Abstract

We consider experimentally three-wave resonant nonlinear interactions of fields propagating in nonlinear media. We investigate the spatial dynamics of two diffractionless beams at frequency ω 1, ω 2 which mix to generate a field at the sum frequency ω 3. If the generated field at ω 3 can sustain a soliton, it decays into solitons at ω 1, ω 2. We report the experimental evidence of the transition from steady frequency wave generation to solitonic decay in nonlinear optics.

© 2009 Optical Society of America

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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. B. Kim, J. Blake, H. Engan, and H. Shaw, "All-fiber acousto-optic frequency shifter," Opt. Lett. 11, 389-391 (1986).
    [CrossRef] [PubMed]
  3. P. Russel, 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]
  4. E. Ibragimov, and A. Struthers, "Second harmonic pulse compression in the soliton regime," Opt. Lett. 21, 1582-1584 (1996).
    [CrossRef] [PubMed]
  5. 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]
  6. F. Baronio, M. Conforti, A. Degasperis, and S. Wabnitz, "Three-wave trapponic solitons for tunable highrepetition rate pulse train generation, " IEEE J. Quantum Electron. 44, 542-546 (2008).
    [CrossRef]
  7. A. Hasegawa, Plasma Instabilities and Nonlinear Effects (Springer-Verlag, Berlin, 2001).
  8. Y. Tsidulko, V. Malkin, and N. Fisch, "Suppression of Superluminous Precursors in High-Power Backward Raman Amplifiers," Phys. Rev. Lett. 88, 235004 (2002).
    [CrossRef] [PubMed]
  9. 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]
  10. A. Craik, Wave Interactions and Fluid Flows (Cambridge Univ. Press, Cambridge, 1985).
  11. K. Lamb, "Tidally generated near-resonant internal wave triads at shelf break," Geophys. Res. Lett. 34, L18607 (2007).
    [CrossRef]
  12. L. Svaasand, "Interaction between elastic surface waves in piezoelectric materials," Appl. Phys. Lett. 15, 300-302 (1969).
    [CrossRef]
  13. Y. N. Karamzin, and A. P. Sukhorukov, "Nonlinear interaction of diffracted light beams in a medium with quadratic nonlinearity: mutual focusing of beams and limitation on the efficiency of optical frequency converters," JEPT Lett. 20, 339-344 (1974).
  14. 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]
  15. V. E. Zakharov, and S. V. Manakov, "Resonant interaction of wave packets in nonlinear media," Jept. Lett. 18, 243-245 (1973).
  16. K. Nozaki, and T. Taniuti, "Propagation of solitary pulses in interactions of plasma waves," J. Phys. Soc. Jpn. 34, 796-800 (1973).
    [CrossRef]
  17. V. E. Zakharov, What is integrability? (Springer Verlag, Berlin, 1991).
  18. V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitajevski, The Theory of Solitons: The Inverse Problem Method (Nauka, Moskow, 1980).

2008

F. Baronio, M. Conforti, A. Degasperis, and S. Wabnitz, "Three-wave trapponic solitons for tunable highrepetition rate pulse train generation, " IEEE J. Quantum Electron. 44, 542-546 (2008).
[CrossRef]

2007

2005

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]

2002

Y. Tsidulko, V. Malkin, and N. Fisch, "Suppression of Superluminous Precursors in High-Power Backward Raman Amplifiers," Phys. Rev. Lett. 88, 235004 (2002).
[CrossRef] [PubMed]

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]

1996

1991

P. Russel, 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]

1986

1979

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]

1974

Y. N. Karamzin, and A. P. Sukhorukov, "Nonlinear interaction of diffracted light beams in a medium with quadratic nonlinearity: mutual focusing of beams and limitation on the efficiency of optical frequency converters," JEPT Lett. 20, 339-344 (1974).

1973

V. E. Zakharov, and S. V. Manakov, "Resonant interaction of wave packets in nonlinear media," Jept. 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]

1969

L. Svaasand, "Interaction between elastic surface waves in piezoelectric materials," Appl. Phys. Lett. 15, 300-302 (1969).
[CrossRef]

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.

F. Baronio, M. Conforti, A. Degasperis, and S. Wabnitz, "Three-wave trapponic solitons for tunable highrepetition rate pulse train generation, " IEEE J. Quantum Electron. 44, 542-546 (2008).
[CrossRef]

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]

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]

Blake, J.

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]

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]

Conforti, M.

F. Baronio, M. Conforti, A. Degasperis, and S. Wabnitz, "Three-wave trapponic solitons for tunable highrepetition rate pulse train generation, " IEEE J. Quantum Electron. 44, 542-546 (2008).
[CrossRef]

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]

Culverhouse, D.

P. Russel, 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]

Degasperis, A.

F. Baronio, M. Conforti, A. Degasperis, and S. Wabnitz, "Three-wave trapponic solitons for tunable highrepetition rate pulse train generation, " IEEE J. Quantum Electron. 44, 542-546 (2008).
[CrossRef]

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]

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]

Engan, H.

Farahi, F.

