Abstract

The details of two soliton collision processes were investigated in detail in a 1 cm long periodically poled KTP crystal for the case when the solitons were excited by inputting only the fundamental beam. The effects on the collision outcomes of the distance of the collision into the sample, collision angle and phase mismatch were measured for different relative phases between the input beams. At small angles (around 0.40) fusion, repulsion and energy transfer processes were observed, while at the collision angles approaching 3.20 the two output soliton beams were essentially unaffected by the interaction. The phase mismatch was varied from 3.5 to -1.5π for the 0.40 collision angle case. The output soliton separation at π input phase difference showed strongly asymmetric behavior with phase mismatch. In general, the measurements indicate a decrease in the interaction strength with increasing phase mismatch. All collision processes were performed in the vicinity of a non-critical phase matching.

© 2004 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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  12. S. Carrasco, S. Polyakov, H. Kim, L. Jankovic, G. I. Stegeman, J. P. Torres, L. Torner, and M. Katz, �??Observation of multiple soliton generation mediated by amplification of asymmetries,�?? Phys. Rev. E 67, 046616 (2003).
    [CrossRef]
  13. S. Polyakov, L. Jankovic, H. Kim, G. Stegeman, S. Carrasco, L. Torner and M. Katz, �??Properties of Quadratic Multi-Soliton Generation Near Phase-Match in Periodically Poled Potassium Titanyl Phosphate,�?? Opt. Express 11, 1328 (2003).
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  14. L. Jankovic, S. Polyakov, G. Stegeman, S. Carrasco, L. Torner, C. Bosshard, and P. Gunter, �??Complex soliton-like pattern generation in Potassium Niobate due to noisy, high intensity, input beams,�?? Opt. Express 11, 2206 (2003).
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  16. C. Simos, V. Couderc, A. Barthelemy, A. V. Buryak, �??Phase-dependent interactions between three-wave spatial solitons in bulk quadratic media,�?? J. Opt. Soc. Am. B 20, 2133 (2003).
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  17. L. Jankovic, H. Kim, S. Polyakov, G. I. Stegeman, Ch. Bosshard and P. Gunter, �??Soliton Birth In Quadratic Spatial Soliton Collisions,�?? Opt. Lett. 28, 1037 (2003).
    [CrossRef] [PubMed]
  18. G. I. Stegeman, L. Jankovic, H. Kim, S. Polyakov, S. Carrasco, L. Torner, Ch. Bosshard, P. Gunter, M. Katz and D. Eger, �??Generation of, and Interactions Between Quadratic Spatial Solitons in Non-Critically-Phase-Matched Crystals,�?? Journal of Nonlinear Optical Physics & Materials 12, 447 (2003).
    [CrossRef]
  19. 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 convertors," JETP Lett. 20, 339 (1974); Yu.N.Karamzin, A.P.Sukhorukov, "Mutual focusing of high-power light beams in media with quadratic nonlinearity," Zh. Eksp. Teor. Phys. 68, 834 (1975) (Sov. Phys.-JETP 41, 414 (1976)).
  20. G.I. Stegeman, D.J. Hagan and L. Torner, �??x(2) Cascading Phenomena and Their Applications to All-Optical Signal Processing, Mode-Locking, Pulse Compression and Solitons,�?? J. Optical and Quant. Electron. 28, 1691 (1996).
    [CrossRef]
  21. G. I. Stegeman, �??Experiments on Quadratic Solitons�??, book chapter for Proceedings of NATO Advanced Research Workshop on Soliton Driven Photonics, A.D. Boardman and A.P. Sukhorukov editors, (Kluwer Academic Publishers, Holland, 2001), pp 21-39.
  22. W. Torruellas, Y. Kivshar and G.I. Stegeman, �??Quadratic Solitons�??, book chapter in Spatial Solitons, S. Trillo and W. Torruellas editors (Springer-Verlag, Berlin, 2001) pp 127-168.
  23. A. V. 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 (2002).
    [CrossRef]
  24. B. Bourliaguet, V. Couderc, A. Barthelemy, G. W. Ross, P. G. R. Smith, D. C. Hanna and C. De Angelis, �??Observation of Quadratic Spatial Solitons in Periodically Poled Lithium Niobate,�?? Opt. Lett. 24, 1410 (1999).
    [CrossRef]
  25. H. Kim, L. Jankovic, G. Stegeman, S. Carrasco, L. Torner, D. Eger and M. Katz, �??Quadratic Spatial Solitons in Periodically Poled KTiOPO4,�?? Opt. Lett. 28, 640 (2003).
    [CrossRef] [PubMed]
  26. M. Katz, D. Eger, H. Kim, L. Jankovic, G. Stegeman, Silvia Carrasco and L. Torner, �??Second Harmonic Generation Tuning Curves In Quasi-Phase-Matched KTP With Narrow, High Intensity Beams,�?? J. Appl. Phys. 93, 8852 (2003).
    [CrossRef]
  27. similar to the case discussed in L. Torner, D. Mihalache, D. Mazilu, E. M. Wright, W. E. Torruellas and G. I. Stegeman, "Stationary trapping of light beams in bulk second-order nonlinear media," Opt. Commun. 121, 149 (1995).
    [CrossRef]
  28. L. Torner and G.I. Stegeman, �??Soliton Evolution in Quasi-Phase-Matched Second-Harmonic Generation,�?? JOSA B (special issue) 14, 3127 (1997).
  29. G. Assanto and G. I. Stegeman, �??The Simple Physics of Quadratic Spatial Solitons,�?? Opt. Exp. 10, 388-96 (2002).
    [CrossRef]
  30. R.A. Fuerst, M.T.G. Canva, D. Baboiu and G.I. Stegeman, �??Properties of Type II Quadratic Solitons Excited by Unbalanced Fundamental Waves,�?? Opt. Lett. 22, 1748 (1997).
    [CrossRef]
  31. A. Englander, R. Lavi, M. Katz, M. Oron, D. Eger, E. Lebiush, G. Rosenman and A. Skliar, �??Highly efficient doubling of a high-repetition-rate diode-pumped laser with bulk periodically poled KTP,�?? Opt. Lett. 22, 1598 (1997).
    [CrossRef]
  32. D.-M. Baboiu, G.I. Stegeman and L. Torner, "Collision of solitary waves in quadratic media," Opt. Lett. 20, 2282 (1995).
    [CrossRef] [PubMed]
  33. C. Etrich, F. Lederer, B.A. Malomed, T. Peschel and U. Peschel, Progress in Optics, E. Wolf editor (Elsevier, New York, 2000) Vol. 41, pp. 483-568.
  34. C. Etrich, U. Peschel , F. Lederer and B. Malomed, �??Collisions of solitary waves in media with a second order nonlinearity,�?? Phys. Rev. B 52, R3444 (1995).

