Abstract

By adaptive control of both spectral phase and amplitude of seed pulses with an acousto-optic programmable dispersion filter located before a pulse stretcher, accurate pulse shaping was achieved for ultrashort laser pulses delivered through a regenerative amplifier. Two-dimensional patterns obtained from frequency-resolved optical gating were used for calculating cost functions in an adaptive control algorithm without pulse shape reconstruction during the control of pulse shape.

© 2002 Optical Society of America

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References

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  1. A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Swyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
    [CrossRef] [PubMed]
  2. J. D. Kmetec, “Ultrafast laser generation of hard x-rays,” IEEE J. Quantum Electron. 28, 2382–2387 (1992).
    [CrossRef]
  3. R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft x-rays,” Nature 406, 164–166 (2000).
    [CrossRef] [PubMed]
  4. B. N. Chichkov, C. Momma, S. Nolte, F. von Alvensleben, and A. Tünnermann, “Femtosecond, picosecond and nanosecond laser ablation of solids,” Appl. Phys. A 63, 109–115 (1996).
    [CrossRef]
  5. A. M. Weiner, J. P. Hertage, and E. M. Kirscher, “High-resolution femtosecond pulse shaping,” J. Opt. Soc. Am. B 5, 1563–1572 (1988).
    [CrossRef]
  6. D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
    [CrossRef]
  7. K. Yamakawa, M. Aoyama, S. Matsuoka, H. Takuma, D. N. Fittinghoff, and C. P. J. Barty, “Ultrahigh-peak and high-average power chirped-pulse amplification of sub-20-fs pulses with Ti: sapphire amplifiers,” IEEE J. Sel. Top. Quantum Electron. 4, 385–394 (1998).
    [CrossRef]
  8. K. Takasago, M. Takekawa, M. Suzuki, K. Komori, and F. Kannari, “Evaluation of femtosecond pulse shaping with low-loss phase-only masks,” IEEE J. Sel. Top. Quantum Electron. 4, 346–352 (1998).
    [CrossRef]
  9. Y. Fujimura, L. Gonzalez, K. Hoki, J. Manz, and Y. Ohtsuki, “Selective preparation of enantiomers by laser pulses: quantum model simulation for H2POSH,” Chem. Phys. Lett. 306, 1–8 (1999).
    [CrossRef]
  10. M. A. Dugan, J. X. Tull, and W. S. Warren, “High-resolution acousto-optic shaping of unamplified and amplified femtosecond laser pulses,” J. Opt. Soc. Am. B 14, 2348–2358 (1997).
    [CrossRef]
  11. F. Verluise, V. Laude, J. P. Huignard, and P. Tournois, “Arbitrary dispersion control of ultrashort optical pulses with acoustic waves,” J. Opt. Soc. Am. B 17, 138–145 (2000).
    [CrossRef]
  12. P. Tournois, “Acousto-optic programmable dispersion filter for adaptive compensation of group delay time dispersion in laser systems,” Opt. Commun. 140, 245–249 (1997).
    [CrossRef]
  13. F. Verluise, V. Laude, Z. Cheng, Ch. Spielman, and P. Tournois, “Amplitude and phase control of ultrashort pulses by use of an acousto-optic programmable dispersive filter: pulse compression and shaping,” Opt. Lett. 25, 575–577 (2000).
    [CrossRef]
  14. R. Trebino and D. J. Kane, “Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating,” J. Opt. Soc. Am. A 10, 1101–1111 (1993).
    [CrossRef]
  15. A. M. Weiner, S. Oudin, D. E. Leaird, and D. H. Reitze, “Shaping of femtosecond pulses using phase-only filters designed by simulated annealing,” J. Opt. Soc. Am. A 10, 1112–1114 (1993).
    [CrossRef]
  16. K. Takasago, T. Itoh, M. Takekawa, K. Utoh, and F. Kan-nari, “Design of frequency-domain filters for femtosecond pulse shaping,” Jpn. J. Appl. Phys., 35, 624–629 (1996).
    [CrossRef]
  17. A. Braun, S. Kane, and T. Norris, “Compensation of self-phase modulation in chirped-pulse amplification laser system,” Opt. Lett. 22, 615–617 (1997).
    [CrossRef] [PubMed]
  18. M. Takeoka, D. Fujishima, and F. Kannari, “Optimization of ultrashort-pulse squeezing by spectral filtering with the Fourier pulse-shaping technique,” Opt. Lett. 26, 1592–1594 (2001).
    [CrossRef]
  19. C. W. Hillegas, J. X. Tull, D. Goswami, D. Strickland, and W. S. Warren, “Femtosecond laser pulse shaping by use of microsecond radio-frequency pulses,” Opt. Lett. 19, 737–739 (1994).
    [CrossRef] [PubMed]

