Abstract

We have used a commercially available liquid-crystal spatial light modulator within a reflective optics pulse-shaping apparatus to shape ultrashort pulses with temporal resolution approaching 10 fs. Using the spatial light modulator as a phase modulator, we produce a variety of complex ultrafast waveforms, including odd pulses, high repetition rate (>23 THz) pulse trains, and asymmetric pulse trains. We also show that it is possible to compensate for large amounts of high-order phase dispersion (in excess of 60π) by appropriate cubic- and quartic-phase modulations of the pulse. Finally, we examine the limitations of shaping ultrabroad-bandwidth pulses. We find that, for specific classes of waveforms, Fourier-transform pulse-shaping techniques can be used for pulses with 5-fs durations, which exceed the current state of the art in ultrashort pulse generation. However, synthesis of general waveforms with 5-fs resolution will require compensating for nonlinear spatial dispersion of frequency in the masking plane.

© 1995 Optical Society of America

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  1. A. M. Weiner, J. P. Heritage, and E. M. Kirschner, “High-resolution femtosecond pulse shaping,” J. Opt. Soc. Am. B 5, 1563 (1988).
    [Crossref]
  2. A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445 (1988).
    [Crossref] [PubMed]
  3. A. M. Weiner, D. E. Leaird, G. P. Wiederrecht, and K. A. Nelson, “Femtosecond pulse sequences used for optical control of molecular motion,” Science 247, 1317 (1990); “Femtosecond multiple-pulse impulsive stimulated Raman scattering spectroscopy,” J. Opt. Soc. Am. B 8, 1264 (1991).
    [Crossref] [PubMed]
  4. H. Rabitz and S. Shi, “Optimal control of molecular motion: making molecules dance,” in Vibrational Spectroscopy, J. Bowman, ed. (Jai, Greenwich, Conn., 1991), Vol. 1, Part A, p. 187.
  5. W. S. Warren, H. Rabitz, and Mohammed Dahleh, “Coherent control of quantum mechanics: the dream is alive,” Science 259, 1581 (1993).
    [Crossref] [PubMed]
  6. Y. Yan, R. E. Gillilan, R. M. Whitnell, K. R. Wilson, and S. Mukamel, “Optical control of molecular dynamics: Liouville-space theory,” J. Chem. Phys. 97, 2320 (1993).
    [Crossref]
  7. B. Kohler, J. L. Krause, R. M. Whitnell, K. R. Wilson, V. V. Yakovlev, and Y. Yan, “Quantum control of vibrational dynamics with tailored light pulses,” in Ultrafast Phenomena IX, G. A. Mourou, A. H. Zewail, P. F. Barbara, and W. H. Knox, eds. (Springer-Verlag, Berlin, 1994), p. 44.
    [Crossref]
  8. P. C. M. Planken, I. Brener, M. C. Nuss, M. S. C. Lou, and S. L. Chuang, “Coherent control of terahertz charge oscillations in a coupled quantum well using phase-locked optical pulses,” Phys. Rev. B 48, 4903 (1993).
    [Crossref]
  9. A. M. Weiner, “Enhancement of coherent charge oscillations in coupled quantum wells by femtosecond pulse shaping,” J. Opt. Soc. Am. B 11, 2480 (1994).
    [Crossref]
  10. P. Hyldgaard, G. D. Sanders, and D. H. Reitze, “Coherent optical control of electron dynamics in asymmetric double quantum wells in the nonimpulsive regime,” presented at the Annual Meeting of the Optical Society of America, Dallas, Tx., October 1994.
  11. D. Umstadter, E. Esarey, and J. Kim, “Nonlinear plasma waves resonantly driven by optimized laser pulse trains,” Phys. Rev. Lett. 72, 1224 (1994).
    [Crossref] [PubMed]
  12. A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, “Programmable femtosecond pulse shaping by use of a multielement liquid-crystal phase modulator,” Opt. Lett. 15, 326 (1990); “Programmable shaping of femtosecond optical pulses by use of 128-element liquid crystal phase modulator,” J. Quantum Electron. 28, 908 (1992).
    [Crossref] [PubMed]
  13. M. A. Wefers and K. A. Nelson, “Programmable phase and amplitude femtosecond pulse shaping,” Opt. Lett. 18, 2032 (1993).
    [Crossref] [PubMed]
  14. C. W. Hillegas, J. X. Tull, D. Goswami, D. Strickland, and W. Warren, “Femtosecond laser pulse shaping by use of microsecond radio-frequency pulses,” Opt. Lett. 19, 737 (1994).
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  15. A. M. Weiner, D. E. Leaird, D. H. Reitze, and E. G. Paek, “Spectral holography of shaped femtosecond pulses,” Opt. Lett. 17, 224 (1992); “Femtosecond spectral holography,” IEEE J. Quantum Electron. 28, 2251 (1992).