. Opt. Soc. Am. B

C. Simos, V. Couderc, A. Barthelemy, A. V. Buryak, �??Phase-dependent interactions between three-wave spatial solitons in bulk quadratic media,�?? J. Opt. Soc. Am. B 20, 2133 (2003).
[CrossRef]

J. Appl. Phys.

M. Katz, D. Eger, H. Kim, L. Jankovic, G. Stegeman, Silvia Carrasco and L. Torner, �??Second Harmonic Generation Tuning Curves In Quasi-Phase-Matched KTP With Narrow, High Intensity Beams,�?? J. Appl. Phys. 93, 8852 (2003).
[CrossRef]

J. Optical and Quant. Electron.

G.I. Stegeman, D.J. Hagan and L. Torner, �??x(2) Cascading Phenomena and Their Applications to All-Optical Signal Processing, Mode-Locking, Pulse Compression and Solitons,�?? J. Optical and Quant. Electron. 28, 1691 (1996).
[CrossRef]

JETP 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 convertors," JETP Lett. 20, 339 (1974); Yu.N.Karamzin, A.P.Sukhorukov, "Mutual focusing of high-power light beams in media with quadratic nonlinearity," Zh. Eksp. Teor. Phys. 68, 834 (1975) (Sov. Phys.-JETP 41, 414 (1976)).

JOSA B

L. Torner and G.I. Stegeman, �??Soliton Evolution in Quasi-Phase-Matched Second-Harmonic Generation,�?? JOSA B (special issue) 14, 3127 (1997).

Journal of Nonlinear Opt. Physics & Mat.

G. I. Stegeman, L. Jankovic, H. Kim, S. Polyakov, S. Carrasco, L. Torner, Ch. Bosshard, P. Gunter, M. Katz and D. Eger, �??Generation of, and Interactions Between Quadratic Spatial Solitons in Non-Critically-Phase-Matched Crystals,�?? Journal of Nonlinear Optical Physics & Materials 12, 447 (2003).
[CrossRef]

Opt. Commun.

similar to the case discussed in L. Torner, D. Mihalache, D. Mazilu, E. M. Wright, W. E. Torruellas and G. I. Stegeman, "Stationary trapping of light beams in bulk second-order nonlinear media," Opt. Commun. 121, 149 (1995).
[CrossRef]

Opt. Exp.

