Abstract

We report the generation of complex soliton-like patterns in non-critically-phase-matched potassium niobate which occur in random spatial patterns from shot-to-shot. Up to five spots have been generated at input intensities of 10’s GW/cm2, many times the single soliton threshold. The mechanism which leads to the symmetry breaking required for the complex patterns is interpreted to be random noise imprinted on the input light.

© 2003 Optical Society of America

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  1. N. N. Akhmediev and A. Ankiewicz, Solitons: Nonlinear Pulses and Beams, (Chapman-Hall, London, 1997).
  2. Yu.S. Kivshar and G. Agrawal, Optical Solitons, (Academic, New York, 2003).
  3. 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]
  4. W. Torruellas, Y. Kivshar, and G.I. Stegeman, “Quadratic Solitons”, in “Spatial Solitons”, S. Trillo and W. Torruellas editors (Springer-Verlag, Berlin, 2001) pp 127–168.
  5. S. Carrasco, L. Torner, J. P. Torres, D. Artigas, E. Lopez-Lago, V. Couderc, and A. Barthelemy, “Quadratic solitons: Existence versus excitation,” IEEE J. Sel. Top. Quantum Elect. 8, 497 (2002).
    [Crossref]
  6. M. Katz, D. Eger, H. Kim, L. Jankovic, G. Stegeman, S. 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]
  7. R. Malendevich, L. Jankovic, S. Polyakov, R. Fuerst, G. I. 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]
  8. S. Polyakov, R. Malendevich, L. Jankovic, G. Stegeman, Ch. Bosshard, and P. Gunter, “Effects of Anisotropic Diffraction on Quadratic Multi Soliton Excitation in Non-critically Phase-matched Crystals,” Opt. Lett. 27, 1049 (2002).
    [Crossref]
  9. 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]
  10. 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).
    [Crossref] [PubMed]
  11. S. Minardi, G. Blasi, P. Di Trapani, A. Varanavicius, G. Valiulis, A. Berzanskis, and A. Piskarskas, “Red solitons: evidence of spatio-temporal instability in Chi2 spatial-soliton dynamics,” arXiv: physics/0304030 (2003), http://arxiv.org/PS_cache/physics/pdf/0304/0304030.pdf
  12. I. Biaggio, P. Kerkoc, L.-S. Wu, P. Günter, and B. Zysset, “Refractive indices of orthorhombic KNbO3. II Phase-matching configurations for nonlinear-optical interactions,” J. Opt. Soc. Am. B 9, 507 (1992).
    [Crossref]
  13. A. D. Ludlow, H. M. Nelson, and S. D. Bergeson, “Two-photon absorption in potassium niobate,” J. Opt. Soc. Am. B 18, 1813 (2001).
    [Crossref]
  14. Ch. Bosshard, R. Spreiter, M. Zgonik, and P. Gunter, “Kerr Nonlinearity via Cascaded Optical Rectification and the Linear Electro-optic Effect,” Phys. Rev. Lett. 74, 2816 (1995).
    [Crossref] [PubMed]

2003 (3)

M. Katz, D. Eger, H. Kim, L. Jankovic, G. Stegeman, S. 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]

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]

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).
[Crossref] [PubMed]

2002 (3)

2001 (1)

1995 (2)

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]

Ch. Bosshard, R. Spreiter, M. Zgonik, and P. Gunter, “Kerr Nonlinearity via Cascaded Optical Rectification and the Linear Electro-optic Effect,” Phys. Rev. Lett. 74, 2816 (1995).
[Crossref] [PubMed]

1992 (1)

Agrawal, G.

Yu.S. Kivshar and G. Agrawal, Optical Solitons, (Academic, New York, 2003).

Akhmediev, N. N.

N. N. Akhmediev and A. Ankiewicz, Solitons: Nonlinear Pulses and Beams, (Chapman-Hall, London, 1997).

Ankiewicz, A.

N. N. Akhmediev and A. Ankiewicz, Solitons: Nonlinear Pulses and Beams, (Chapman-Hall, London, 1997).

Artigas, D.

S. Carrasco, L. Torner, J. P. Torres, D. Artigas, E. Lopez-Lago, V. Couderc, and A. Barthelemy, “Quadratic solitons: Existence versus excitation,” IEEE J. Sel. Top. Quantum Elect. 8, 497 (2002).
[Crossref]

Barthelemy, A.

S. Carrasco, L. Torner, J. P. Torres, D. Artigas, E. Lopez-Lago, V. Couderc, and A. Barthelemy, “Quadratic solitons: Existence versus excitation,” IEEE J. Sel. Top. Quantum Elect. 8, 497 (2002).
[Crossref]

Bergeson, S. D.

Berzanskis, A.

