Abstract

We have achieved highly stable amplification of femtosecond pulses to the millijoule level with pulse-to-pulse energy fluctuations below those of the pump source. Our Ti:Al2O3 amplifier produces pulses with a root-mean-square fluctuation in pulse energy of 0.42%, which is the lowest value to our knowledge for any optical pulse amplifier reported to date. Pump-noise suppression by a factor of 40 is demonstrated for the first time to our knowledge. We discuss this high-stability behavior through model simulations.

© 1994 Optical Society of America

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References

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  1. See, for example, J.-L. Martin, A. Migus, G. A. Mourou, and A. H. Zewail, eds., Ultrafast Phenomena VIII (Springer-Verlag, Berlin, 1993).
    [Crossref]
  2. R. L. Fork, C. V. Shank, C. Hirlimann, R. Yen, and W. J. Tomlinson, Opt. Lett. 8, 1 (1983).
    [Crossref] [PubMed]
  3. W. Koechner, J. Appl. Phys. 44, 3162 (1973).
    [Crossref]
  4. See, for example, specifications for the TR series Ultrafast Amplifiers produced by Continuum, Santa Clara, California.
  5. F. Salin, J. Squier, G. Mourou, and G. Vaillancourt, Opt. Lett. 16, 1965 (1991).
  6. L. M. Frantz and J. S. Nodvik, J. Appl. Phys. 34, 2346 (1963).
    [Crossref]
  7. W. H. Lowdermilk and J. E. Murray, J. Appl. Phys. 51, 2436 (1980).
    [Crossref]
  8. M. M. Tilleman and J. H. Jacob, Appl. Phys. Lett. 50, 121 (1987).
    [Crossref]
  9. C. Le Blanc, G. Grillon, J. P. Chambaret, A. Migus, and A. Antonetti, Opt. Lett. 18, 140 (1993).
    [Crossref]
  10. P. F. Moulton, J. Opt. Soc. Am. B 3, 125 (1986).
    [Crossref]
  11. A. Sullivan, H. Hamster, H. C. Kapteyn, S. Gordon, W. White, H. Nathel, R. J. Blair, and R. W. Falcone, Opt. Lett. 16, 1407 (1991).
    [Crossref]

1993 (1)

1991 (2)

F. Salin, J. Squier, G. Mourou, and G. Vaillancourt, Opt. Lett. 16, 1965 (1991).

A. Sullivan, H. Hamster, H. C. Kapteyn, S. Gordon, W. White, H. Nathel, R. J. Blair, and R. W. Falcone, Opt. Lett. 16, 1407 (1991).
[Crossref]

1987 (1)

M. M. Tilleman and J. H. Jacob, Appl. Phys. Lett. 50, 121 (1987).
[Crossref]

1986 (1)

1983 (1)

1980 (1)

W. H. Lowdermilk and J. E. Murray, J. Appl. Phys. 51, 2436 (1980).
[Crossref]

1973 (1)

W. Koechner, J. Appl. Phys. 44, 3162 (1973).
[Crossref]

1963 (1)

L. M. Frantz and J. S. Nodvik, J. Appl. Phys. 34, 2346 (1963).
[Crossref]

Antonetti, A.

Blair, R. J.

A. Sullivan, H. Hamster, H. C. Kapteyn, S. Gordon, W. White, H. Nathel, R. J. Blair, and R. W. Falcone, Opt. Lett. 16, 1407 (1991).
[Crossref]

Chambaret, J. P.

Falcone, R. W.

A. Sullivan, H. Hamster, H. C. Kapteyn, S. Gordon, W. White, H. Nathel, R. J. Blair, and R. W. Falcone, Opt. Lett. 16, 1407 (1991).
[Crossref]

Fork, R. L.

Frantz, L. M.

L. M. Frantz and J. S. Nodvik, J. Appl. Phys. 34, 2346 (1963).
[Crossref]

Gordon, S.

A. Sullivan, H. Hamster, H. C. Kapteyn, S. Gordon, W. White, H. Nathel, R. J. Blair, and R. W. Falcone, Opt. Lett. 16, 1407 (1991).
[Crossref]

Grillon, G.

Hamster, H.

A. Sullivan, H. Hamster, H. C. Kapteyn, S. Gordon, W. White, H. Nathel, R. J. Blair, and R. W. Falcone, Opt. Lett. 16, 1407 (1991).
[Crossref]

Hirlimann, C.

Jacob, J. H.

M. M. Tilleman and J. H. Jacob, Appl. Phys. Lett. 50, 121 (1987).
[Crossref]

Kapteyn, H. C.

A. Sullivan, H. Hamster, H. C. Kapteyn, S. Gordon, W. White, H. Nathel, R. J. Blair, and R. W. Falcone, Opt. Lett. 16, 1407 (1991).
[Crossref]

Koechner, W.

