1369 (2011).
[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).

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

A. Degasperis, M. Conforti, F. Baronio, and S. Wabnitz, “Stable control of pulse speed in parametric three-wave solitons,” Phys. Rev. Lett. 97, 093901 (2006).

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).

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).

Degasperis, A.

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]

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

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).

M. Conforti, F. Baronio, and A. Degasperis, “Modulational instability of dark solitons in three wave resonant interaction,” Physica D 240, 1362–1369 (2011).
[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).

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

A. Degasperis, M. Conforti, F. Baronio, and S. Wabnitz, “Stable control of pulse speed in parametric three-wave solitons,” Phys. Rev. Lett. 97, 093901 (2006).

Demircan, A.

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

Di Trapani, P.

A. Buryak, P. Di Trapani, D. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[Crossref]

Dias, F.

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.

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, 3644–3651 (2008).
[Crossref] [PubMed]

Eggleton, B. J.

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).

Genty, G.

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

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, 3644–3651 (2008).
[Crossref] [PubMed]

Grelu, Ph.

S. Chen, J. M. Soto-Crespo, and Ph. Grelu, “Dark three-sister rogue waves in normally dispersive optical fibers with random birefringence,” Opt. Express 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).

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).

Haelterman, M.

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

Hoffmann, N.

A. Chabchoub, N. Hoffmann, M. Onorato, and N. Akhmediev, “Super rogue waves: Observation of a higher-order breather in water waves,” Phys. Rev. X 2, 011015 (2012).

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).

Ibragimov, E.

Jalali, B.

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

D. J. Kedziora, A. Ankiewicz, and N. Akhmediev, “Classifying the hierarchy of nonlinear-Schrödinger-equation rogue-wave solutions,” Phys. Rev. E 88, 013207 (2013).
[Crossref]

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

Kibler, B.

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).

Lombardo, S.

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

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]

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).

Manakov, S. V.

V. E. Zakharov and S. V. Manakov, “Resonant interaction of wave packets in nonlinear media,” Jept. Lett. 18, 243–245 (1973).

Millot, G.

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]

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]

Nibbering, E. T. J.

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

Onorato, M.

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]

A. Chabchoub, N. Hoffmann, M. Onorato, and N. Akhmediev, “Super rogue waves: Observation of a higher-order breather in water waves,” Phys. Rev. X 2, 011015 (2012).

Picozzi, A.

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

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]

Schulman, E. I.

V. E. Zakharov and E. I. Schulman, “To the integrability of the system of two coupled nonlinear Schrödinger equations,” Physica D 4, 270–274 (1982).
[Crossref]

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).

Skryabin, D.

A. Buryak, P. Di Trapani, D. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[Crossref]

Skupin, S.

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

Solli, D. R.

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, 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).

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

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).

Steinmeyer, G.

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

Struthers, A.

Taki, M.

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]

Trillo, S.

A. Buryak, P. Di Trapani, D. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[Crossref]

Wabnitz, S.

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).

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

A. Degasperis, M. Conforti, F. Baronio, and S. Wabnitz, “Stable control of pulse speed in parametric three-wave solitons,” Phys. Rev. Lett. 97, 093901 (2006).

Zakharov, V. E.

V. E. Zakharov and E. I. Schulman, “To the integrability of the system of two coupled nonlinear Schrödinger equations,” Physica D 4, 270–274 (1982).
[Crossref]

V. E. Zakharov and S. V. Manakov, “Resonant interaction of wave packets in nonlinear media,” Jept. Lett. 18, 243–245 (1973).

Jept. Lett. (1)

V. E. Zakharov and S. V. Manakov, “Resonant interaction of wave packets in nonlinear media,” Jept. Lett. 18, 243–245 (1973).

Nature (London) (1)

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

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).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Phys. Lett. A (2)

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]

Phys. Rep. (2)

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]

A. Buryak, P. Di Trapani, D. Skryabin, and S. Trillo, “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications,” Phys. Rep. 370, 63–235 (2002).
[Crossref]

Phys. Rev. E (4)

D. J. Kedziora, A. Ankiewicz, and N. Akhmediev, “Classifying the hierarchy of nonlinear-Schrödinger-equation rogue-wave solutions,” Phys. Rev. E 88, 013207 (2013).
[Crossref]

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

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).

Phys. Rev. Lett. (9)

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]

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

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).

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).

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

A. Degasperis, M. Conforti, F. Baronio, and S. Wabnitz, “Stable control of pulse speed in parametric three-wave solitons,” Phys. Rev. Lett. 97, 093901 (2006).

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).

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

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).

Phys. Rev. X (1)

A. Chabchoub, N. Hoffmann, M. Onorato, and N. Akhmediev, “Super rogue waves: Observation of a higher-order breather in water waves,” Phys. Rev. X 2, 011015 (2012).

