Abstract

The properties of the multi-quadratic-soliton generation process have been investigated both theoretically and experimentally near and on phase-match in non-critically-phase-matched, periodically poled, potassium titanyl phosphate (PPKTP). It was found that multi-soliton generation occurs primarily due to asymmetry in the input beam and at phase-matching. The number of solitons generated depended on the input intensity in a non-trivial way.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. Yu.N.Karamzin and 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)).
  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]
  3. R. Schiek, Y. Baek and G. I. Stegeman, �??One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in plannar waveguides,�?? Phys. Rev. E 53, 1138 (1996).
    [CrossRef]
  4. P. Di Trapani, G. Valiulis, W. Chianglia and A. Adreoni, �??Two-dimensional spatial solitary waves from traveling-wave parametric amplification of the quantum noise,�?? Phys. Rev. Lett. 80, 265 (1998).
    [CrossRef]
  5. X. Liu, L. J. Qian and F. W. Wise, �??Generation of optical spatiotemporal solitons,�?? Phys. Rev. Lett. 82, 4631 (1999).
    [CrossRef]
  6. 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]
  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. 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]
  9. For an overview, see L.Torner and G.I. Stegeman, �??Multicolor Solitons,�?? Opt. Photon. News 12, (2), 36 (2001).
    [CrossRef]
  10. For a comprehensive review , see 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]
  11. 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]
  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. Carrasco, L. Torner, J. P. Torres, D. Artigas, E. López-Lago, V. Couderc, and A. Barthélémy, �??Quadratic Solitons: Existence versus Excitation,�?? IEEE J. Sel. Top. Quantum Elect. 8, 497 (2002).
    [CrossRef]
  14. 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., in press
  15. 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]
  16. G. Rosenman, Kh. Garb, A. Skliar, M. Oron, D. Eger and M. Katz, �??Low temperature periodic electrical poling of flux-grown KTiOPO4 and isomorphic crystals,�?? Appl. Phys. Lett. 73, 865 (1998).
    [CrossRef]
  17. S. V. Polyakov and G. I. Stegeman, �??Quadratic Solitons in Anisotropic Media: Variational Approach,�?? Phys. Rev. E 66, 046622-1 (2002).
    [CrossRef]
  18. A. V. Buryak, Y. S. Kivshar, and V. V. Steblina, �??Self-trapping of light beams and parametric solitons in diffractive quadratic media,�?? Phys. Rev. A 52, 1670 (1995); L. Torner, D. Mihalache, D. Mazilu, E. M. Wright, W. E. Torruelas, and G. I. Stegeman, �??Stationary trapping of light beams in bulk second-order nonlinear media,�?? Opt. Commun. 121, 149 (1995).
    [CrossRef] [PubMed]
  19. N. N. Akhmediev and A. Ankiewicz, Solitons: Nonlinear Pulses and Beams, (Chapman and Hall, London, 1997).
  20. G. Assanto and G. Stegeman, �??The Simple Physics of Quadratic Spatial Solitons,�?? Opt. Express, 10, 388 (2002).
    [CrossRef] [PubMed]
  21. A. D. Boardman, K. Xie and A. Sangarpaul, �??Stability of scalar spatial solitons in cascadable nonlinear media,�?? Phys. Rev. A 52, 4099 (1995).
    [CrossRef] [PubMed]

Appl. Phys. Lett. (1)

G. Rosenman, Kh. Garb, A. Skliar, M. Oron, D. Eger and M. Katz, �??Low temperature periodic electrical poling of flux-grown KTiOPO4 and isomorphic crystals,�?? Appl. Phys. Lett. 73, 865 (1998).
[CrossRef]

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

S. Carrasco, L. Torner, J. P. Torres, D. Artigas, E. López-Lago, V. Couderc, and A. Barthélémy, �??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., in press

Opt. Express (1)

Opt. Lett. (5)

Phys Rep. (1)

For a comprehensive review , see 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. A (2)

A. D. Boardman, K. Xie and A. Sangarpaul, �??Stability of scalar spatial solitons in cascadable nonlinear media,�?? Phys. Rev. A 52, 4099 (1995).
[CrossRef] [PubMed]

A. V. Buryak, Y. S. Kivshar, and V. V. Steblina, �??Self-trapping of light beams and parametric solitons in diffractive quadratic media,�?? Phys. Rev. A 52, 1670 (1995); L. Torner, D. Mihalache, D. Mazilu, E. M. Wright, W. E. Torruelas, and G. I. Stegeman, �??Stationary trapping of light beams in bulk second-order nonlinear media,�?? Opt. Commun. 121, 149 (1995).
[CrossRef] [PubMed]

