Abstract

Cascaded second-order effects are studied in the femtosecond regime in β-barium borate by use of the Z-scan technique. Large nonlinear phase shifts can be obtained near the second-harmonic-generation phase-matching condition for a Ti:sapphire laser. Solution of the nonlinear propagation equations for femtosecond pulses yields good agreement with experiment and also demonstrates that the description of cascaded effects by an effective nonlinear refractive index is no longer valid in the ultrafast domain and that these effects are less efficient for ultrashort pulses. The cascade-induced negative nonlinear phase shift in β-barium borate is shown to be responsible for the self-compression observed in a prismless femtosecond visible optical parametric oscillator.

© 1995 Optical Society of America

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References

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  1. T. J. Driscoll, G. M. Gale, F. Hache, Opt. Commun. 110, 638 (1994).
    [CrossRef]
  2. C. Flytzanis, in Quantum Electronics: A Treatise, H. Rabin, C. L. Tang, eds. (Academic, New York, 1975), Vol. 1, Pt. A, p. 53.
  3. R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, H. Vanherzeele, Opt. Lett. 17, 28 (1992).
    [CrossRef] [PubMed]
  4. A. Piskarskas, A. Stabinis, A. Yankauskas, Sov. J. Quantum Electron. 15, 1179 (1985)R. Laenen, H. Graener, A. Laubereau, J. Opt. Soc. Am. B 8, 1085 (1991).
    [CrossRef]
  5. M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagen, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
    [CrossRef]
  6. R. Danielius, P. Di Trapani, A. Dubietis, A. Piskarskas, D. Podenas, G. P. Banfi, Opt. Lett. 18, 574 (1993).
    [CrossRef] [PubMed]
  7. G. M. Gale, M. Cavallari, T. J. Driscoll, F. Hache, Opt. Lett. 20, 1562 (1995).
    [CrossRef] [PubMed]
  8. G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989), p. 114.

1995

1994

T. J. Driscoll, G. M. Gale, F. Hache, Opt. Commun. 110, 638 (1994).
[CrossRef]

1993

1992

1990

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagen, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

1985

A. Piskarskas, A. Stabinis, A. Yankauskas, Sov. J. Quantum Electron. 15, 1179 (1985)R. Laenen, H. Graener, A. Laubereau, J. Opt. Soc. Am. B 8, 1085 (1991).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989), p. 114.

Banfi, G. P.

Cavallari, M.

Danielius, R.

DeSalvo, R.

Di Trapani, P.

Driscoll, T. J.

Dubietis, A.

Flytzanis, C.

C. Flytzanis, in Quantum Electronics: A Treatise, H. Rabin, C. L. Tang, eds. (Academic, New York, 1975), Vol. 1, Pt. A, p. 53.

Gale, G. M.

Hache, F.

Hagan, D. J.

Hagen, D. J.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagen, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Piskarskas, A.

R. Danielius, P. Di Trapani, A. Dubietis, A. Piskarskas, D. Podenas, G. P. Banfi, Opt. Lett. 18, 574 (1993).
[CrossRef] [PubMed]

A. Piskarskas, A. Stabinis, A. Yankauskas, Sov. J. Quantum Electron. 15, 1179 (1985)R. Laenen, H. Graener, A. Laubereau, J. Opt. Soc. Am. B 8, 1085 (1991).
[CrossRef]

Podenas, D.

Said, A. A.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagen, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Sheik-Bahae, M.

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, H. Vanherzeele, Opt. Lett. 17, 28 (1992).
[CrossRef] [PubMed]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagen, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Stabinis, A.

A. Piskarskas, A. Stabinis, A. Yankauskas, Sov. J. Quantum Electron. 15, 1179 (1985)R. Laenen, H. Graener, A. Laubereau, J. Opt. Soc. Am. B 8, 1085 (1991).
[CrossRef]

Stegeman, G.

Van Stryland, E. W.

R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, H. Vanherzeele, Opt. Lett. 17, 28 (1992).
[CrossRef] [PubMed]

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagen, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Vanherzeele, H.

Wei, T. H.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagen, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Yankauskas, A.

A. Piskarskas, A. Stabinis, A. Yankauskas, Sov. J. Quantum Electron. 15, 1179 (1985)R. Laenen, H. Graener, A. Laubereau, J. Opt. Soc. Am. B 8, 1085 (1991).
[CrossRef]

IEEE J. Quantum Electron.

M. Sheik-Bahae, A. A. Said, T. H. Wei, D. J. Hagen, E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Opt. Commun.

T. J. Driscoll, G. M. Gale, F. Hache, Opt. Commun. 110, 638 (1994).
[CrossRef]

Opt. Lett.

Sov. J. Quantum Electron.

A. Piskarskas, A. Stabinis, A. Yankauskas, Sov. J. Quantum Electron. 15, 1179 (1985)R. Laenen, H. Graener, A. Laubereau, J. Opt. Soc. Am. B 8, 1085 (1991).
[CrossRef]

Other

C. Flytzanis, in Quantum Electronics: A Treatise, H. Rabin, C. L. Tang, eds. (Academic, New York, 1975), Vol. 1, Pt. A, p. 53.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989), p. 114.

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Figures (4)

Fig. 1
Fig. 1

Nonlinear phase shift, normalized to the input pulse energy (filled circles), and depletion of the fundamental beam (open diamonds) as functions of the external phase-mismatch angle Δθ. The solid curves are a fit obtained by solution of the nonlinear propagation equations.

Fig. 2
Fig. 2

Calculated temporal shape of the pulses and phase shift in a 1-mm BBO crystal for (a) 0.0° and (b) 0.3° phase-mismatch angles Δθ. In each figure the solid thin curve is the input fundamental pulse, the dashed curve is the output fundamental pulse, the dotted curve is the output harmonic pulse, and the solid thick curve is the phase of the output fundamental beam.

Fig. 3
Fig. 3

Calculated induced phase shift versus external phase-mismatch angle Δθ for 50-fs (filled circles), 100-fs (open diamonds), and 300-fs (solid triangles) pulse durations. The peak intensity is kept constant in these calculations.

Fig. 4
Fig. 4

Signal wavelength for which self-compression is observed in the prismless femtosecond BBO OPO versus internal angle between the crystal z axis and beam direction (filled circles). The solid line corresponds to the phase-matching angle for signal SHG, and the dashed line is a least-squares fit to the experimental data.

Equations (1)

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E F z + 1 υ F E F t = i ω F 2 η F c χ eff ( 2 ) E H E F * exp ( i Δ k z ) + i ω F 2 η F c χ ( 3 ) ( E F 2 E F + 2 E H 2 E H ) , E H z + 1 v H E H t = i ω H 2 η H c χ eff ( 2 ) E F 2 exp ( - i Δ k z ) + i ω H 2 η H c χ ( 3 ) ( E H 2 E H + 2 E F 2 E F ) ,

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