Abstract

We present a calculation of the chirp generated in laser pulses shorter than 100 fsec on propagation through a saturable absorber (DODCI in ethylene glycol). The calculation takes into account the absorber saturation and the solvent nonlinear refractive index. At pulse energies greater than 10 nJ the chirp tends to be predominantly positive, and it increases rapidly as the pulse duration becomes shorter than 50 fsec. At pulse energies in the 1–7-nJ range the chirp is mostly negative for pulses longer than 30 fsec.

© 1986 Optical Society of America

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References

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  1. J. A. Valdmanis, R. L. Fork, J. P. Gordon, Opt. Lett. 10, 131 (1985).
    [CrossRef] [PubMed]
  2. O. E. Martinez, R. L. Fork, J. P. Gordon, Opt. Lett. 9, 156 (1984).
    [CrossRef] [PubMed]
  3. W. Rudolph, B. Wilhemi, Opt. Commun. 49, 371 (1984).
    [CrossRef]
  4. D. Kuhlke, W. Rudolph, Opt. Quantum Electron. 16, 57 (1984).
    [CrossRef]
  5. S. de Silvestri, P. Laporta, O. Svelto, IEEE J. Quantum Electron. QE-20, 533 (1984).
    [CrossRef]
  6. G. H. C. New, Opt. Commun. 1, 188 (1972).
    [CrossRef]
  7. A. M. Weidner, E. P. Ippen, Opt. Lett. 9, 53 (1984).
    [CrossRef]
  8. M. S. Stix, E. P. Ippen, IEEE J. Quantum Electron. QE-19, 520 (1983).
    [CrossRef]
  9. M. S. Stix, Opt. Lett. 10, 269 (1985).
  10. R. L. Fork, O. E. Martinez, J. P. Gordon, Opt. Lett 9, 150 (1984).
    [CrossRef] [PubMed]
  11. W. Dietel, J. J. Fontaine, J. C. Diels, Opt. Lett. 8, 4 (1983).
    [CrossRef] [PubMed]
  12. W. Dietel, E. Dopel, D. Kuhlke, B. Wilhelmi, Opt. Commun. 43, 133 (1982).

1985 (2)

1984 (6)

A. M. Weidner, E. P. Ippen, Opt. Lett. 9, 53 (1984).
[CrossRef]

O. E. Martinez, R. L. Fork, J. P. Gordon, Opt. Lett. 9, 156 (1984).
[CrossRef] [PubMed]

R. L. Fork, O. E. Martinez, J. P. Gordon, Opt. Lett 9, 150 (1984).
[CrossRef] [PubMed]

W. Rudolph, B. Wilhemi, Opt. Commun. 49, 371 (1984).
[CrossRef]

D. Kuhlke, W. Rudolph, Opt. Quantum Electron. 16, 57 (1984).
[CrossRef]

S. de Silvestri, P. Laporta, O. Svelto, IEEE J. Quantum Electron. QE-20, 533 (1984).
[CrossRef]

1983 (2)

M. S. Stix, E. P. Ippen, IEEE J. Quantum Electron. QE-19, 520 (1983).
[CrossRef]

W. Dietel, J. J. Fontaine, J. C. Diels, Opt. Lett. 8, 4 (1983).
[CrossRef] [PubMed]

1982 (1)

W. Dietel, E. Dopel, D. Kuhlke, B. Wilhelmi, Opt. Commun. 43, 133 (1982).

1972 (1)

G. H. C. New, Opt. Commun. 1, 188 (1972).
[CrossRef]

de Silvestri, S.

S. de Silvestri, P. Laporta, O. Svelto, IEEE J. Quantum Electron. QE-20, 533 (1984).
[CrossRef]

Diels, J. C.

Dietel, W.

W. Dietel, J. J. Fontaine, J. C. Diels, Opt. Lett. 8, 4 (1983).
[CrossRef] [PubMed]

W. Dietel, E. Dopel, D. Kuhlke, B. Wilhelmi, Opt. Commun. 43, 133 (1982).

Dopel, E.

W. Dietel, E. Dopel, D. Kuhlke, B. Wilhelmi, Opt. Commun. 43, 133 (1982).

Fontaine, J. J.

Fork, R. L.

Gordon, J. P.

Ippen, E. P.

A. M. Weidner, E. P. Ippen, Opt. Lett. 9, 53 (1984).
[CrossRef]

M. S. Stix, E. P. Ippen, IEEE J. Quantum Electron. QE-19, 520 (1983).
[CrossRef]

Kuhlke, D.