W. Koechner, J. Appl. Phys. 44, 3162 (1973).
[Crossref]

Le Blanc, C.

Lowdermilk, W. H.

W. H. Lowdermilk and J. E. Murray, J. Appl. Phys. 51, 2436 (1980).
[Crossref]

Migus, A.

Moulton, P. F.

Mourou, G.

F. Salin, J. Squier, G. Mourou, and G. Vaillancourt, Opt. Lett. 16, 1965 (1991).

Murray, J. E.

W. H. Lowdermilk and J. E. Murray, J. Appl. Phys. 51, 2436 (1980).
[Crossref]

Nathel, H.

A. Sullivan, H. Hamster, H. C. Kapteyn, S. Gordon, W. White, H. Nathel, R. J. Blair, and R. W. Falcone, Opt. Lett. 16, 1407 (1991).
[Crossref]

Nodvik, J. S.

L. M. Frantz and J. S. Nodvik, J. Appl. Phys. 34, 2346 (1963).
[Crossref]

Salin, F.

F. Salin, J. Squier, G. Mourou, and G. Vaillancourt, Opt. Lett. 16, 1965 (1991).

Shank, C. V.

Squier, J.

F. Salin, J. Squier, G. Mourou, and G. Vaillancourt, Opt. Lett. 16, 1965 (1991).

Sullivan, A.

A. Sullivan, H. Hamster, H. C. Kapteyn, S. Gordon, W. White, H. Nathel, R. J. Blair, and R. W. Falcone, Opt. Lett. 16, 1407 (1991).
[Crossref]

Tilleman, M. M.

M. M. Tilleman and J. H. Jacob, Appl. Phys. Lett. 50, 121 (1987).
[Crossref]

Tomlinson, W. J.

Vaillancourt, G.

F. Salin, J. Squier, G. Mourou, and G. Vaillancourt, Opt. Lett. 16, 1965 (1991).

White, W.

A. Sullivan, H. Hamster, H. C. Kapteyn, S. Gordon, W. White, H. Nathel, R. J. Blair, and R. W. Falcone, Opt. Lett. 16, 1407 (1991).
[Crossref]

Yen, R.

Appl. Phys. Lett. (1)

M. M. Tilleman and J. H. Jacob, Appl. Phys. Lett. 50, 121 (1987).
[Crossref]

J. Appl. Phys. (3)

L. M. Frantz and J. S. Nodvik, J. Appl. Phys. 34, 2346 (1963).
[Crossref]

W. H. Lowdermilk and J. E. Murray, J. Appl. Phys. 51, 2436 (1980).
[Crossref]

W. Koechner, J. Appl. Phys. 44, 3162 (1973).
[Crossref]

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

Opt. Lett. (4)

A. Sullivan, H. Hamster, H. C. Kapteyn, S. Gordon, W. White, H. Nathel, R. J. Blair, and R. W. Falcone, Opt. Lett. 16, 1407 (1991).
[Crossref]

F. Salin, J. Squier, G. Mourou, and G. Vaillancourt, Opt. Lett. 16, 1965 (1991).

R. L. Fork, C. V. Shank, C. Hirlimann, R. Yen, and W. J. Tomlinson, Opt. Lett. 8, 1 (1983).
[Crossref] [PubMed]

C. Le Blanc, G. Grillon, J. P. Chambaret, A. Migus, and A. Antonetti, Opt. Lett. 18, 140 (1993).
[Crossref]

Other (2)

See, for example, J.-L. Martin, A. Migus, G. A. Mourou, and A. H. Zewail, eds., Ultrafast Phenomena VIII (Springer-Verlag, Berlin, 1993).
[Crossref]

See, for example, specifications for the TR series Ultrafast Amplifiers produced by Continuum, Santa Clara, California.

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Figures (12)

Fig. 1
Fig. 1

Influence of loss per pass on the existence on points of high pulse-to-pulse stability. The amplified pulse fluence normalized by the saturation fluence J out ( p ) / J sat as a function of pass number p is shown. Four manifolds, each consisting of five curves, are shown, demonstrating the influence of pump fluctuations of ±2.5% and ±5% around a central value. The only difference between the manifolds is the loss per pass, characterized by the loss factor R. which takes values of 0.90, 0.94, 0.965, and 1.

Fig. 2
Fig. 2

Amplifier output fluctuation versus pass number for the examples of Fig. 1.

Fig. 3
Fig. 3

Creation of stationary behavior through variation of seed fluence. Five pump fluctuation manifolds are shown. The only difference between the manifolds is in the value of the seed fluence J in ( 0 ). J in ( 0 ) / J sat is varied from 4.5 × 10−10 to 4.5 × 10−2 in 2-order-of-magnitude steps as indicated by the labels on the manifolds. Stationary behavior is optimized near J in ( 0 ) / J sat equal to 4.5 × 10−8.