    [Crossref] [PubMed]
  16. A. M. Weiner and D. E. Leaird, “Femtosecond signal processing by second-order spectral holography,” Opt. Lett. 19, 123 (1994).
    [Crossref] [PubMed]
  17. M. C. Nuss, M. Li, T. H. Chiu, A. M. Weiner, and A. Partovi, “Time-to-space mapping of femtosecond pulses,” Opt. Lett. 19, 664 (1994).
    [Crossref] [PubMed]
  18. D. H. Reitze, A. M. Weiner, and D. E. Leaird, “Shaping of wide bandwidth, 20 fsec optical pulses,” Appl. Phys. Lett. 61, 1260 (1992).
    [Crossref]
  19. D. H. Reitze, A. M. Weiner, and D. E. Leaird, “Spatial soliton pulse compression,” Opt. Lett. 16, 1409 (1991).
    [Crossref] [PubMed]
  20. J. Zhou, G. Taft, C. Shi, H. C. Kapteyn, and M. C. Murnane, “Sub-10 fs pulse generation in Ti:sapphire: capabilities and ultimate limits,” in Ultrafast Phenomena IX, G. A. Mourou, A. H. Zewail, P. F. Barbara, and W. H. Knox, eds. (Springer-Verlag, Berlin, 1994), p. 39.
    [Crossref]
  21. I. P. Christov, M. M. Murnane, H. C. Kapteyn, J. P. Zhou, and C. P. Huang, “Fourth-order dispersion-limited solitary pulses,” Opt. Lett. 19, 1465 (1994).
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  22. J. D. Kmetec, J. J. Macklin, and J. F. Young, “0.5-TW, 125-fs Ti:sapphire laser,” Opt. Lett. 16, 1001 (1991).
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  23. A. Sullivan, H. Hamster, H. C. Kapteyn, S. Gordon, W. White, H. Nathel, R. J. Blair, and R. W. Falcone, “Multiterawatt, 100-fs laser,” Opt. Lett. 16, 1406 (1991).
    [Crossref] [PubMed]
  24. C. P. Barty, C. L. Gordon, and B. E. Lemoff, “Multiterawatt 30-fs ti-sapphire laser system,” Opt. Lett. 18, 1442 (1994).
    [Crossref]
  25. W. E. White, F. G. Patterson, R. L. Combs, D. F. Price, and R. L. Shepherd, “Compensation of higher-order frequency-dependent phase terms in chirped-pulse amplification systems,” Opt. Lett. 18, 1343 (1993).
    [Crossref] [PubMed]
  26. B. E. Lemoff and C. P. J. Barty, “Quintic-phase-limited, spatially uniform expansion and recompression of ultrashort optical pulses,” Opt. Lett. 18, 1651 (1993).
    [Crossref] [PubMed]
  27. M. T. Asaki, C. P. Huang, D. Garvey, J. P. Zhou, H. C. Kapteyn, and M. M. Murnane, “Generation of 11-fs pulses from a self-mode-locked Ti-sapphire laser,” Opt. Lett. 18, 977 (1993).
    [Crossref] [PubMed]
  28. See, for example, E. Hecht and A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1976), p. 323.
  29. J. E. Rothenberg, D. Grischkowsky, and A. C. Balant, “Observation of the formation of the 0π pulse,” Phys. Rev. Lett. 53, 552 (1984).
    [Crossref]
  30. A. M. Weiner and D. E. Leaird, “Generation of terahertz-rate trains of femtosecond pulses by phase-only filtering,” Opt. Lett. 15, 51 (1990).
    [Crossref] [PubMed]
  31. See, for example, W. H. Press, S. A. Teukolsky, W. T. Vettering, and B. P. Flannery, Numerical Recipes (Cambridge U. Press, Cambridge, 1992), Chap. 10.
  32. 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. B 10, 1112 (1993).
    [Crossref]
  33. E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. 5, 454 (1969).
    [Crossref]
  34. R. L. Fork, O. E. Martinez, and J. P. Gordon, “Negative dispersion using pairs of prisms,” Opt. Lett. 9, 150 (1984).
    [Crossref] [PubMed]
  35. R. L. Fork, C. H. Brito-Cruz, P. C. Becker, and C. V. Shank, “Compression of optical pulses to six femtoseconds using cubic phase compensation,” Opt. Lett. 12, 483 (1987).
    [Crossref] [PubMed]
  36. J. P. Zhou, C. P. Huang, C. Y. Shi, M. M. Murnane, and H. C. Kapteyn, “Generation of 21-fs millijoule-energy pulses by use of Ti-sapphire,” Opt. Lett. 19, 126 (1994).
    [Crossref] [PubMed]
  37. See, for example, G. P. Agrawal, “Nonlinear Fiber Optics (Academic, Boston, 1989), Chap. 1.
  38. M. Stern, J. P. Heritage, and E. W. Chase, “Grating compensation of 3rd-order fiber dispersion,” IEEE J. Quantum Electron. 28, 2742 (1992).
    [Crossref]
  39. R. W. Thurston, J. P. Heritage, A. M. Weiner, and W. J. Tomlinson, “Analysis of picosecond pulse shape synthesis by spectral masking in a grating pulse compressor,” IEEE J. Quantum Electron. 22, 682 (1986).
    [Crossref]