S. Minardi, G. Blasi, P. Di Trapani, A. Varanavicius, G. Valiulis, A. Berzanskis, and A. Piskarskas, “Red solitons: evidence of spatio-temporal instability in Chi2 spatial-soliton dynamics,” arXiv: physics/0304030 (2003), http://arxiv.org/PS_cache/physics/pdf/0304/0304030.pdf

Biaggio, I.

Blasi, G.

S. Minardi, G. Blasi, P. Di Trapani, A. Varanavicius, G. Valiulis, A. Berzanskis, and A. Piskarskas, “Red solitons: evidence of spatio-temporal instability in Chi2 spatial-soliton dynamics,” arXiv: physics/0304030 (2003), http://arxiv.org/PS_cache/physics/pdf/0304/0304030.pdf

Bosshard, Ch.

Carrasco, S.

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]

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).
[Crossref] [PubMed]

M. Katz, D. Eger, H. Kim, L. Jankovic, G. Stegeman, S. 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]

S. Carrasco, L. Torner, J. P. Torres, D. Artigas, E. Lopez-Lago, V. Couderc, and A. Barthelemy, “Quadratic solitons: Existence versus excitation,” IEEE J. Sel. Top. Quantum Elect. 8, 497 (2002).
[Crossref]

Couderc, V.

S. Carrasco, L. Torner, J. P. Torres, D. Artigas, E. Lopez-Lago, V. Couderc, and A. Barthelemy, “Quadratic solitons: Existence versus excitation,” IEEE J. Sel. Top. Quantum Elect. 8, 497 (2002).
[Crossref]

Di Trapani, P.

S. Minardi, G. Blasi, P. Di Trapani, A. Varanavicius, G. Valiulis, A. Berzanskis, and A. Piskarskas, “Red solitons: evidence of spatio-temporal instability in Chi2 spatial-soliton dynamics,” arXiv: physics/0304030 (2003), http://arxiv.org/PS_cache/physics/pdf/0304/0304030.pdf

Eger, D.

M. Katz, D. Eger, H. Kim, L. Jankovic, G. Stegeman, S. 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]

Fuerst, R.

Gunter, P.

Günter, P.

Hagan, D J.

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]

Jankovic, L.

Katz, M.

M. Katz, D. Eger, H. Kim, L. Jankovic, G. Stegeman, S. 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]

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]

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).
[Crossref] [PubMed]

Kerkoc, P.

Kim, H.

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).
[Crossref] [PubMed]

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]

M. Katz, D. Eger, H. Kim, L. Jankovic, G. Stegeman, S. 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]

Kivshar, Y.

W. Torruellas, Y. Kivshar, and G.I. Stegeman, “Quadratic Solitons”, in “Spatial Solitons”, S. Trillo and W. Torruellas editors (Springer-Verlag, Berlin, 2001) pp 127–168.

Kivshar, Yu.S.

Yu.S. Kivshar and G. Agrawal, Optical Solitons, (Academic, New York, 2003).

Lopez-Lago, E.

S. Carrasco, L. Torner, J. P. Torres, D. Artigas, E. Lopez-Lago, V. Couderc, and A. Barthelemy, “Quadratic solitons: Existence versus excitation,” IEEE J. Sel. Top. Quantum Elect. 8, 497 (2002).
[Crossref]

Ludlow, A. D.

Malendevich, R.

Menyuk, C. R.

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]

Minardi, S.

S. Minardi, G. Blasi, P. Di Trapani, A. Varanavicius, G. Valiulis, A. Berzanskis, and A. Piskarskas, “Red solitons: evidence of spatio-temporal instability in Chi2 spatial-soliton dynamics,” arXiv: physics/0304030 (2003), http://arxiv.org/PS_cache/physics/pdf/0304/0304030.pdf

Nelson, H. M.

Piskarskas, A.

S. Minardi, G. Blasi, P. Di Trapani, A. Varanavicius, G. Valiulis, A. Berzanskis, and A. Piskarskas, “Red solitons: evidence of spatio-temporal instability in Chi2 spatial-soliton dynamics,” arXiv: physics/0304030 (2003), http://arxiv.org/PS_cache/physics/pdf/0304/0304030.pdf

Polyakov, S.

Spreiter, R.

Ch. Bosshard, R. Spreiter, M. Zgonik, and P. Gunter, “Kerr Nonlinearity via Cascaded Optical Rectification and the Linear Electro-optic Effect,” Phys. Rev. Lett. 74, 2816 (1995).
[Crossref] [PubMed]

Stegeman, G.

Stegeman, G. I.

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]

R. Malendevich, L. Jankovic, S. Polyakov, R. Fuerst, G. I. 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]

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]

Stegeman, G.I.

