Abstract

We report experimental evidence for trapping of two-dimensional (2 + 1) spatial solitary waves in a KTP crystal resulting from its second-order nonlinearity. In addition, dragging of the solitary beams is observed as a function of fundamental input intensity and of the relative phase difference between the fundamental and the second harmonic when beams at both frequencies are coherently launched.

© 1995 Optical Society of America

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References

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  1. M. I. Sundheimer, Ch. Bosshard, E. W. Van Stryland, G. I. Stegeman, J. D. Bierlein, Opt. Lett. 18, 1397 (1993); D. Y. Kim, W. E. Torruellas, J. Kang, C. Bosshard, G. I. Stegeman, P. Vidakovic, J. Zyss, W. E. Moerner, R. Twieg, G. Bjorklund, Opt. Lett. 19, 868 (1994).
    [CrossRef] [PubMed]
  2. G. I. Stegeman, W. E. Torruellas, “Nonlinear materials for information processing and communications,” Philos. Trans. R. Soc. London (to be published).
  3. R. Schiek, Y. Baek, G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second order nonlinearities in planar waveguides,” submitted toPhys. Rev. Lett.; Y. Baek, R. Shiek, G. I. Stegeman, “All-optical response of a hybrid Mach–Zehnder interferometer owing to the cascaded second-order nonlinearity,” submitted toOpt. Lett.
  4. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
    [CrossRef] [PubMed]
  5. Y. Silberberg, Opt. Lett. 15, 1282 (1990).
    [CrossRef] [PubMed]
  6. C. R. Menyuk, J. Opt. Soc. Am. B 5, 392 (1988).
    [CrossRef]

1995 (1)

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

1993 (1)

1990 (1)

1988 (1)

Baek, Y.

R. Schiek, Y. Baek, G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second order nonlinearities in planar waveguides,” submitted toPhys. Rev. Lett.; Y. Baek, R. Shiek, G. I. Stegeman, “All-optical response of a hybrid Mach–Zehnder interferometer owing to the cascaded second-order nonlinearity,” submitted toOpt. Lett.

Bierlein, J. D.

Bosshard, Ch.

Hagan, D. J.

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

Menyuk, C. R.

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

C. R. Menyuk, J. Opt. Soc. Am. B 5, 392 (1988).
[CrossRef]

Schiek, R.

R. Schiek, Y. Baek, G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second order nonlinearities in planar waveguides,” submitted toPhys. Rev. Lett.; Y. Baek, R. Shiek, G. I. Stegeman, “All-optical response of a hybrid Mach–Zehnder interferometer owing to the cascaded second-order nonlinearity,” submitted toOpt. Lett.

Silberberg, Y.

Stegeman, G. I.

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

M. I. Sundheimer, Ch. Bosshard, E. W. Van Stryland, G. I. Stegeman, J. D. Bierlein, Opt. Lett. 18, 1397 (1993); D. Y. Kim, W. E. Torruellas, J. Kang, C. Bosshard, G. I. Stegeman, P. Vidakovic, J. Zyss, W. E. Moerner, R. Twieg, G. Bjorklund, Opt. Lett. 19, 868 (1994).
[CrossRef] [PubMed]

R. Schiek, Y. Baek, G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second order nonlinearities in planar waveguides,” submitted toPhys. Rev. Lett.; Y. Baek, R. Shiek, G. I. Stegeman, “All-optical response of a hybrid Mach–Zehnder interferometer owing to the cascaded second-order nonlinearity,” submitted toOpt. Lett.

G. I. Stegeman, W. E. Torruellas, “Nonlinear materials for information processing and communications,” Philos. Trans. R. Soc. London (to be published).

Sundheimer, M. I.

Torner, L.

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

Torruellas, W. E.

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

G. I. Stegeman, W. E. Torruellas, “Nonlinear materials for information processing and communications,” Philos. Trans. R. Soc. London (to be published).

Van Stryland, E. W.

Wang, Z.

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

J. Opt. Soc. Am. B (1)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

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

Other (2)

G. I. Stegeman, W. E. Torruellas, “Nonlinear materials for information processing and communications,” Philos. Trans. R. Soc. London (to be published).

R. Schiek, Y. Baek, G. I. Stegeman, “One-dimensional spatial solitary waves due to cascaded second order nonlinearities in planar waveguides,” submitted toPhys. Rev. Lett.; Y. Baek, R. Shiek, G. I. Stegeman, “All-optical response of a hybrid Mach–Zehnder interferometer owing to the cascaded second-order nonlinearity,” submitted toOpt. Lett.

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Figures (3)

Fig. 1
Fig. 1

Numerical demonstration of trapping and dragging for no second-harmonic input for the three fields involved in the type II interaction. Note that all three fields are centered at r = 0 at the entrance of the KTP crystal. Slices of the 2D transverse output beams along the natural walk-off direction (in units of micrometers) are shown as a function of the input fundamental peak intensity, vertical axis. Fun Ord. Pol., Fundamental ordinary polarization; Fun. Ext. Pol., fundamental extraordinary polarization; S.H. Ext. Pol., second-harmonic extraordinary polarization.

Fig. 2
Fig. 2

Experimental setup required for observation of the dragging of 2D spatial solitary waves in quadratic media during seeding with a second-harmonic beam. The dashed lines show the displaced second-harmonic beam. P, polarizer.

Fig. 3
Fig. 3

(Left) Numerical calculations demonstrating mutual trapping and dragging of the fundamental (FUN) and the second harmonic (SHG) at the output of a 1-cm-long KTP crystal (axes in units of micrometers). The input second-harmonic field has a phase front tilt and a waist of 20 μm, resulting as shown into a 12.5-μm waist at the output of the 1-cm-long KTP crystal. (Right) Experimental transverse profile measurements at the output of the KTP crystal, demonstrating trapping and dragging as a function of the nitrogen cell pressure, or equivalently the input phase difference between the fundamental and harmonic fields. The second harmonic was launched with a 0.6° vertical angle relative to the fundamental beam. The horizontal axis is the extraordinary axis, defining the direction of walk-off owing to natural birefringence, and the vertical axis is the axis of artificial walk-off imposed by the seeded SHG beam. The axes are in units of micrometers.

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