Abstract

We show numerically and experimentally that spatial trapping can be induced in quadratic media even if the pump pulse’s duration is shorter than the group-delay mismatch between fundamental wave and second-harmonic components. The influence of phase mismatch and pulse power on the trapping effect is discussed. Spatial, temporal, and spectral behaviors that accompany self-trapped propagation are highlighted.

© 2002 Optical Society of America

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References

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  1. G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
    [CrossRef]
  2. Y. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976).
  3. M. J. Werner and P. D. Drummond, Opt. Lett. 19, 613 (1993).
    [CrossRef]
  4. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
    [CrossRef] [PubMed]
  5. R. Schiek, Y. Baek, G. Krijnen, G. I. Stegeman, I. Baumann, and W. Sohler, Opt. Lett. 21, 940 (1996).
    [CrossRef] [PubMed]
  6. S. Kim, Z. Wang, D. J. Hagan, E. W. Van Stryland, A. Kobyakov, F. Lederer, and G. Assanto, IEEE J. Quantum Electron. 34, 666 (1998).
    [CrossRef]
  7. S. Carrasco, J. P. Torres, D. Antigas, and L. Torner, Opt. Commun. 192, 347 (2001).
    [CrossRef]

2001 (1)

S. Carrasco, J. P. Torres, D. Antigas, and L. Torner, Opt. Commun. 192, 347 (2001).
[CrossRef]

1998 (1)

S. Kim, Z. Wang, D. J. Hagan, E. W. Van Stryland, A. Kobyakov, F. Lederer, and G. Assanto, IEEE J. Quantum Electron. 34, 666 (1998).
[CrossRef]

1996 (2)

1995 (1)

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

1993 (1)

1976 (1)

Y. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976).

Antigas, D.

S. Carrasco, J. P. Torres, D. Antigas, and L. Torner, Opt. Commun. 192, 347 (2001).
[CrossRef]

Assanto, G.

S. Kim, Z. Wang, D. J. Hagan, E. W. Van Stryland, A. Kobyakov, F. Lederer, and G. Assanto, IEEE J. Quantum Electron. 34, 666 (1998).
[CrossRef]

Baek, Y.

Baumann, I.

Carrasco, S.

S. Carrasco, J. P. Torres, D. Antigas, and L. Torner, Opt. Commun. 192, 347 (2001).
[CrossRef]

Drummond, P. D.

Hagan, D. J.

S. Kim, Z. Wang, D. J. Hagan, E. W. Van Stryland, A. Kobyakov, F. Lederer, and G. Assanto, IEEE J. Quantum Electron. 34, 666 (1998).
[CrossRef]

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Karamzin, Y. N.

Y. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976).

Kim, S.

S. Kim, Z. Wang, D. J. Hagan, E. W. Van Stryland, A. Kobyakov, F. Lederer, and G. Assanto, IEEE J. Quantum Electron. 34, 666 (1998).
[CrossRef]

Kobyakov, A.

S. Kim, Z. Wang, D. J. Hagan, E. W. Van Stryland, A. Kobyakov, F. Lederer, and G. Assanto, IEEE J. Quantum Electron. 34, 666 (1998).
[CrossRef]

Krijnen, G.

Lederer, F.

S. Kim, Z. Wang, D. J. Hagan, E. W. Van Stryland, A. Kobyakov, F. Lederer, and G. Assanto, IEEE J. Quantum Electron. 34, 666 (1998).
[CrossRef]

Menyuk, C. R.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Schiek, R.

Sohler, W.

Stegeman, G. I.

R. Schiek, Y. Baek, G. Krijnen, G. I. Stegeman, I. Baumann, and W. Sohler, Opt. Lett. 21, 940 (1996).
[CrossRef] [PubMed]

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Sukhorukov, A. P.

Y. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976).

Torner, L.

S. Carrasco, J. P. Torres, D. Antigas, and L. Torner, Opt. Commun. 192, 347 (2001).
[CrossRef]

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Torres, J. P.

S. Carrasco, J. P. Torres, D. Antigas, and L. Torner, Opt. Commun. 192, 347 (2001).
[CrossRef]

Torruellas, W. E.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Van Stryland, E. W.

S. Kim, Z. Wang, D. J. Hagan, E. W. Van Stryland, A. Kobyakov, F. Lederer, and G. Assanto, IEEE J. Quantum Electron. 34, 666 (1998).
[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Wang, Z.

S. Kim, Z. Wang, D. J. Hagan, E. W. Van Stryland, A. Kobyakov, F. Lederer, and G. Assanto, IEEE J. Quantum Electron. 34, 666 (1998).
[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Werner, M. J.

IEEE J. Quantum Electron. (1)

S. Kim, Z. Wang, D. J. Hagan, E. W. Van Stryland, A. Kobyakov, F. Lederer, and G. Assanto, IEEE J. Quantum Electron. 34, 666 (1998).
[CrossRef]

Opt. Commun. (1)

S. Carrasco, J. P. Torres, D. Antigas, and L. Torner, Opt. Commun. 192, 347 (2001).
[CrossRef]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

Phys. Rev. Lett. (1)

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

Y. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976).

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Figures (4)

Fig. 1
Fig. 1

Top, spatial profile of the FF output in the quasi-linear regime (low intensity) and in the self-trapped regime (high intensity, I=66 MW/cm2); dotted curves, experimental data; solid curves, numerical simulations. Bottom, evolution of the FF output beam’s FWHM versus input FF intensity; filled circles, experimental data; solid curve, simulations. Here ΔkL=18π.

Fig. 2
Fig. 2

Power threshold of self-trapping versus phase mismatch. Filled circles, experimental data; solid curve, numerical simulations.

Fig. 3
Fig. 3

Top, calculated FF (solid curve) and SH (dotted curve) pulses at output. Bottom, autocorrelation traces in intensity of the FF at output (solid curve, numerical simulation; dotted curve, experimental data). Here ΔkL=18π and I=66 MW/cm2.

Fig. 4
Fig. 4

Top, measured and bottom, calculated output pulse spectra at the FF (solid curves) and at the SH (dotted curves) after a twofold expansion of the SH scale. Here ΔkL=18π and I=120 MW/cm2.

Equations (2)

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

E1x,y,z,t=½Wywx,z,t×exp-jβω0z+ω0t+c.c.,  E2x,y,z,t=½Vyvx,z,t×exp-jβ2ω0z+2ω0t+c.c.,
jwz-jβω0wt-βω022wt2+12βω02wx2+χ2ω02 cnω0VW2dyW2 dyvw* exp-jΔkz=0,  jvz-jβ2ω0vt-β2ω022vt2+12β2ω02vx2+χ2ω02 cn2ω0VW2dyV2 dyw2 expjΔkz =0,

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