G. Assanto and G. I. Stegeman, �??The Simple Physics of Quadratic Spatial Solitons,�?? Opt. Exp. 10, 388-96 (2002).
[CrossRef]

Opt. Express

Opt. Lett.

L. Jankovic, H. Kim, S. Polyakov, G. I. Stegeman, Ch. Bosshard and P. Gunter, �??Soliton Birth In Quadratic Spatial Soliton Collisions,�?? Opt. Lett. 28, 1037 (2003).
[CrossRef] [PubMed]

E. A. Ultanir, G. I. Stegeman, C. H. Lange, and F. Lederer, �??Interactions of Dissipative Spatial Solitons,�?? Opt. Lett. 29, 283 (2004).
[CrossRef] [PubMed]

J. S. Aitchison, A. M. Weiner, Y. Silberberg, D. E. Leaird, M. K. Oliver, J. L. Jackel, and P. W. Smith, �??Experimental observation of spatial soliton interactions,�?? Opt. Lett. 16, 15 (1991).
[CrossRef] [PubMed]

L. Torner, C. R. Menyuk and G.I. Stegeman, �??Excitation of soliton-like waves with cascaded nonlinearities,�?? Opt. Lett. 19, 1615 (1994).
[CrossRef] [PubMed]

D.-M. Baboiu, G.I. Stegeman and L. Torner, "Collision of solitary waves in quadratic media," Opt. Lett. 20, 2282 (1995).
[CrossRef] [PubMed]

A. Englander, R. Lavi, M. Katz, M. Oron, D. Eger, E. Lebiush, G. Rosenman and A. Skliar, �??Highly efficient doubling of a high-repetition-rate diode-pumped laser with bulk periodically poled KTP,�?? Opt. Lett. 22, 1598 (1997).
[CrossRef]

R.A. Fuerst, M.T.G. Canva, D. Baboiu and G.I. Stegeman, �??Properties of Type II Quadratic Solitons Excited by Unbalanced Fundamental Waves,�?? Opt. Lett. 22, 1748 (1997).
[CrossRef]

B. Constantini, C. De Angelis, A. Barthelemy, B. Bourliaguet and V. Kermene, �??Collisions between Type-II two dimensional quadratic solitons,�?? Opt. Lett. 23, 424 (1998).
[CrossRef]

B. Bourliaguet, V. Couderc, A. Barthelemy, G. W. Ross, P. G. R. Smith, D. C. Hanna and C. De Angelis, �??Observation of Quadratic Spatial Solitons in Periodically Poled Lithium Niobate,�?? Opt. Lett. 24, 1410 (1999).
[CrossRef]

for example, M.F. Shih and M. Segev, �??Incoherent collisions between two-dimensional bright steady-state photorefractive spatial screening solitons,�?? Opt. Lett. 21, 1538 (1996).
[CrossRef] [PubMed]

R. Malendevich, L. Jankovic, S. Polyakov, R. Fuerst, G. Stegeman, Ch. Bosshard and P. Gunter, �??Two-Dimensional Type I Quadratic Spatial Solitons in KNbO3 Near Non-Critical Phase-Matching,�?? Opt. Lett. 27, 631 (2002).
[CrossRef]

M. Peccianti, K. A. Brzdakiewicz and G. Assanto, �??Nonlocal spatial soliton interactions in nematic liquid crystals,�?? Opt. Lett. 27, 1460 (2002).
[CrossRef]

H. Kim, L. Jankovic, G. Stegeman, S. Carrasco, L. Torner, D. Eger and M. Katz, �??Quadratic Spatial Solitons in Periodically Poled KTiOPO4,�?? Opt. Lett. 28, 640 (2003).
[CrossRef] [PubMed]

Opt. Quant. Elect.

R. Schiek, Y. Baek, G. Stegeman and W. Sohler, �??Interactions between one dimensional quadratic solitons-like beams,�?? Opt. Quant. Elect. 30, 861 (1998).
[CrossRef]

Phys. Rep.