1994 (8)

1993 (8)

W. E. White, F. G. Patterson, R. L. Combs, D. F. Price, and R. L. Shepherd, “Compensation of higher-order frequency-dependent phase terms in chirped-pulse amplification systems,” Opt. Lett. 18, 1343 (1993).
[Crossref] [PubMed]

B. E. Lemoff and C. P. J. Barty, “Quintic-phase-limited, spatially uniform expansion and recompression of ultrashort optical pulses,” Opt. Lett. 18, 1651 (1993).
[Crossref] [PubMed]

M. T. Asaki, C. P. Huang, D. Garvey, J. P. Zhou, H. C. Kapteyn, and M. M. Murnane, “Generation of 11-fs pulses from a self-mode-locked Ti-sapphire laser,” Opt. Lett. 18, 977 (1993).
[Crossref] [PubMed]

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. B 10, 1112 (1993).
[Crossref]

M. A. Wefers and K. A. Nelson, “Programmable phase and amplitude femtosecond pulse shaping,” Opt. Lett. 18, 2032 (1993).
[Crossref] [PubMed]

W. S. Warren, H. Rabitz, and Mohammed Dahleh, “Coherent control of quantum mechanics: the dream is alive,” Science 259, 1581 (1993).
[Crossref] [PubMed]

Y. Yan, R. E. Gillilan, R. M. Whitnell, K. R. Wilson, and S. Mukamel, “Optical control of molecular dynamics: Liouville-space theory,” J. Chem. Phys. 97, 2320 (1993).
[Crossref]

