Abstract

We consider the spectral theory of three–wave interactions to predict the initiation, formation and dynamics of an ensemble of bright–dark–bright soliton triads in frequency conversion processes. Spatial observation of non–interacting triads ensemble in a KTP crystal confirms theoretical prediction and numerical simulations.

© 2011 OSA

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  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]
  2. V. E. Zakharov and S. V. Manakov, “Resonant interaction of wave packets in nonlinear media,” JETP Lett. 18, 243–245 (1973).
  3. V. E. Zakharov, What is Integrability? (Springer-Verlag, 1991).
  4. A. Hasegawa, Plasma Instabilities and Nonlinear Effects (Springer-Verlag, 2001).
  5. W. Cheng, Y. Avitzour, Y. Ping, S. Suckewer, N. Fisch, M. Hur, and J. Wurtele, “Reaching the nonlinear regime of raman amplification of ultrashort laser pulses,” Phys. Rev. Lett. 94, 045003 (2005).
    [CrossRef] [PubMed]
  6. E. Ibragimov and A. Struthers, “Second harmonic pulse compression in the soliton regime,” Opt. Lett. 21, 1582–1584 (1996).
    [CrossRef] [PubMed]
  7. A. Picozzi and M. Haelterman, “Spontaneous formation of symbiotic solitary waves in a backward quasi-phase-matched parametric oscillator,” Opt. Lett. 23, 1808–1810 (1998).
    [CrossRef]
  8. 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).
    [CrossRef] [PubMed]
  9. 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]
  10. A. Craik, Wave Interactions and Fluid Flows (Cambridge Univ. Press, 1985).
  11. K. Lamb, “Tidally generated near-resonant internal wave triads at shelf break,” Geophys. Res. Lett. 34, L18607 (2007).
    [CrossRef]
  12. E. Segre, Collected Papers of Enrico Fermi (University of Chicago Press, 1965).
  13. J. Ibanez and E. Verdaguer, “Soliton collision in general-relativity,” Phys. Rev. Lett. 51, 1313 (1983).
    [CrossRef]
  14. A. R. Osborne, M. Onorato, M. Serio, and L. Bergamasco, “Soliton creation and destruction, resonant interactions, and inelastic collisions in shallow water waves,” Phys. Rev. Lett. 81, 3559 (1998).
    [CrossRef]
  15. B. Damski and W. Zurek, “Soliton creation during a Bose-Einstein Condensation,” Phys. Rev. Lett. 104, 160404 (2010).
    [CrossRef] [PubMed]
  16. Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic Press, 2003).
  17. C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, “Observation of a gradient catastrophe generating solitons,” Phys. Rev. Lett. 102, 083902 (2009).
    [CrossRef] [PubMed]
  18. K. Nozaki and T. Taniuti, “Propagation of solitary pulses in interactions of plasma waves,” J. Phys. Soc. Jpn. 34, 796–800 (1973).
    [CrossRef]
  19. A. Abdolvand, A. Nazarkin, A. Chugreev, C. Kaminski, and P. Russel, “Solitary pulse generation by backward raman scattering in H-2-filled photonic crystal fibers,” Phys. Rev. Lett. 103, 183902 (2009).
    [CrossRef] [PubMed]
  20. F. Baronio, M. Conforti, M. Andreana, V. Couderc, C. De Angelis, S. Wabnitz, A. Barthelemy, and A. Degasperis, “Frequency generation and solitonic decay in three wave interactions,” Opt. Express 17, 13889–13894 (2009).
    [CrossRef] [PubMed]
  21. F. Baronio, M. Conforti, C. De Angelis, A. Degasperis, M. Andreana, V. Couderc, and A. Barthelemy, “Velocity-locked solitary waves in quadratic media,” Phys. Rev. Lett 104, 113902 (2010).
    [CrossRef] [PubMed]
  22. A. Degasperis, M. Conforti, F. Baronio, S. Wabnitz, and S. Lombardo, “The three-wave resonant interaction equations: spectral and numerical methods,” Lett. Math. Phys. 96, 367 (2011).
    [CrossRef]
  23. 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]
  24. A. Fratalocchi, C. Conti, G. Ruocco, and S. Trillo “Free-energy transition in a gas of noninteracting nonlinear wave particles,” Phys. Rev. Lett. 101, 044101 (2008).
    [CrossRef] [PubMed]

