Abstract

We demonstrate theoretically and experimentally compensation for positive Kerr phase shifts with negative phases generated by cascade quadratic processes. Experiments show correction of small-scale self-focusing and whole-beam self-focusing in the spatial domain and self-phase modulation in the temporal domain.

© 2001 Optical Society of America

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References

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  1. See, for example, E. S. Bliss, D. R. Speck, J. F. Holzrichter, J. H. Erkkila, and A. J. Glass, Appl. Phys. Lett. 25, 448 (1974).
    [CrossRef]
  2. See, for example, G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).
  3. D. Strickland and G. Mourou, Opt. Commun. 56, 219 (1985).
    [CrossRef]
  4. U. Roth, F. Loewenthal, R. Tommasini, J. E. Balmer, and H. P. Weber, IEEE J. Quantum Electron. 36, 687 (2000).
    [CrossRef]
  5. O. A. Konoplev and D. D. Meyerhofer, IEEE J. Sel. Top. Quantum Electron. 4, 459 (1998).
    [CrossRef]
  6. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, and H. Vanherzeele, Opt. Lett. 17, 28 (1992).
    [CrossRef] [PubMed]
  7. X. Liu, K. Beckwitt, and F. W. Wise, Phys. Rev. E 62, 1328 (2000).
    [CrossRef]
  8. X. Liu, L. Qian, and F. W. Wise, Opt. Lett.24, 1777 (1999).
    [CrossRef]

2000 (2)

U. Roth, F. Loewenthal, R. Tommasini, J. E. Balmer, and H. P. Weber, IEEE J. Quantum Electron. 36, 687 (2000).
[CrossRef]

X. Liu, K. Beckwitt, and F. W. Wise, Phys. Rev. E 62, 1328 (2000).
[CrossRef]

1998 (1)

O. A. Konoplev and D. D. Meyerhofer, IEEE J. Sel. Top. Quantum Electron. 4, 459 (1998).
[CrossRef]

1992 (1)

1985 (1)

D. Strickland and G. Mourou, Opt. Commun. 56, 219 (1985).
[CrossRef]

1974 (1)

See, for example, E. S. Bliss, D. R. Speck, J. F. Holzrichter, J. H. Erkkila, and A. J. Glass, Appl. Phys. Lett. 25, 448 (1974).
[CrossRef]

Agrawal, G. P.

See, for example, G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).

Balmer, J. E.

U. Roth, F. Loewenthal, R. Tommasini, J. E. Balmer, and H. P. Weber, IEEE J. Quantum Electron. 36, 687 (2000).
[CrossRef]

Beckwitt, K.

X. Liu, K. Beckwitt, and F. W. Wise, Phys. Rev. E 62, 1328 (2000).
[CrossRef]

Bliss, E. S.

See, for example, E. S. Bliss, D. R. Speck, J. F. Holzrichter, J. H. Erkkila, and A. J. Glass, Appl. Phys. Lett. 25, 448 (1974).
[CrossRef]

DeSalvo, R.

Erkkila, J. H.

See, for example, E. S. Bliss, D. R. Speck, J. F. Holzrichter, J. H. Erkkila, and A. J. Glass, Appl. Phys. Lett. 25, 448 (1974).
[CrossRef]

Glass, A. J.

See, for example, E. S. Bliss, D. R. Speck, J. F. Holzrichter, J. H. Erkkila, and A. J. Glass, Appl. Phys. Lett. 25, 448 (1974).
[CrossRef]

Hagan, D. J.

Holzrichter, J. F.

See, for example, E. S. Bliss, D. R. Speck, J. F. Holzrichter, J. H. Erkkila, and A. J. Glass, Appl. Phys. Lett. 25, 448 (1974).
[CrossRef]

Konoplev, O. A.

O. A. Konoplev and D. D. Meyerhofer, IEEE J. Sel. Top. Quantum Electron. 4, 459 (1998).
[CrossRef]

Liu, X.

X. Liu, K. Beckwitt, and F. W. Wise, Phys. Rev. E 62, 1328 (2000).
[CrossRef]

X. Liu, L. Qian, and F. W. Wise, Opt. Lett.24, 1777 (1999).
[CrossRef]

Loewenthal, F.

U. Roth, F. Loewenthal, R. Tommasini, J. E. Balmer, and H. P. Weber, IEEE J. Quantum Electron. 36, 687 (2000).
[CrossRef]

Meyerhofer, D. D.