2001 (1)

2000 (3)

1999 (1)

Y. Fujimura, L. Gonzalez, K. Hoki, J. Manz, and Y. Ohtsuki, “Selective preparation of enantiomers by laser pulses: quantum model simulation for H2POSH,” Chem. Phys. Lett. 306, 1–8 (1999).
[CrossRef]

1998 (3)

K. Yamakawa, M. Aoyama, S. Matsuoka, H. Takuma, D. N. Fittinghoff, and C. P. J. Barty, “Ultrahigh-peak and high-average power chirped-pulse amplification of sub-20-fs pulses with Ti: sapphire amplifiers,” IEEE J. Sel. Top. Quantum Electron. 4, 385–394 (1998).
[CrossRef]

K. Takasago, M. Takekawa, M. Suzuki, K. Komori, and F. Kannari, “Evaluation of femtosecond pulse shaping with low-loss phase-only masks,” IEEE J. Sel. Top. Quantum Electron. 4, 346–352 (1998).
[CrossRef]

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Swyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[CrossRef] [PubMed]

1997 (3)

1996 (2)

K. Takasago, T. Itoh, M. Takekawa, K. Utoh, and F. Kan-nari, “Design of frequency-domain filters for femtosecond pulse shaping,” Jpn. J. Appl. Phys., 35, 624–629 (1996).
[CrossRef]

B. N. Chichkov, C. Momma, S. Nolte, F. von Alvensleben, and A. Tünnermann, “Femtosecond, picosecond and nanosecond laser ablation of solids,” Appl. Phys. A 63, 109–115 (1996).
[CrossRef]

1994 (1)

1993 (2)

1992 (1)

J. D. Kmetec, “Ultrafast laser generation of hard x-rays,” IEEE J. Quantum Electron. 28, 2382–2387 (1992).
[CrossRef]

1988 (1)

1985 (1)

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

Aoyama, M.

K. Yamakawa, M. Aoyama, S. Matsuoka, H. Takuma, D. N. Fittinghoff, and C. P. J. Barty, “Ultrahigh-peak and high-average power chirped-pulse amplification of sub-20-fs pulses with Ti: sapphire amplifiers,” IEEE J. Sel. Top. Quantum Electron. 4, 385–394 (1998).
[CrossRef]

Assion, A.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Swyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[CrossRef] [PubMed]

Backus, S.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft x-rays,” Nature 406, 164–166 (2000).
[CrossRef] [PubMed]

Bartels, R.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft x-rays,” Nature 406, 164–166 (2000).
[CrossRef] [PubMed]

Barty, C. P. J.

K. Yamakawa, M. Aoyama, S. Matsuoka, H. Takuma, D. N. Fittinghoff, and C. P. J. Barty, “Ultrahigh-peak and high-average power chirped-pulse amplification of sub-20-fs pulses with Ti: sapphire amplifiers,” IEEE J. Sel. Top. Quantum Electron. 4, 385–394 (1998).
[CrossRef]

Baumert, T.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Swyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[CrossRef] [PubMed]

Bergt, M.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Swyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[CrossRef] [PubMed]

Braun, A.

Brixner, T.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Swyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[CrossRef] [PubMed]

Cheng, Z.