2011 (1)

A. Degasperis, M. Conforti, F. Baronio, S. Wabnitz, and S. Lombardo, “The three-wave resonant interaction equations: spectral and numerical methods,” Lett. Math. Phys. 96, 367 (2011).
[CrossRef]

2010 (2)

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

B. Damski and W. Zurek, “Soliton creation during a Bose-Einstein Condensation,” Phys. Rev. Lett. 104, 160404 (2010).
[CrossRef] [PubMed]

2009 (3)

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, “Observation of a gradient catastrophe generating solitons,” Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef] [PubMed]

A. Abdolvand, A. Nazarkin, A. Chugreev, C. Kaminski, and P. Russel, “Solitary pulse generation by backward raman scattering in H-2-filled photonic crystal fibers,” Phys. Rev. Lett. 103, 183902 (2009).
[CrossRef] [PubMed]

F. Baronio, M. Conforti, M. Andreana, V. Couderc, C. De Angelis, S. Wabnitz, A. Barthelemy, and A. Degasperis, “Frequency generation and solitonic decay in three wave interactions,” Opt. Express 17, 13889–13894 (2009).
[CrossRef] [PubMed]

2008 (1)

A. Fratalocchi, C. Conti, G. Ruocco, and S. Trillo “Free-energy transition in a gas of noninteracting nonlinear wave particles,” Phys. Rev. Lett. 101, 044101 (2008).
[CrossRef] [PubMed]

2007 (2)

2006 (2)

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]

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).
[CrossRef] [PubMed]

2005 (1)

W. Cheng, Y. Avitzour, Y. Ping, S. Suckewer, N. Fisch, M. Hur, and J. Wurtele, “Reaching the nonlinear regime of raman amplification of ultrashort laser pulses,” Phys. Rev. Lett. 94, 045003 (2005).
[CrossRef] [PubMed]

1998 (2)

A. R. Osborne, M. Onorato, M. Serio, and L. Bergamasco, “Soliton creation and destruction, resonant interactions, and inelastic collisions in shallow water waves,” Phys. Rev. Lett. 81, 3559 (1998).
[CrossRef]

A. Picozzi and M. Haelterman, “Spontaneous formation of symbiotic solitary waves in a backward quasi-phase-matched parametric oscillator,” Opt. Lett. 23, 1808–1810 (1998).
[CrossRef]

1996 (1)

1983 (1)

J. Ibanez and E. Verdaguer, “Soliton collision in general-relativity,” Phys. Rev. Lett. 51, 1313 (1983).
[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 (2)

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

K. Nozaki and T. Taniuti, “Propagation of solitary pulses in interactions of plasma waves,” J. Phys. Soc. Jpn. 34, 796–800 (1973).
[CrossRef]

Abdolvand, A.

A. Abdolvand, A. Nazarkin, A. Chugreev, C. Kaminski, and P. Russel, “Solitary pulse generation by backward raman scattering in H-2-filled photonic crystal fibers,” Phys. Rev. Lett. 103, 183902 (2009).
[CrossRef] [PubMed]

Agrawal, G. P.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic Press, 2003).

Andreana, M.

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

F. Baronio, M. Conforti, M. Andreana, V. Couderc, C. De Angelis, S. Wabnitz, A. Barthelemy, and A. Degasperis, “Frequency generation and solitonic decay in three wave interactions,” Opt. Express 17, 13889–13894 (2009).
[CrossRef] [PubMed]

Avitzour, Y.

W. Cheng, Y. Avitzour, Y. Ping, S. Suckewer, N. Fisch, M. Hur, and J. Wurtele, “Reaching the nonlinear regime of raman amplification of ultrashort laser pulses,” Phys. Rev. Lett. 94, 045003 (2005).
[CrossRef] [PubMed]

Baronio, F.

A. Degasperis, M. Conforti, F. Baronio, S. Wabnitz, and S. Lombardo, “The three-wave resonant interaction equations: spectral and numerical methods,” Lett. Math. Phys. 96, 367 (2011).
[CrossRef]

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

F. Baronio, M. Conforti, M. Andreana, V. Couderc, C. De Angelis, S. Wabnitz, A. Barthelemy, and A. Degasperis, “Frequency generation and solitonic decay in three wave interactions,” Opt. Express 17, 13889–13894 (2009).
[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, 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]

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).
[CrossRef] [PubMed]

Barthelemy, A.