O. A. Konoplev and D. D. Meyerhofer, IEEE J. Sel. Top. Quantum Electron. 4, 459 (1998).
[CrossRef]

Mourou, G.

D. Strickland and G. Mourou, Opt. Commun. 56, 219 (1985).
[CrossRef]

Qian, L.

X. Liu, L. Qian, and F. W. Wise, Opt. Lett.24, 1777 (1999).
[CrossRef]

Roth, U.

U. Roth, F. Loewenthal, R. Tommasini, J. E. Balmer, and H. P. Weber, IEEE J. Quantum Electron. 36, 687 (2000).
[CrossRef]

Sheik-Bahae, M.

Speck, D. R.

See, for example, E. S. Bliss, D. R. Speck, J. F. Holzrichter, J. H. Erkkila, and A. J. Glass, Appl. Phys. Lett. 25, 448 (1974).
[CrossRef]

Stegeman, G.

Strickland, D.

D. Strickland and G. Mourou, Opt. Commun. 56, 219 (1985).
[CrossRef]

Tommasini, R.

U. Roth, F. Loewenthal, R. Tommasini, J. E. Balmer, and H. P. Weber, IEEE J. Quantum Electron. 36, 687 (2000).
[CrossRef]

Van Stryland, E. W.

Vanherzeele, H.

Weber, H. P.

U. Roth, F. Loewenthal, R. Tommasini, J. E. Balmer, and H. P. Weber, IEEE J. Quantum Electron. 36, 687 (2000).
[CrossRef]

Wise, F. W.

X. Liu, K. Beckwitt, and F. W. Wise, Phys. Rev. E 62, 1328 (2000).
[CrossRef]

X. Liu, L. Qian, and F. W. Wise, Opt. Lett.24, 1777 (1999).
[CrossRef]

Appl. Phys. Lett. (1)

See, for example, E. S. Bliss, D. R. Speck, J. F. Holzrichter, J. H. Erkkila, and A. J. Glass, Appl. Phys. Lett. 25, 448 (1974).
[CrossRef]

IEEE J. Quantum Electron. (1)

U. Roth, F. Loewenthal, R. Tommasini, J. E. Balmer, and H. P. Weber, IEEE J. Quantum Electron. 36, 687 (2000).
[CrossRef]

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

O. A. Konoplev and D. D. Meyerhofer, IEEE J. Sel. Top. Quantum Electron. 4, 459 (1998).
[CrossRef]

Opt. Commun. (1)

D. Strickland and G. Mourou, Opt. Commun. 56, 219 (1985).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. E (1)

X. Liu, K. Beckwitt, and F. W. Wise, Phys. Rev. E 62, 1328 (2000).
[CrossRef]

Other (2)

X. Liu, L. Qian, and F. W. Wise, Opt. Lett.24, 1777 (1999).
[CrossRef]

See, for example, G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).

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Figures (5)

Fig. 1
Fig. 1

Simulated transverse intensity profile (a) at input with seeded periodic intensity modulation, (b) after propagation through 6  cm of fused silica, (c) with optimal compensation ΦnetNL0, and (d) overcompensating for the Kerr phase ΦnetNL<0.

Fig. 2
Fig. 2

Beam profiles after the fused-silica sample (a) in the linear propagation regime, (b) at high intensity without compensation, (c) with a BBO Kerr phase shift only, (d) with cascade overcompensating for the Kerr phase, (e) with cascade optimally compensating for the Kerr phase, and (f) with cascade undercompensating for the Kerr phase.

Fig. 3
Fig. 3

Beam waist versus ΔkL in units of the low-intensity beam waist (dashed line). The dotted line shows the beam waist without compensation. The inset shows vertical line scans of the transverse intensity profile at the horizontal beam wing for (i) linear propagation, (ii) uncompensated WBSF, and (iii) optimal compensation at ΔkL520π.

Fig. 4
Fig. 4

Deviation of the beam from Gaussian versus ΔkL, where 0 represents a perfectly Gaussian beam and the dashed line represents the deviation in the low-intensity propagation regime. The dotted line represents deviation without compensation. The inset shows vertical line scans of the transverse intensity profile at the horizontal beam center for (i) linear propagation, (ii) uncompensated SSSF, and (iii) optimal compensation at ΔkL580π.

Fig. 5
Fig. 5

Spectrum of the uncompensated Ti:sapphire amplifier output (dotted curve) and after compensation (solid curve) and the spectrum corresponding to the transform limit (dashed curve).

Equations (1)

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ΦNL-Γ2L2/ΔkL,

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