Chichkov, B. N.

B. N. Chichkov, C. Momma, S. Nolte, F. von Alvensleben, and A. Tünnermann, “Femtosecond, picosecond and nanosecond laser ablation of solids,” Appl. Phys. A 63, 109–115 (1996).
[CrossRef]

Christov, I. P.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft x-rays,” Nature 406, 164–166 (2000).
[CrossRef] [PubMed]

Dugan, M. A.

Fittinghoff, D. N.

K. Yamakawa, M. Aoyama, S. Matsuoka, H. Takuma, D. N. Fittinghoff, and C. P. J. Barty, “Ultrahigh-peak and high-average power chirped-pulse amplification of sub-20-fs pulses with Ti: sapphire amplifiers,” IEEE J. Sel. Top. Quantum Electron. 4, 385–394 (1998).
[CrossRef]

Fujimura, Y.

Y. Fujimura, L. Gonzalez, K. Hoki, J. Manz, and Y. Ohtsuki, “Selective preparation of enantiomers by laser pulses: quantum model simulation for H2POSH,” Chem. Phys. Lett. 306, 1–8 (1999).
[CrossRef]

Fujishima, D.

Gerber, G.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Swyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[CrossRef] [PubMed]

Gonzalez, L.

Y. Fujimura, L. Gonzalez, K. Hoki, J. Manz, and Y. Ohtsuki, “Selective preparation of enantiomers by laser pulses: quantum model simulation for H2POSH,” Chem. Phys. Lett. 306, 1–8 (1999).
[CrossRef]

Goswami, D.

Hertage, J. P.

Hillegas, C. W.

Hoki, K.

Y. Fujimura, L. Gonzalez, K. Hoki, J. Manz, and Y. Ohtsuki, “Selective preparation of enantiomers by laser pulses: quantum model simulation for H2POSH,” Chem. Phys. Lett. 306, 1–8 (1999).
[CrossRef]

Huignard, J. P.

Itoh, T.

K. Takasago, T. Itoh, M. Takekawa, K. Utoh, and F. Kan-nari, “Design of frequency-domain filters for femtosecond pulse shaping,” Jpn. J. Appl. Phys., 35, 624–629 (1996).
[CrossRef]

Kane, D. J.

Kane, S.

Kannari, F.

M. Takeoka, D. Fujishima, and F. Kannari, “Optimization of ultrashort-pulse squeezing by spectral filtering with the Fourier pulse-shaping technique,” Opt. Lett. 26, 1592–1594 (2001).
[CrossRef]

K. Takasago, M. Takekawa, M. Suzuki, K. Komori, and F. Kannari, “Evaluation of femtosecond pulse shaping with low-loss phase-only masks,” IEEE J. Sel. Top. Quantum Electron. 4, 346–352 (1998).
[CrossRef]

Kan-nari, F.

K. Takasago, T. Itoh, M. Takekawa, K. Utoh, and F. Kan-nari, “Design of frequency-domain filters for femtosecond pulse shaping,” Jpn. J. Appl. Phys., 35, 624–629 (1996).
[CrossRef]

Kapteyn, H. C.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft x-rays,” Nature 406, 164–166 (2000).
[CrossRef] [PubMed]

Kiefer, B.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Swyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[CrossRef] [PubMed]

Kirscher, E. M.

Kmetec, J. D.

J. D. Kmetec, “Ultrafast laser generation of hard x-rays,” IEEE J. Quantum Electron. 28, 2382–2387 (1992).
[CrossRef]

Komori, K.

K. Takasago, M. Takekawa, M. Suzuki, K. Komori, and F. Kannari, “Evaluation of femtosecond pulse shaping with low-loss phase-only masks,” IEEE J. Sel. Top. Quantum Electron. 4, 346–352 (1998).
[CrossRef]

Laude, V.

Leaird, D. E.

Manz, J.