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

F. Baronio, M. Conforti, M. Andreana, V. Couderc, C. De Angelis, S. Wabnitz, A. Barthelemy, and A. Degasperis, “Frequency generation and solitonic decay in three wave interactions,” Opt. Express 17, 13889–13894 (2009).
[CrossRef] [PubMed]

Bergamasco, L.

A. R. Osborne, M. Onorato, M. Serio, and L. Bergamasco, “Soliton creation and destruction, resonant interactions, and inelastic collisions in shallow water waves,” Phys. Rev. Lett. 81, 3559 (1998).
[CrossRef]

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]

Cheng, W.

W. Cheng, Y. Avitzour, Y. Ping, S. Suckewer, N. Fisch, M. Hur, and J. Wurtele, “Reaching the nonlinear regime of raman amplification of ultrashort laser pulses,” Phys. Rev. Lett. 94, 045003 (2005).
[CrossRef] [PubMed]

Chugreev, A.

A. Abdolvand, A. Nazarkin, A. Chugreev, C. Kaminski, and P. Russel, “Solitary pulse generation by backward raman scattering in H-2-filled photonic crystal fibers,” Phys. Rev. Lett. 103, 183902 (2009).
[CrossRef] [PubMed]

Conforti, M.

A. Degasperis, M. Conforti, F. Baronio, S. Wabnitz, and S. Lombardo, “The three-wave resonant interaction equations: spectral and numerical methods,” Lett. Math. Phys. 96, 367 (2011).
[CrossRef]

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

F. Baronio, M. Conforti, M. Andreana, V. Couderc, C. De Angelis, S. Wabnitz, A. Barthelemy, and A. Degasperis, “Frequency generation and solitonic decay in three wave interactions,” Opt. Express 17, 13889–13894 (2009).
[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, 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]

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).
[CrossRef] [PubMed]

Conti, C.

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, “Observation of a gradient catastrophe generating solitons,” Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef] [PubMed]

A. Fratalocchi, C. Conti, G. Ruocco, and S. Trillo “Free-energy transition in a gas of noninteracting nonlinear wave particles,” Phys. Rev. Lett. 101, 044101 (2008).
[CrossRef] [PubMed]

Couderc, V.

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

F. Baronio, M. Conforti, M. Andreana, V. Couderc, C. De Angelis, S. Wabnitz, A. Barthelemy, and A. Degasperis, “Frequency generation and solitonic decay in three wave interactions,” Opt. Express 17, 13889–13894 (2009).
[CrossRef] [PubMed]

Craik, A.

A. Craik, Wave Interactions and Fluid Flows (Cambridge Univ. Press, 1985).

Damski, B.

B. Damski and W. Zurek, “Soliton creation during a Bose-Einstein Condensation,” Phys. Rev. Lett. 104, 160404 (2010).
[CrossRef] [PubMed]

De Angelis, C.

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

F. Baronio, M. Conforti, M. Andreana, V. Couderc, C. De Angelis, S. Wabnitz, A. Barthelemy, and A. Degasperis, “Frequency generation and solitonic decay in three wave interactions,” Opt. Express 17, 13889–13894 (2009).
[CrossRef] [PubMed]

Degasperis, A.

A. Degasperis, M. Conforti, F. Baronio, S. Wabnitz, and S. Lombardo, “The three-wave resonant interaction equations: spectral and numerical methods,” Lett. Math. Phys. 96, 367 (2011).
[CrossRef]

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

F. Baronio, M. Conforti, M. Andreana, V. Couderc, C. De Angelis, S. Wabnitz, A. Barthelemy, and A. Degasperis, “Frequency generation and solitonic decay in three wave interactions,” Opt. Express 17, 13889–13894 (2009).
[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, 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]

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).
[CrossRef] [PubMed]

Fisch, N.

W. Cheng, Y. Avitzour, Y. Ping, S. Suckewer, N. Fisch, M. Hur, and J. Wurtele, “Reaching the nonlinear regime of raman amplification of ultrashort laser pulses,” Phys. Rev. Lett. 94, 045003 (2005).
[CrossRef] [PubMed]

Fratalocchi, A.