Fig. 4
Fig. 4

Creation of stationary behavior through variation of pump fluence. Three different pump fluctuation manifolds are shown. The only difference between the manifolds is in the value of the pump fluence, J pump J sto ( 0 ). Jpump/Jsat takes values of 0.68, 1.0, and 2.0. Stationary behavior is optimum near Jpump/Jsat equal to 2.

Fig. 5
Fig. 5

Stability of stationary points to seed fluctuation. Normalized output fluence jout versus normalized seed fluence jin is shown for underdamped and critically damped stationary points (R = 0.94, 0.965) of Fig. 2. jout and jin are equal to unity at the stationary point. Seed fluctuations are approximately 15-fold suppressed.

Fig. 6
Fig. 6

Stability of stationary points to pump fluctuation. Normalized output fluence jout versus normalized pump fluence jsto is shown for underdamped and critically damped stationary points (R = 0.94, 0.965) of Fig. 2. jout and jsto are equal to unity at the stationary point.

Fig. 7
Fig. 7

Sensitivity of stationary points to loss variations. The two stationary points discussed here occur for R equal to 0.94 and 0.965 near pass numbers 35 and 60, respectively, in Fig. 2. The critically damped case shows a narrow resonance with stationary behavior optimized at R = 0.9645 and pump noise suppression by a factor of 74.

Fig. 8
Fig. 8

Shift of stationary point that is due to simultaneous seed and pump fluctuations. Amplifier output fluctuation as a function of pass is shown for ±20% seed fluctuation, ±1% pump fluctuation, and total output fluctuation that is due to simultaneous seed and pump fluctuation. The parameter values for this example are J in ( 0 ) / J sat , J sto ( 0 ) / J sat, and R equal to 4.5 × 108, 0.64, and 0.94, respectively.

Fig. 9
Fig. 9

Experimental setup, consisting of femtosecond oscillator, grating stretcher, isolator, regenerative amplifier cavity, and Nd:YAG pump laser. λ/2’s, half-wave plates; Pol’s, polarizers; M’s, mirrors; L’s, lenses; FR, Faraday rotator; TFP, thin-film polarizer; PC, Pockels cell; VRM, vertical roof mirror. M4 is below the incident beam.

Fig. 10
Fig. 10

Amplifier output energy as a function of the number of passes. Three data sets are shown and labeled with pump energy and loss factor. The set with pump energy 13.5 mJ is not directly comparable with the remaining two sets. For the exact experimental parameters, see the text. The error bars shown on one data set correspond to the standard deviation of the pulse-to-pulse energy fluctuation and are typical for all three sets. Standard deviations for larger pass numbers are smaller than the data point markers. The pump-fluctuation manifold shown represents a fit of Eq. (1) to the data set with pump energy 13.5 mJ. The parameters for the central curve of the manifold are J in ( 0 ) = 0.1 nJ / mm 2, Jsat = 22 mJ/mm2, J sto ( 0 ) = 18.2 mJ / mm 2, R = 0.942. The remaining curves differ by ±2.5% and ±5% in absorbed pump fluence. The stationary point is according to the fit near pass 31, experimentally near pass 32.

Fig. 11
Fig. 11

Amplifier output fluctuation. The standard deviations of the output energy in percent as a function of the number of single passes are shown. The fluctuation data shown correspond to the output-energy data of Fig. 10. The minima of pulse-to-pulse fluctuations for intermediate pass numbers demonstrate stationary behavior as predicted by our modeling. A minimum fluctuation of 0.42% is observed for the data set with 12-mJ pump energy at pass 32.

Fig. 12
Fig. 12

Amplifier output as a function of pump and seed near the operating point of lowest output fluctuation; compare Fig. 11. Normalized output fluence, jout, as a function of normalized seed fluence, jin, and normalized pump fluence, jsto, is shown. All fluences are normalized to one at the experimentally observed stationary point, e.g., jsto equal to one corresponds to a 12-mJ pump. The pass number is fixed at 32. The linear fit gives a seed noise suppression of 13.5. Pump noise at the operating point is suppressed by a factor of 3.4. Pump-noise suppression by a factor of 40 is achieved near jsto = 1.088.

Equations (4)

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J out ( p ) = J sat ln ( 1 + G 0 ( p ) { exp [ J in ( p ) / J sat ] - 1 } ) ,
G 0 ( p ) = exp [ J sto ( p ) / J sat ] .
J in ( p + 1 ) = R J out ( p )
J sto ( p + 1 ) = J sto ( p ) - [ J out ( p ) - J in ( p ) ] .

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