Phys. Rev. E (3)

S. V. Polyakov and G. I. Stegeman, �??Quadratic Solitons in Anisotropic Media: Variational Approach,�?? Phys. Rev. E 66, 046622-1 (2002).
[CrossRef]

R. Schiek, Y. Baek and G. I. Stegeman, �??One-dimensional spatial solitary waves due to cascaded second-order nonlinearities in plannar waveguides,�?? Phys. Rev. E 53, 1138 (1996).
[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]

Phys. Rev. Lett. (3)

P. Di Trapani, G. Valiulis, W. Chianglia and A. Adreoni, �??Two-dimensional spatial solitary waves from traveling-wave parametric amplification of the quantum noise,�?? Phys. Rev. Lett. 80, 265 (1998).
[CrossRef]

X. Liu, L. J. Qian and F. W. Wise, �??Generation of optical spatiotemporal solitons,�?? Phys. Rev. Lett. 82, 4631 (1999).
[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]

Sov. Phys.-JETP (1)

Yu.N.Karamzin and 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)).

Other (2)

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

For an overview, see L.Torner and G.I. Stegeman, �??Multicolor Solitons,�?? Opt. Photon. News 12, (2), 36 (2001).
[CrossRef]

Supplementary Material (5)

» Media 1: GIF (456 KB)     
» Media 2: GIF (173 KB)     
» Media 3: GIF (1364 KB)     
» Media 4: GIF (404 KB)     
» Media 5: GIF (531 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1.
Fig. 1.

Experimental setup. The prism (inset) can be moved into the path of the beam to alter the direction of the beam asymmetry (but not its shape).

Fig. 2.
Fig. 2.

(456 KB) Simulation of the spatial evolution of three soliton generation on phase match with a high input intensity fundamental beam (three times higher than single soliton threshold 3.4GW/cm2, where the input intensity of 1 a.u. in the simulations corresponds to approximately 14GW/cm2). Left-hand-side the fundamental; Right-hand-side the harmonic. The propagation distance between successive frames is about 0.1 in units of diffraction lengths. Simulation parameters: D11=0.0943, D12=0.0847, D21=0.0478, D22=0.0423, α1,2=0, input intensity=0.73 a.u., and the Eqs. (1), (2) are normalized to set Γ=0.01.

Fig. 3.
Fig. 3.

The divergence angle (a.u.) and number of solitons predicted by CW simulations after 5 diffraction lengths as a function of input intensity (in arbitrary units). A gaussian beam input with w 1=w 2 was assumed with the anisotropic diffraction appropriate for PPKTP.

Fig. 4.
Fig. 4.

(172 KB) FW spatial field for different temporal snapshots at 10 diffraction lengths for an elliptical input beam with w1/w2=1.07. The inset sketches the shape of the temporal profile and the moving dot shows the location of the temporal slice shown.

Fig. 5.
Fig. 5.

Fundamental (FW) and second harmonic (SH) output patterns for two cases. (a) Single soliton generation. (b) Multi-soliton generation for a strongly asymmetric input beam. Insets show the input beams.

Fig. 6.
Fig. 6.

(1.33 MB) Multiple shots of the fundamental beam output patterns obtained with increasing the intensity from 0.5 GW/cm2 to 26 GW/cm2.

Fig. 7.
Fig. 7.

(404 KB) Calculated evolution with propagation distance of the fundamental (left-hand-side) and the harmonic (right-hand-side) at ΔkL≈15π under the same conditions as Fig. 2 (for which ΔkL=0).

Fig. 8.
Fig. 8.

(531 KB) Evolution of the output fundamental beam pattern with changing phase-mismatch, ΔkL, and fixed intensity. Note that there is a change in the camera sensitivity scale at around +0.2π to enhance the satellite peaks which saturates the output on the central soliton.

Equations (2)

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

i A 1 x + ( D 11 2 A 1 z 2 + D 12 2 A 1 y 2 ) + α 2 ( ω ) 2 A 1 2 A 1 = Γ A 2 A 1 * exp ( i Δ k x )
i A 2 x + ( D 21 2 A 2 z 2 + D 22 2 A 2 y 2 ) + α 2 ( ω ) 2 A 2 2 A 2 = Γ A 1 2 exp ( i Δ k x )

Metrics