D. Kuhlke, W. Rudolph, Opt. Quantum Electron. 16, 57 (1984).
[CrossRef]

W. Dietel, E. Dopel, D. Kuhlke, B. Wilhelmi, Opt. Commun. 43, 133 (1982).

Laporta, P.

S. de Silvestri, P. Laporta, O. Svelto, IEEE J. Quantum Electron. QE-20, 533 (1984).
[CrossRef]

Martinez, O. E.

New, G. H. C.

G. H. C. New, Opt. Commun. 1, 188 (1972).
[CrossRef]

Rudolph, W.

D. Kuhlke, W. Rudolph, Opt. Quantum Electron. 16, 57 (1984).
[CrossRef]

W. Rudolph, B. Wilhemi, Opt. Commun. 49, 371 (1984).
[CrossRef]

Stix, M. S.

M. S. Stix, Opt. Lett. 10, 269 (1985).

M. S. Stix, E. P. Ippen, IEEE J. Quantum Electron. QE-19, 520 (1983).
[CrossRef]

Svelto, O.

S. de Silvestri, P. Laporta, O. Svelto, IEEE J. Quantum Electron. QE-20, 533 (1984).
[CrossRef]

Valdmanis, J. A.

Weidner, A. M.

Wilhelmi, B.

W. Dietel, E. Dopel, D. Kuhlke, B. Wilhelmi, Opt. Commun. 43, 133 (1982).

Wilhemi, B.

W. Rudolph, B. Wilhemi, Opt. Commun. 49, 371 (1984).
[CrossRef]

IEEE J. Quantum Electron. (2)

S. de Silvestri, P. Laporta, O. Svelto, IEEE J. Quantum Electron. QE-20, 533 (1984).
[CrossRef]

M. S. Stix, E. P. Ippen, IEEE J. Quantum Electron. QE-19, 520 (1983).
[CrossRef]

Opt. Commun. (3)

G. H. C. New, Opt. Commun. 1, 188 (1972).
[CrossRef]

W. Rudolph, B. Wilhemi, Opt. Commun. 49, 371 (1984).
[CrossRef]

W. Dietel, E. Dopel, D. Kuhlke, B. Wilhelmi, Opt. Commun. 43, 133 (1982).

Opt. Lett (1)

R. L. Fork, O. E. Martinez, J. P. Gordon, Opt. Lett 9, 150 (1984).
[CrossRef] [PubMed]

Opt. Lett. (5)

Opt. Quantum Electron. (1)

D. Kuhlke, W. Rudolph, Opt. Quantum Electron. 16, 57 (1984).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Instantaneous frequency shift along the pulse caused by the saturation of the absorber (dashed–dotted lines) and by the nonlinear index of the solvent (dashed lines). The resulting shift is shown by the solid line. The input pulse profile is shown for reference (double-dotted–dashed line). The pulse energy is 1.0 nJ in (a) and 15.0 nJ in (b), and the pulse duration is 50 fsec in both cases.

Fig. 2
Fig. 2

Average chirp coefficient as a function of the pulse energy for three different values of the pulse duration.

Fig. 3
Fig. 3

Chirp coefficient at the peak of the pulse as a function of the pulse duration for four different values of the pulse energy.

Tables (1)

Tables Icon

Table 1 Parameters Used for the Calculation of the Frequency Shift δω

Equations (9)

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I ( t ) = I 0 exp [ - ( 4 ln 2 ) t 2 / τ 2 ] ,
g ( ω ) = 2 × { π Δ ω [ 1 + 4 ( ω 0 - ω ) 2 Δ ω 2 ] } - 1 ,
n R = π 2 ( ω 0 - ω ) c ω 0 α g ( ω ) .
α = α 0 exp [ - - t I ( θ ) d θ E s ] ,
ϕ ( t ) = - n 2 ω l c I ( t ) - G ( ω ) ω l c α ( t ) ,
G ( ω ) π 2 ( ω 0 - ω ) c ω 0 g ( ω ) .
δ w = - n 2 ω l c d I d t - G ( ω ) ω l c d α ( t ) d t .
δ ω g = 2 π l λ { 5.23 n 2 E 0 τ 3 t exp [ - ( 4 ln 2 ) t 2 τ 2 ] + 0.94 α 0 E 0 E s τ G ( ω ) exp [ - ( 4 ln 2 ) t 2 τ 2 - E t E s ] } ,
C ¯ = - C ( t ) I ( t ) d t - I ( t ) d t .

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