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, “Observation of a gradient catastrophe generating solitons,” Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef] [PubMed]

A. Fratalocchi, C. Conti, G. Ruocco, and S. Trillo “Free-energy transition in a gas of noninteracting nonlinear wave particles,” Phys. Rev. Lett. 101, 044101 (2008).
[CrossRef] [PubMed]

Haelterman, M.

Hasegawa, A.

A. Hasegawa, Plasma Instabilities and Nonlinear Effects (Springer-Verlag, 2001).

Hur, M.

W. Cheng, Y. Avitzour, Y. Ping, S. Suckewer, N. Fisch, M. Hur, and J. Wurtele, “Reaching the nonlinear regime of raman amplification of ultrashort laser pulses,” Phys. Rev. Lett. 94, 045003 (2005).
[CrossRef] [PubMed]

Ibanez, J.

J. Ibanez and E. Verdaguer, “Soliton collision in general-relativity,” Phys. Rev. Lett. 51, 1313 (1983).
[CrossRef]

Ibragimov, E.

Kaminski, C.

A. Abdolvand, A. Nazarkin, A. Chugreev, C. Kaminski, and P. Russel, “Solitary pulse generation by backward raman scattering in H-2-filled photonic crystal fibers,” Phys. Rev. Lett. 103, 183902 (2009).
[CrossRef] [PubMed]

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]

Kivshar, Y. S.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic Press, 2003).

Lamb, K.

K. Lamb, “Tidally generated near-resonant internal wave triads at shelf break,” Geophys. Res. Lett. 34, L18607 (2007).
[CrossRef]

Lombardo, S.

A. Degasperis, M. Conforti, F. Baronio, S. Wabnitz, and S. Lombardo, “The three-wave resonant interaction equations: spectral and numerical methods,” Lett. Math. Phys. 96, 367 (2011).
[CrossRef]

Manakov, S. V.

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

Nazarkin, A.

A. Abdolvand, A. Nazarkin, A. Chugreev, C. Kaminski, and P. Russel, “Solitary pulse generation by backward raman scattering in H-2-filled photonic crystal fibers,” Phys. Rev. Lett. 103, 183902 (2009).
[CrossRef] [PubMed]

Nozaki, K.

K. Nozaki and T. Taniuti, “Propagation of solitary pulses in interactions of plasma waves,” J. Phys. Soc. Jpn. 34, 796–800 (1973).
[CrossRef]

Onorato, M.

A. R. Osborne, M. Onorato, M. Serio, and L. Bergamasco, “Soliton creation and destruction, resonant interactions, and inelastic collisions in shallow water waves,” Phys. Rev. Lett. 81, 3559 (1998).
[CrossRef]

Osborne, A. R.

A. R. Osborne, M. Onorato, M. Serio, and L. Bergamasco, “Soliton creation and destruction, resonant interactions, and inelastic collisions in shallow water waves,” Phys. Rev. Lett. 81, 3559 (1998).
[CrossRef]

Peccianti, M.

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, “Observation of a gradient catastrophe generating solitons,” Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef] [PubMed]

Picozzi, A.

Ping, Y.

W. Cheng, Y. Avitzour, Y. Ping, S. Suckewer, N. Fisch, M. Hur, and J. Wurtele, “Reaching the nonlinear regime of raman amplification of ultrashort laser pulses,” Phys. Rev. Lett. 94, 045003 (2005).
[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]

Ruocco, G.

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, “Observation of a gradient catastrophe generating solitons,” Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef] [PubMed]

A. Fratalocchi, C. Conti, G. Ruocco, and S. Trillo “Free-energy transition in a gas of noninteracting nonlinear wave particles,” Phys. Rev. Lett. 101, 044101 (2008).
[CrossRef] [PubMed]

Russel, P.

A. Abdolvand, A. Nazarkin, A. Chugreev, C. Kaminski, and P. Russel, “Solitary pulse generation by backward raman scattering in H-2-filled photonic crystal fibers,” Phys. Rev. Lett. 103, 183902 (2009).
[CrossRef] [PubMed]

Segre, E.

E. Segre, Collected Papers of Enrico Fermi (University of Chicago Press, 1965).

Serio, M.

A. R. Osborne, M. Onorato, M. Serio, and L. Bergamasco, “Soliton creation and destruction, resonant interactions, and inelastic collisions in shallow water waves,” Phys. Rev. Lett. 81, 3559 (1998).
[CrossRef]

Struthers, A.

Suckewer, S.