Physica D (2)

M. Conforti, F. Baronio, and A. Degasperis, “Modulational instability of dark solitons in three wave resonant interaction,” Physica D 240, 1362–1369 (2011).
[Crossref]

V. E. Zakharov and E. I. Schulman, “To the integrability of the system of two coupled nonlinear Schrödinger equations,” Physica D 4, 270–274 (1982).
[Crossref]

Rev. Mod. Phys. (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]

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Figures (6)

Fig. 1
Fig. 1 WHL optical rogue waves formed at a1 = 1, V1 = 9 and V2 = 1: (a)–(c) surface plots; (d)–(f) contour distributions. (g) shows the watch trait by superimposing the above three components in one image. Here γ3 = 1 and the other structural parameters are zero.
Fig. 2
Fig. 2 Rogue wave sextets obtained under the same initial parameters as in Fig. 1, but with γ1 = 200i, γ3 = 1, γ5 = 1000, γ6 = 300, and γ2 = γ4 = 0.
Fig. 3
Fig. 3 Evolutions of the effective energy In (or Pn) with respect to t (or x) for: (a), (c) the WHL rogue wave case; (b), (d) the rogue wave sextet case.
Fig. 4
Fig. 4 Simulations of the WHL optical rogue waves shown in Fig. 1 under otherwise identical parameter conditions. (a)–(c) show the unperturbed numerical results, while (d)–(f) are results obtained by perturbing the initial profiles with white noise.
Fig. 5
Fig. 5 (a) The map of the MI gain versus V2 and Ω for a1 = 1 and V1 = 9. The superimposed image in (a) results from calculations of two cubic equations in Eq. (9). (b) shows the growth rate (green line) versus Ω for a specific V2 = 1, as indicated by the dash-dotted line in (a). The blue cross in (b) indicates the maximum value of the growth rate.
Fig. 6
Fig. 6 Simulations of the WHL optical rogue waves formed at a1 = 1, V1 = 9, and V2 = 4, initially perturbed by white noise of intensity ε = 5 × 104.

Equations (9)

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

u 1 t + V 1 u 1 x = u 2 * u 3 * , u 2 t + V 2 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 ] ,
δ = σ 1 a 1 = σ 2 a 2 .
u 1 [ 2 ] = u 10 { 1 + 3 i θ 1 ( λ 0 λ 0 * ) [ R 0 * ( R 1 m 22 S 1 m 21 ) + S 0 * ( S 1 m 11 R 1 m 12 ) ] σ 1 a 1 ( m 11 m 22 m 12 m 21 ) } , u 2 [ 2 ] = u 20 { 1 + 3 i θ 1 ( λ 0 λ 0 * ) [ R 2 * ( R 0 m 22 S 0 m 21 ) + S 2 * ( S 0 m 11 R 0 m 12 ) ] σ 2 a 2 ( m 11 m 22 m 12 m 21 ) } , u 3 [ 2 ] = u 30 { 1 + 3 i θ 1 ( λ 0 λ 0 * ) [ R 1 * ( R 2 m 22 S 2 m 21 ) + S 1 * ( S 2 m 11 R 2 m 12 ) ] σ 1 σ 2 a 3 ( m 11 m 22 m 12 m 21 ) } ,
R 0 = γ 1 + 2 γ 2 ξ + 4 γ 3 ( ξ 2 + 2 ξ + 3 i ρ ) , R j = γ 1 + 2 γ 2 ( ξ 3 θ j ) + 4 γ 3 [ ξ 2 + 3 i ρ 2 i ( 1 ) j ( ξ / θ j 3 ) ] , S 0 = γ 1 c 0 + γ 2 d 0 + γ 3 e 0 + γ 4 + 2 γ 5 ξ + 4 γ 6 ( ξ 2 + 2 ξ + 3 i ρ ) , S j = γ 1 c j + γ 2 d j + γ 3 e j + γ 4 + 2 γ 5 ( ξ 3 θ j ) + 4 γ 6 [ ξ 2 + 3 i ρ 2 i ( 1 ) j ( ξ / θ j 3 ) ] , m 11 = | R 0 | 2 + | R 1 | 2 + | R 2 | 2 , m 12 = R 0 * S 0 + R 1 * S 1 + R 2 * S 2 m 11 m 21 * , m 22 = | S 0 | 2 + | S 1 | 2 + | S 2 | 2 m 12 m 21 ,
ξ = 6 A 2 [ t + i ( 1 V 1 θ 1 1 V 2 θ 2 ) x ] , ρ = 2 A ( 1 V 2 1 V 1 ) x , η = 6 A ( 1 V 2 + 1 V 1 ) x , c 0 = 1 6 ξ 3 + ξ 2 + 1 2 ( η + 3 i ξ ρ ) , c j = c 0 3 2 ( ξ 2 + 3 i ρ ) θ j 3 ( ξ 1 ) θ j , d 0 = 1 12 ξ 4 + ξ 3 + ξ 2 + 4 3 ξ 9 4 ρ 2 + 3 i 2 ρ ξ ( ξ + 2 ) + η ξ , d j = d 0 3 3 [ ξ 2 + 5 ξ + 9 i ρ + ( 1 ) j i ( 4 θ j 3 ξ ) ] [ θ j ξ ( 1 ) j i ] 3 θ j η , e 0 = 2 i ( 3 η + 2 ) ρ + 2 η ξ ( ξ + 2 ) + 1 9 ξ ( ξ 2 + 6 ξ + 9 i ρ ) 2 2 45 ξ ( ξ 4 120 ξ 60 ) , e j = e 0 3 θ j ( ξ 2 + 3 i ρ ) 2 4 3 η [ θ j ξ ( 1 ) j i ] 12 3 i ( ξ 1 ) ρ θ j + ξ ( ξ 3 6 ξ 2 4 ) + ( 1 ) j i 3 3 ( ξ 2 ) ( ξ 3 + 12 ξ 4 ) .
d d t ( I 1 + I 2 ) = d d t ( I 2 + I 3 ) = 0 ,
d d x ( V 1 P 1 + V 2 P 2 ) = d d x ( V 2 P 2 + V 3 P 3 ) = 0.
Ω μ ( μ V 1 ) ( μ V 2 ) ± 2 A 2 [ ( V 1 V 2 1 + V 2 V 1 ) μ 2 ( V 1 + V 2 ) μ + V 1 V 2 ] = 0 ,

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