P. C. M. Planken, I. Brener, M. C. Nuss, M. S. C. Lou, and S. L. Chuang, “Coherent control of terahertz charge oscillations in a coupled quantum well using phase-locked optical pulses,” Phys. Rev. B 48, 4903 (1993).
[Crossref]

1992 (3)

A. M. Weiner, D. E. Leaird, D. H. Reitze, and E. G. Paek, “Spectral holography of shaped femtosecond pulses,” Opt. Lett. 17, 224 (1992); “Femtosecond spectral holography,” IEEE J. Quantum Electron. 28, 2251 (1992).
[Crossref] [PubMed]

D. H. Reitze, A. M. Weiner, and D. E. Leaird, “Shaping of wide bandwidth, 20 fsec optical pulses,” Appl. Phys. Lett. 61, 1260 (1992).
[Crossref]

M. Stern, J. P. Heritage, and E. W. Chase, “Grating compensation of 3rd-order fiber dispersion,” IEEE J. Quantum Electron. 28, 2742 (1992).
[Crossref]

1991 (3)

1990 (3)

1988 (2)

A. M. Weiner, J. P. Heritage, and E. M. Kirschner, “High-resolution femtosecond pulse shaping,” J. Opt. Soc. Am. B 5, 1563 (1988).
[Crossref]

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445 (1988).
[Crossref] [PubMed]

1987 (1)

1986 (1)

R. W. Thurston, J. P. Heritage, A. M. Weiner, and W. J. Tomlinson, “Analysis of picosecond pulse shape synthesis by spectral masking in a grating pulse compressor,” IEEE J. Quantum Electron. 22, 682 (1986).
[Crossref]

1984 (2)

R. L. Fork, O. E. Martinez, and J. P. Gordon, “Negative dispersion using pairs of prisms,” Opt. Lett. 9, 150 (1984).
[Crossref] [PubMed]

J. E. Rothenberg, D. Grischkowsky, and A. C. Balant, “Observation of the formation of the 0π pulse,” Phys. Rev. Lett. 53, 552 (1984).
[Crossref]

1969 (1)

E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. 5, 454 (1969).
[Crossref]

Agrawal, G. P.

See, for example, G. P. Agrawal, “Nonlinear Fiber Optics (Academic, Boston, 1989), Chap. 1.

Asaki, M. T.

Balant, A. C.

J. E. Rothenberg, D. Grischkowsky, and A. C. Balant, “Observation of the formation of the 0π pulse,” Phys. Rev. Lett. 53, 552 (1984).
[Crossref]

Barty, C. P.

C. P. Barty, C. L. Gordon, and B. E. Lemoff, “Multiterawatt 30-fs ti-sapphire laser system,” Opt. Lett. 18, 1442 (1994).
[Crossref]

Barty, C. P. J.

Becker, P. C.

Blair, R. J.

Brener, I.

P. C. M. Planken, I. Brener, M. C. Nuss, M. S. C. Lou, and S. L. Chuang, “Coherent control of terahertz charge oscillations in a coupled quantum well using phase-locked optical pulses,” Phys. Rev. B 48, 4903 (1993).
[Crossref]

Brito-Cruz, C. H.

Chase, E. W.

M. Stern, J. P. Heritage, and E. W. Chase, “Grating compensation of 3rd-order fiber dispersion,” IEEE J. Quantum Electron. 28, 2742 (1992).
[Crossref]

Chiu, T. H.

Christov, I. P.

Chuang, S. L.

P. C. M. Planken, I. Brener, M. C. Nuss, M. S. C. Lou, and S. L. Chuang, “Coherent control of terahertz charge oscillations in a coupled quantum well using phase-locked optical pulses,” Phys. Rev. B 48, 4903 (1993).
[Crossref]

Combs, R. L.