W. Cheng, Y. Avitzour, Y. Ping, S. Suckewer, N. Fisch, M. Hur, and J. Wurtele, “Reaching the nonlinear regime of raman amplification of ultrashort laser pulses,” Phys. Rev. Lett. 94, 045003 (2005).
[CrossRef] [PubMed]

Taniuti, T.

K. Nozaki and T. Taniuti, “Propagation of solitary pulses in interactions of plasma waves,” J. Phys. Soc. Jpn. 34, 796–800 (1973).
[CrossRef]

Trillo, S.

C. Conti, A. Fratalocchi, M. Peccianti, G. Ruocco, and S. Trillo, “Observation of a gradient catastrophe generating solitons,” Phys. Rev. Lett. 102, 083902 (2009).
[CrossRef] [PubMed]

A. Fratalocchi, C. Conti, G. Ruocco, and S. Trillo “Free-energy transition in a gas of noninteracting nonlinear wave particles,” Phys. Rev. Lett. 101, 044101 (2008).
[CrossRef] [PubMed]

Verdaguer, E.

J. Ibanez and E. Verdaguer, “Soliton collision in general-relativity,” Phys. Rev. Lett. 51, 1313 (1983).
[CrossRef]

Wabnitz, S.

A. Degasperis, M. Conforti, F. Baronio, S. Wabnitz, and S. Lombardo, “The three-wave resonant interaction equations: spectral and numerical methods,” Lett. Math. Phys. 96, 367 (2011).
[CrossRef]

F. Baronio, M. Conforti, M. Andreana, V. Couderc, C. De Angelis, S. Wabnitz, A. Barthelemy, and A. Degasperis, “Frequency generation and solitonic decay in three wave interactions,” Opt. Express 17, 13889–13894 (2009).
[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, 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]

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).
[CrossRef] [PubMed]

Wurtele, J.

W. Cheng, Y. Avitzour, Y. Ping, S. Suckewer, N. Fisch, M. Hur, and J. Wurtele, “Reaching the nonlinear regime of raman amplification of ultrashort laser pulses,” Phys. Rev. Lett. 94, 045003 (2005).
[CrossRef] [PubMed]

Zakharov, V. E.

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

V. E. Zakharov, What is Integrability? (Springer-Verlag, 1991).

Zurek, W.

B. Damski and W. Zurek, “Soliton creation during a Bose-Einstein Condensation,” Phys. Rev. Lett. 104, 160404 (2010).
[CrossRef] [PubMed]

Geophys. Res. Lett. (1)

K. Lamb, “Tidally generated near-resonant internal wave triads at shelf break,” Geophys. Res. Lett. 34, L18607 (2007).
[CrossRef]

J. Phys. Soc. Jpn. (1)

K. Nozaki and T. Taniuti, “Propagation of solitary pulses in interactions of plasma waves,” J. Phys. Soc. Jpn. 34, 796–800 (1973).
[CrossRef]

JETP Lett. (1)

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

Lett. Math. Phys. (1)

A. Degasperis, M. Conforti, F. Baronio, S. Wabnitz, and S. Lombardo, “The three-wave resonant interaction equations: spectral and numerical methods,” Lett. Math. Phys. 96, 367 (2011).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. E (1)

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]

Phys. Rev. Lett (1)

F. Baronio, M. Conforti, C. De Angelis, A. Degasperis, M. Andreana, V. Couderc, and A. Barthelemy, “Velocity-locked solitary waves in quadratic media,” Phys. Rev. Lett 104, 113902 (2010).
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Phys. Rev. Lett. (8)

W. Cheng, Y. Avitzour, Y. Ping, S. Suckewer, N. Fisch, M. Hur, and J. Wurtele, “Reaching the nonlinear regime of raman amplification of ultrashort laser pulses,” Phys. Rev. Lett. 94, 045003 (2005).
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A. Fratalocchi, C. Conti, G. Ruocco, and S. Trillo “Free-energy transition in a gas of noninteracting nonlinear wave particles,” Phys. Rev. Lett. 101, 044101 (2008).
[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).
[CrossRef] [PubMed]

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Rev. Mod. Phys. (1)

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A. Hasegawa, Plasma Instabilities and Nonlinear Effects (Springer-Verlag, 2001).