Y. Fujimura, L. Gonzalez, K. Hoki, J. Manz, and Y. Ohtsuki, “Selective preparation of enantiomers by laser pulses: quantum model simulation for H2POSH,” Chem. Phys. Lett. 306, 1–8 (1999).
[CrossRef]

Matsuoka, S.

K. Yamakawa, M. Aoyama, S. Matsuoka, H. Takuma, D. N. Fittinghoff, and C. P. J. Barty, “Ultrahigh-peak and high-average power chirped-pulse amplification of sub-20-fs pulses with Ti: sapphire amplifiers,” IEEE J. Sel. Top. Quantum Electron. 4, 385–394 (1998).
[CrossRef]

Misoguti, L.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft x-rays,” Nature 406, 164–166 (2000).
[CrossRef] [PubMed]

Momma, C.

B. N. Chichkov, C. Momma, S. Nolte, F. von Alvensleben, and A. Tünnermann, “Femtosecond, picosecond and nanosecond laser ablation of solids,” Appl. Phys. A 63, 109–115 (1996).
[CrossRef]

Mourou, G.

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

Murnane, M. M.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft x-rays,” Nature 406, 164–166 (2000).
[CrossRef] [PubMed]

Nolte, S.

B. N. Chichkov, C. Momma, S. Nolte, F. von Alvensleben, and A. Tünnermann, “Femtosecond, picosecond and nanosecond laser ablation of solids,” Appl. Phys. A 63, 109–115 (1996).
[CrossRef]

Norris, T.

Ohtsuki, Y.

Y. Fujimura, L. Gonzalez, K. Hoki, J. Manz, and Y. Ohtsuki, “Selective preparation of enantiomers by laser pulses: quantum model simulation for H2POSH,” Chem. Phys. Lett. 306, 1–8 (1999).
[CrossRef]

Oudin, S.

Reitze, D. H.

Spielman, Ch.

Strehle, M.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Swyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[CrossRef] [PubMed]

Strickland, D.

Suzuki, M.

K. Takasago, M. Takekawa, M. Suzuki, K. Komori, and F. Kannari, “Evaluation of femtosecond pulse shaping with low-loss phase-only masks,” IEEE J. Sel. Top. Quantum Electron. 4, 346–352 (1998).
[CrossRef]

Swyfried, V.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Swyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[CrossRef] [PubMed]

Takasago, K.

K. Takasago, M. Takekawa, M. Suzuki, K. Komori, and F. Kannari, “Evaluation of femtosecond pulse shaping with low-loss phase-only masks,” IEEE J. Sel. Top. Quantum Electron. 4, 346–352 (1998).
[CrossRef]

K. Takasago, T. Itoh, M. Takekawa, K. Utoh, and F. Kan-nari, “Design of frequency-domain filters for femtosecond pulse shaping,” Jpn. J. Appl. Phys., 35, 624–629 (1996).
[CrossRef]

Takekawa, M.

K. Takasago, M. Takekawa, M. Suzuki, K. Komori, and F. Kannari, “Evaluation of femtosecond pulse shaping with low-loss phase-only masks,” IEEE J. Sel. Top. Quantum Electron. 4, 346–352 (1998).
[CrossRef]

K. Takasago, T. Itoh, M. Takekawa, K. Utoh, and F. Kan-nari, “Design of frequency-domain filters for femtosecond pulse shaping,” Jpn. J. Appl. Phys., 35, 624–629 (1996).
[CrossRef]

Takeoka, M.

Takuma, H.

K. Yamakawa, M. Aoyama, S. Matsuoka, H. Takuma, D. N. Fittinghoff, and C. P. J. Barty, “Ultrahigh-peak and high-average power chirped-pulse amplification of sub-20-fs pulses with Ti: sapphire amplifiers,” IEEE J. Sel. Top. Quantum Electron. 4, 385–394 (1998).
[CrossRef]

Tournois, P.

Trebino, R.

Tull, J. X.

Tünnermann, A.