A. V. 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 (2002).
[CrossRef]

Phys. Rev. B

C. Etrich, U. Peschel , F. Lederer and B. Malomed, �??Collisions of solitary waves in media with a second order nonlinearity,�?? Phys. Rev. B 52, R3444 (1995).

Phys. Rev. E

S. Carrasco, S. Polyakov, H. Kim, L. Jankovic, G. I. Stegeman, J. P. Torres, L. Torner, and M. Katz, �??Observation of multiple soliton generation mediated by amplification of asymmetries,�?? Phys. Rev. E 67, 046616 (2003).
[CrossRef]

Phys. Rev. Lett.

W.E. Torruellas, Z. Wang, D.J. Hagan, E.W. VanStryland, G.I. Stegeman, L. Torner and C.R. Menyuk, "Observation of Two-Dimensional Spatial Solitary Waves in a Quadratic Medium," Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

J. Meier, G. I. Stegeman, Y. Silberberg, R. Morandotti and J.S. Aitchison, �??Nonlinear Optical Beam Interactions In Waveguide Arrays,�?? Phys. Rev. Lett. in press.

Proc. of NATO Adv. Res. Wksh. on Sol. Dr

G. I. Stegeman, �??Experiments on Quadratic Solitons�??, book chapter for Proceedings of NATO Advanced Research Workshop on Soliton Driven Photonics, A.D. Boardman and A.P. Sukhorukov editors, (Kluwer Academic Publishers, Holland, 2001), pp 21-39.

Science

G. I. Stegeman and M. Segev �??Optical Spatial Solitons and Their Interactions: Universality and Diversity,�?? Science 286, 1518 (1999).
[CrossRef] [PubMed]

Spatial Solitons

W. Torruellas, Y. Kivshar and G.I. Stegeman, �??Quadratic Solitons�??, book chapter in Spatial Solitons, S. Trillo and W. Torruellas editors (Springer-Verlag, Berlin, 2001) pp 127-168.

W. Torruellas, Y. Kivshar and G.I. Stegeman, �??Quadratic Solitons�??, book chapter in Spatial Solitons, S. Trillo and W. Torruellas editors (Springer-Verlag, Berlin, 2001) pp 127-168.

Other

C. Etrich, F. Lederer, B.A. Malomed, T. Peschel and U. Peschel, Progress in Optics, E. Wolf editor (Elsevier, New York, 2000) Vol. 41, pp. 483-568.

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Figures (13)

Fig. 1.
Fig. 1.

The experimental set-up used to investigate quadratic soliton collisions.

Fig. 2.
Fig. 2.

Interaction geometries (a) The collision point. (b) The interaction region.

Fig. 3.
Fig. 3.

Collage of output beam patterns obtained from quadratic solitons colliding at distances of 4.1mm (upper set) and 6.6mm (lower set) into the sample for eight different phase differences between the input FW beams.

Fig. 4.
Fig. 4.

Output beam patterns for solitons colliding 7.5mm from the input facet at a 0.440 angle, for various relative phases between the input FW beams.

Fig. 5.
Fig. 5.

Threshold soliton intensity versus sample temperature (corresponds to phase-mismatch).

Fig. 6.
Fig. 6.

Dependence of the output patterns versus relative input FW phase at phase-match (upper set) and a phase-mismatch of 3.5π. Input soliton intensities were 5.2 GW/cm2 and 8.0 GW/cm2 respectively, both at 1.7x the threshold intensity.

Fig. 7.
Fig. 7.

Collage of output beam patterns obtained for a collision angle of 0.40 for different phase-mismatch. Here the PM temperature corresponds to 43.60.

Fig. 8.
Fig. 8.

(a) Separation of output beams versus phase-mismatch (and temperature) for π relative phase between the two FW input beams. (b) Separation between the output solitons at various input intensities obtained from numerical simulations of soliton collision processes. The initial relative phase between the beams was fixed at π.

Fig. 9.
Fig. 9.

Numerical simulations of the soliton collisions at different intensities and phase mismatch. FW beam profile is shown only.

Fig. 10.
Fig. 10.

Output beam separation as a function of relative phase between the two FW input beams for a number of different temperatures, i.e. phase-mismatch.

Fig. 11.
Fig. 11.

Collage of output beam patterns for a variety of relative FW beam input phases and incidence angles.

Fig. 12.
Fig. 12.

Output beam (soliton) separation versus the relative FW input phase for three different incidence angles at phase-match.

Fig. 13.
Fig. 13.

FW and SHG output intensity as function of the relative phase for three phase matching conditions.

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