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Figures (7)

Fig. 1
Fig. 1

Frequency conversion. Numerical dynamics of the beams ϕ 1 (a), ϕ 2 (b), ϕ 3 (c) in the sξ plane.

Fig. 2
Fig. 2

Single-soliton triad generation. a) Beam profiles ϕ 1 (blue line), ϕ 2 (red line), ϕ 3 (green line) at input ξ = 0 (dashed lines) and at output ξ = 12 (solid lines). b) Eigenvalue λ and spectral eigenfunctions ψ 1 (blue line), ψ 2 (red line), ψ 3 (green line) corresponding to input data at ξ = 0. c) Spectral informations at ξ = 12. Numerical dynamics of the beams ϕ 1 (d), ϕ 2 (e), ϕ 3 (f) in the s – ξ plane.

Fig. 3
Fig. 3

Soliton triads. (a) Beam profiles ϕ 1 (blue line), ϕ 2 (red line), ϕ 3 (green line) at input ξ = 0 (dashed lines) and at output ξ = 12 (solid lines). (b)-(c) Eigenvalue λ and spectral eigenfunctions ψ 1 (blue line), ψ 2 (red line), ψ 3 (green line) corresponding to envelope input data at ξ = 0 (dashed lines) and ξ = 12 (solid lines). Numerical dynamics of the beams ϕ 1 (d), ϕ 2 (e), ϕ 3 (f) in the s – ξ plane.

Fig. 4
Fig. 4

Soliton triads. Numerical dynamics of the beams ϕ 1 (a), ϕ 2 (b), ϕ 3 (c) in the sξ plane.

Fig. 5
Fig. 5

Left, experimental set-up. M1, M2, M3, M4: mirrors. P1: polarizer. L1, L2: lenses. Right, schematic representation of the optical noncollinear configuration in the KTP crystal.

Fig. 6
Fig. 6

Left column, numerical dynamics of the beam E 2 in the x – z (y = 0) plane. Central column, numerical, and right column, experimental results at the exit face of the KTP crystal presenting the spatial x – y output profiles of E 2. Upper row, frequency conversion regime (I 1 = 10MW/cm 2, I 2 = 0.03MW/cm 2); central row, soliton triad generation (I 1 = 50MW/cm 2, I 2 = 0.2MW/cm 2); lower row, non-interacting soliton triad ensemble (I 1 = 500MW/cm 2, I 2 = 5MW/cm 2).

Fig. 7
Fig. 7

Left column, numerical dynamics of the beam E 3 in the xz (y = 0) plane. Central column, numerical, and right column, experimental results at the exit face of the KTP crystal presenting the spatial xy output profiles of E 3. Upper row, frequency conversion regime (I 1 = 10MW/cm 2, I 2 = 0.03MW/cm 2); central row, soliton triad generation (I 1 = 50MW/cm 2, I 2 = 0.2MW/cm 2); lower row, non-interacting soliton triad ensemble (I 1 = 500MW/cm 2, I 2 = 5MW/cm 2).

Equations (6)

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( z + ρ 1 x ) E 1 + 1 2 i k 1 ( 2 x 2 + 2 y 2 ) E 1 = i χ 1 E 2 * E 3 , ( z + ρ 2 x ) E 2 + 1 2 i k 2 ( 2 x 2 + 2 y 2 ) E 2 = i χ 2 E 1 * E 3 , ( z + ρ 3 x ) E 3 + 1 2 i k 3 ( 2 x 2 + 2 y 2 ) E 3 = i χ 3 E 1 E 2 .
( ξ + δ 1 s ) ϕ 1 = i ϕ 2 * ϕ 3 , ( ξ + δ 2 s ) ϕ 2 = i ϕ 1 * ϕ 3 , ( ξ + δ 3 s ) ϕ 3 = i ϕ 1 ϕ 2 ,
( ξ + ν n s ) Q n = σ n Q n + 1 * Q n + 2 * n = 1 , 2 , 3 , mod 3 .
ψ s = [ i λ A + E ( s , ξ ) ] ψ ,
ψ ξ = [ i λ B + F ( s , ξ ) ] ψ + ψ C ,
E = ( 0 u 3 v 2 v 3 0 u 1 u 2 v 1 0 ) , F = ( 0 ν 3 u 3 ν 2 v 2 ν 3 v 3 0 ν 1 u 1 ν 2 u 2 ν 1 v 1 0 ) ,

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