W. Torruellas, Y. Kivshar, and G.I. Stegeman, “Quadratic Solitons”, in “Spatial Solitons”, S. Trillo and W. Torruellas editors (Springer-Verlag, Berlin, 2001) pp 127–168.

Torner, L.

M. Katz, D. Eger, H. Kim, L. Jankovic, G. Stegeman, S. 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]

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).
[Crossref] [PubMed]

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]

S. Carrasco, L. Torner, J. P. Torres, D. Artigas, E. Lopez-Lago, V. Couderc, and A. Barthelemy, “Quadratic solitons: Existence versus excitation,” IEEE J. Sel. Top. Quantum Elect. 8, 497 (2002).
[Crossref]

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]

Torres, J. P.

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]

S. Carrasco, L. Torner, J. P. Torres, D. Artigas, E. Lopez-Lago, V. Couderc, and A. Barthelemy, “Quadratic solitons: Existence versus excitation,” IEEE J. Sel. Top. Quantum Elect. 8, 497 (2002).
[Crossref]

Torruellas, W.

W. Torruellas, Y. Kivshar, and G.I. Stegeman, “Quadratic Solitons”, in “Spatial Solitons”, S. Trillo and W. Torruellas editors (Springer-Verlag, Berlin, 2001) pp 127–168.

Torruellas, W. E.

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]

Valiulis, G.

S. Minardi, G. Blasi, P. Di Trapani, A. Varanavicius, G. Valiulis, A. Berzanskis, and A. Piskarskas, “Red solitons: evidence of spatio-temporal instability in Chi2 spatial-soliton dynamics,” arXiv: physics/0304030 (2003), http://arxiv.org/PS_cache/physics/pdf/0304/0304030.pdf

VanStryland, E. W.

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]

Varanavicius, A.

S. Minardi, G. Blasi, P. Di Trapani, A. Varanavicius, G. Valiulis, A. Berzanskis, and A. Piskarskas, “Red solitons: evidence of spatio-temporal instability in Chi2 spatial-soliton dynamics,” arXiv: physics/0304030 (2003), http://arxiv.org/PS_cache/physics/pdf/0304/0304030.pdf

Wang, Z.

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]

Wu, L.-S.

Zgonik, M.

Ch. Bosshard, R. Spreiter, M. Zgonik, and P. Gunter, “Kerr Nonlinearity via Cascaded Optical Rectification and the Linear Electro-optic Effect,” Phys. Rev. Lett. 74, 2816 (1995).
[Crossref] [PubMed]

Zysset, B.

IEEE J. Sel. Top. Quantum Elect. (1)

S. Carrasco, L. Torner, J. P. Torres, D. Artigas, E. Lopez-Lago, V. Couderc, and A. Barthelemy, “Quadratic solitons: Existence versus excitation,” IEEE J. Sel. Top. Quantum Elect. 8, 497 (2002).
[Crossref]

J. Appl. Phys. (1)

M. Katz, D. Eger, H. Kim, L. Jankovic, G. Stegeman, S. 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. Opt. Soc. Am. B (2)

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. E (1)

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. (2)

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]

Ch. Bosshard, R. Spreiter, M. Zgonik, and P. Gunter, “Kerr Nonlinearity via Cascaded Optical Rectification and the Linear Electro-optic Effect,” Phys. Rev. Lett. 74, 2816 (1995).
[Crossref] [PubMed]

Other (4)

S. Minardi, G. Blasi, P. Di Trapani, A. Varanavicius, G. Valiulis, A. Berzanskis, and A. Piskarskas, “Red solitons: evidence of spatio-temporal instability in Chi2 spatial-soliton dynamics,” arXiv: physics/0304030 (2003), http://arxiv.org/PS_cache/physics/pdf/0304/0304030.pdf

W. Torruellas, Y. Kivshar, and G.I. Stegeman, “Quadratic Solitons”, in “Spatial Solitons”, S. Trillo and W. Torruellas editors (Springer-Verlag, Berlin, 2001) pp 127–168.

N. N. Akhmediev and A. Ankiewicz, Solitons: Nonlinear Pulses and Beams, (Chapman-Hall, London, 1997).

Yu.S. Kivshar and G. Agrawal, Optical Solitons, (Academic, New York, 2003).

Supplementary Material (3)

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Figures (3)

Fig. 1.
Fig. 1.

A typical, experimental intensity distribution of the input beam in 2 and 3D.

Fig. 2.
Fig. 2.

(Movies 128KB, 288KB and 423KB) Three collages of output beam patterns obtained for peak input fundamental beam intensities of 8 GW/cm2, 15 GW/cm2 and 30 GW/cm2. Successive frames correspond to successive laser pulses at the same peak input intensity.

Fig. 3.
Fig. 3.

Selection of four output patterns obtained under different conditions.

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