B. N. Chichkov, C. Momma, S. Nolte, F. von Alvensleben, and A. Tünnermann, “Femtosecond, picosecond and nanosecond laser ablation of solids,” Appl. Phys. A 63, 109–115 (1996).
[CrossRef]

Utoh, K.

K. Takasago, T. Itoh, M. Takekawa, K. Utoh, and F. Kan-nari, “Design of frequency-domain filters for femtosecond pulse shaping,” Jpn. J. Appl. Phys., 35, 624–629 (1996).
[CrossRef]

Vdovin, G.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft x-rays,” Nature 406, 164–166 (2000).
[CrossRef] [PubMed]

Verluise, F.

von Alvensleben, F.

B. N. Chichkov, C. Momma, S. Nolte, F. von Alvensleben, and A. Tünnermann, “Femtosecond, picosecond and nanosecond laser ablation of solids,” Appl. Phys. A 63, 109–115 (1996).
[CrossRef]

Warren, W. S.

Weiner, A. M.

Yamakawa, K.

K. Yamakawa, M. Aoyama, S. Matsuoka, H. Takuma, D. N. Fittinghoff, and C. P. J. Barty, “Ultrahigh-peak and high-average power chirped-pulse amplification of sub-20-fs pulses with Ti: sapphire amplifiers,” IEEE J. Sel. Top. Quantum Electron. 4, 385–394 (1998).
[CrossRef]

Zeek, E.

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft x-rays,” Nature 406, 164–166 (2000).
[CrossRef] [PubMed]

Appl. Phys. A (1)

B. N. Chichkov, C. Momma, S. Nolte, F. von Alvensleben, and A. Tünnermann, “Femtosecond, picosecond and nanosecond laser ablation of solids,” Appl. Phys. A 63, 109–115 (1996).
[CrossRef]

Chem. Phys. Lett. (1)

Y. Fujimura, L. Gonzalez, K. Hoki, J. Manz, and Y. Ohtsuki, “Selective preparation of enantiomers by laser pulses: quantum model simulation for H2POSH,” Chem. Phys. Lett. 306, 1–8 (1999).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. D. Kmetec, “Ultrafast laser generation of hard x-rays,” IEEE J. Quantum Electron. 28, 2382–2387 (1992).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

K. Yamakawa, M. Aoyama, S. Matsuoka, H. Takuma, D. N. Fittinghoff, and C. P. J. Barty, “Ultrahigh-peak and high-average power chirped-pulse amplification of sub-20-fs pulses with Ti: sapphire amplifiers,” IEEE J. Sel. Top. Quantum Electron. 4, 385–394 (1998).
[CrossRef]

K. Takasago, M. Takekawa, M. Suzuki, K. Komori, and F. Kannari, “Evaluation of femtosecond pulse shaping with low-loss phase-only masks,” IEEE J. Sel. Top. Quantum Electron. 4, 346–352 (1998).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (3)

Jpn. J. Appl. Phys. (1)

K. Takasago, T. Itoh, M. Takekawa, K. Utoh, and F. Kan-nari, “Design of frequency-domain filters for femtosecond pulse shaping,” Jpn. J. Appl. Phys., 35, 624–629 (1996).
[CrossRef]

Nature (1)

R. Bartels, S. Backus, E. Zeek, L. Misoguti, G. Vdovin, I. P. Christov, M. M. Murnane, and H. C. Kapteyn, “Shaped-pulse optimization of coherent emission of high-harmonic soft x-rays,” Nature 406, 164–166 (2000).
[CrossRef] [PubMed]

Opt. Commun. (2)

D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef]

P. Tournois, “Acousto-optic programmable dispersion filter for adaptive compensation of group delay time dispersion in laser systems,” Opt. Commun. 140, 245–249 (1997).
[CrossRef]

Opt. Lett. (4)

Science (1)

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Swyfried, M. Strehle, and G. Gerber, “Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses,” Science 282, 919–922 (1998).
[CrossRef] [PubMed]

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Figures (21)

Fig. 1
Fig. 1

Setup for adaptive pulse shaping: P’s Polarizers; G’s, gratings; FR, Faraday rotator; PC, Pockels cell; PG, polarization-gated FROG.