P. Russel, 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]

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]

Y. Tsidulko, V. Malkin, and N. Fisch, "Suppression of Superluminous Precursors in High-Power Backward Raman Amplifiers," Phys. Rev. Lett. 88, 235004 (2002).
[CrossRef] [PubMed]

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]

Ibragimov, E.

Karamzin, Y. N.

Y. N. Karamzin, and A. P. Sukhorukov, "Nonlinear interaction of diffracted light beams in a medium with quadratic nonlinearity: mutual focusing of beams and limitation on the efficiency of optical frequency converters," JEPT Lett. 20, 339-344 (1974).

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]

Kim, B.

Lamb, K.

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

Malkin, V.

Y. Tsidulko, V. Malkin, and N. Fisch, "Suppression of Superluminous Precursors in High-Power Backward Raman Amplifiers," Phys. Rev. Lett. 88, 235004 (2002).
[CrossRef] [PubMed]

Manakov, S. V.

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

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]

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]

Russel, P.

P. Russel, 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]

Shaw, H.

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]

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]

Sukhorukov, A. P.

Y. N. Karamzin, and A. P. Sukhorukov, "Nonlinear interaction of diffracted light beams in a medium with quadratic nonlinearity: mutual focusing of beams and limitation on the efficiency of optical frequency converters," JEPT Lett. 20, 339-344 (1974).

Svaasand, L.

L. Svaasand, "Interaction between elastic surface waves in piezoelectric materials," Appl. Phys. Lett. 15, 300-302 (1969).
[CrossRef]

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.

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]

Tsidulko, Y.

Y. Tsidulko, V. Malkin, and N. Fisch, "Suppression of Superluminous Precursors in High-Power Backward Raman Amplifiers," Phys. Rev. Lett. 88, 235004 (2002).
[CrossRef] [PubMed]

Wabnitz, S.

F. Baronio, M. Conforti, A. Degasperis, and S. Wabnitz, "Three-wave trapponic solitons for tunable highrepetition rate pulse train generation, " IEEE J. Quantum Electron. 44, 542-546 (2008).
[CrossRef]

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]

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," Jept. Lett. 18, 243-245 (1973).

Appl. Phys. Lett.

L. Svaasand, "Interaction between elastic surface waves in piezoelectric materials," Appl. Phys. Lett. 15, 300-302 (1969).
[CrossRef]

Geophys. Res. Lett.

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

IEEE J. Quantum Electron.

P. Russel, 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]

F. Baronio, M. Conforti, A. Degasperis, and S. Wabnitz, "Three-wave trapponic solitons for tunable highrepetition rate pulse train generation, " IEEE J. Quantum Electron. 44, 542-546 (2008).
[CrossRef]

J. Phys. Soc. Jpn.

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

JEPT Lett.

Y. N. Karamzin, and A. P. Sukhorukov, "Nonlinear interaction of diffracted light beams in a medium with quadratic nonlinearity: mutual focusing of beams and limitation on the efficiency of optical frequency converters," JEPT Lett. 20, 339-344 (1974).

Jept. Lett.

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

Opt. Express

Opt. Lett.

Phys. Rep.

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. Lett.

Y. Tsidulko, V. Malkin, and N. Fisch, "Suppression of Superluminous Precursors in High-Power Backward Raman Amplifiers," Phys. Rev. Lett. 88, 235004 (2002).
[CrossRef] [PubMed]

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]

Rev. Mod. Phys.

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]

Other

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

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

V. E. Zakharov, What is integrability? (Springer Verlag, Berlin, 1991).

V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitajevski, The Theory of Solitons: The Inverse Problem Method (Nauka, Moskow, 1980).

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Figures (4)

Fig. 1.
Fig. 1.

Numerical xz TWRI dynamics of waves at frequency ω 1 and ω 2 which mix to generate a field at the sum frequency ω 3. (a) Linear, (b) frequency conversion, and (c) solitonic regime.

Fig. 2.
Fig. 2.

Schematic representation of the optical non collinear TWRI interaction in a KTP crystal.

Fig. 3.
Fig. 3.

Experimental results at the exit face of the KTP crystal presenting the spatial output profile of Eω , E , Eeω and Eo ω . (a) Linear regime, I = 1MW/cm 2; (b) frequency conversion, I = 0.1GW/cm 2; (c) solitonic decay I = 2.5GW/cm 2. The white line in the panels labeled Eω represents the intersection between the exit face of the crystal and the ordinary plane. The inset in panel (c) refers to the output profile of E without attenuation filters.

Fig. 4.
Fig. 4.

Solitonic decay, I = 2.5GW/cm 2. Experimental (dashed lines) and numerical (solid lines) spatial output profiles at the exit face of the KTP crystal along x, intersection between the exit face of the crystal and the ordinary plane. Ee ω (red lines), and Eo ω (blue lines).

Equations (3)

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

(z+V1x)ϕ1=η1K*ϕ2* ϕ3 ,
(z+V2x)ϕ2=η2K*ϕ1*ϕ3,
(z+V3x)ϕ3=η3Kϕ1ϕ2.

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