Fig. 2
Fig. 2

Algorithm of a simulated annealing method for designing a filter function of the AOPDF.

Fig. 3
Fig. 3

Spectral profiles before (dashed curves) and after (solid curves) compensation for gain narrowing and residual dispersion.

Fig. 4
Fig. 4

Temporal profiles before (dashed curve) and after (solid curve) compensation for gain narrowing and residual dispersion. Dotted curve, transform-limited pulse reduced from the spectral profile after compensation.

Fig. 5
Fig. 5

Spectral amplitude and phase profiles (solid curves) reconstructed from the FROG trace after compensation only for second-order dispersion with the pulse compressor. The reversed phase profile (dashed curve) was applied to the AOPDF to compensate for the entire dispersion in the next step (see the text).

Fig. 6
Fig. 6

(a) Temporal profile and (b) spectral profile reconstructed when a reversed phase is added to a filter function of the AOPDF.

Fig. 7
Fig. 7

Initial FROG trace.

Fig. 8
Fig. 8

FROG traces of (a) a target profile and (b) an optimized profile. The target profile is a Fourier-transform-limited pulse with a spectral width of 16 nm (FWHM).

Fig. 9
Fig. 9

Targeted (dashed curves) and optimized (solid curves) temporal profiles reconstructed from the FROG traces of Fig. 8.

Fig. 10
Fig. 10

Evolution of the cost function and system temperature during the SA optimization.

Fig. 11
Fig. 11

Acoustic signal design to shape two separate pulses. Acoustic signals of S1(t/α) and S2(t/α) that have different coefficients of the first order of the Fourier phase are superposed in the temporal domain, which is equivalent to spectral modulation of both phase and amplitude.

Fig. 12
Fig. 12

FROG traces of (a) a target profile and (b) an optimized profile. The target profile is two separate pulses with a peak intensity ratio of 1 to 1 and a pulse separation of 150 fs. Each pulse width is 42 fs.

Fig. 13
Fig. 13

Target (dashed curves) and optimized (solid curves) temporal profiles reconstructed from the FROG traces of Fig. 12.

Fig. 14
Fig. 14

Optimized (a) amplitude function and (b) phase function of the AOPDF filter during shaping of two separate pulses. The explicitly designed ideal filter functions are also shown (dashed curves).

Fig. 15
Fig. 15

FROG traces of (a) a target profile and (b) an optimized profile. The target profile is two separate pulses that have different center carrier wavelengths with a peak intensity of 1 to 1, a pulse separation of 200 fs, a pulse width of 60 fs (FWHM) for each pulse, and center wavelengths of 795 and 805 nm.

Fig. 16
Fig. 16

Target (dashed curves) and optimized (solid curves) spectral profiles reconstructed from the FROG traces of Fig. 15.

Fig. 17
Fig. 17

Target (dashed curves) and optimized (solid curves) temporal profiles reconstructed from the FROG traces of Fig. 15.

Fig. 18
Fig. 18

FROG traces of (a) the target profile and (b) the optimized profile. The target profile is a 30-fs Fourier-transform-limited pulse.

Fig. 19
Fig. 19

Target (dashed curves) and optimized (solid curves) spectral profiles reconstructed from the FROG traces of Fig. 18.

Fig. 20
Fig. 20

Target (dashed curves) and optimized (solid curves) temporal profiles reconstructed from the FROG traces of Fig. 18.

Fig. 21
Fig. 21

Optimized (a) amplitude function and (b) phase function of the AOPDF for shaping of a Fourier-transform-limited pulse that has been compensated for gain narrowing and residual dispersion.

Equations (3)

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Cost=1N×M i=0N-1j=0M-1[IFROGTarget(ωi, τj)-IFROGShaped(ωi, τj)]21/2,
Eout(t)Ein(t)S(t/α).
α=Δn(V/c),

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