Dahleh, Mohammed

W. S. Warren, H. Rabitz, and Mohammed Dahleh, “Coherent control of quantum mechanics: the dream is alive,” Science 259, 1581 (1993).
[Crossref] [PubMed]

Esarey, E.

D. Umstadter, E. Esarey, and J. Kim, “Nonlinear plasma waves resonantly driven by optimized laser pulse trains,” Phys. Rev. Lett. 72, 1224 (1994).
[Crossref] [PubMed]

Falcone, R. W.

Flannery, B. P.

See, for example, W. H. Press, S. A. Teukolsky, W. T. Vettering, and B. P. Flannery, Numerical Recipes (Cambridge U. Press, Cambridge, 1992), Chap. 10.

Fork, R. L.

Garvey, D.

Gillilan, R. E.

Y. Yan, R. E. Gillilan, R. M. Whitnell, K. R. Wilson, and S. Mukamel, “Optical control of molecular dynamics: Liouville-space theory,” J. Chem. Phys. 97, 2320 (1993).
[Crossref]

Gordon, C. L.

C. P. Barty, C. L. Gordon, and B. E. Lemoff, “Multiterawatt 30-fs ti-sapphire laser system,” Opt. Lett. 18, 1442 (1994).
[Crossref]

Gordon, J. P.

Gordon, S.

Goswami, D.

Grischkowsky, D.

J. E. Rothenberg, D. Grischkowsky, and A. C. Balant, “Observation of the formation of the 0π pulse,” Phys. Rev. Lett. 53, 552 (1984).
[Crossref]

Hamster, H.

Hawkins, R. J.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445 (1988).
[Crossref] [PubMed]

Hecht, E.

See, for example, E. Hecht and A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1976), p. 323.

Heritage, J. P.

M. Stern, J. P. Heritage, and E. W. Chase, “Grating compensation of 3rd-order fiber dispersion,” IEEE J. Quantum Electron. 28, 2742 (1992).
[Crossref]

A. M. Weiner, J. P. Heritage, and E. M. Kirschner, “High-resolution femtosecond pulse shaping,” J. Opt. Soc. Am. B 5, 1563 (1988).
[Crossref]

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445 (1988).
[Crossref] [PubMed]

R. W. Thurston, J. P. Heritage, A. M. Weiner, and W. J. Tomlinson, “Analysis of picosecond pulse shape synthesis by spectral masking in a grating pulse compressor,” IEEE J. Quantum Electron. 22, 682 (1986).
[Crossref]

Hillegas, C. W.

Huang, C. P.

Hyldgaard, P.

P. Hyldgaard, G. D. Sanders, and D. H. Reitze, “Coherent optical control of electron dynamics in asymmetric double quantum wells in the nonimpulsive regime,” presented at the Annual Meeting of the Optical Society of America, Dallas, Tx., October 1994.

Kapteyn, H. C.

Kim, J.

D. Umstadter, E. Esarey, and J. Kim, “Nonlinear plasma waves resonantly driven by optimized laser pulse trains,” Phys. Rev. Lett. 72, 1224 (1994).
[Crossref] [PubMed]

Kirschner, E. M.

A. M. Weiner, J. P. Heritage, and E. M. Kirschner, “High-resolution femtosecond pulse shaping,” J. Opt. Soc. Am. B 5, 1563 (1988).
[Crossref]

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445 (1988).
[Crossref] [PubMed]

Kmetec, J. D.

Kohler, B.

B. Kohler, J. L. Krause, R. M. Whitnell, K. R. Wilson, V. V. Yakovlev, and Y. Yan, “Quantum control of vibrational dynamics with tailored light pulses,” in Ultrafast Phenomena IX, G. A. Mourou, A. H. Zewail, P. F. Barbara, and W. H. Knox, eds. (Springer-Verlag, Berlin, 1994), p. 44.
[Crossref]

Krause, J. L.

B. Kohler, J. L. Krause, R. M. Whitnell, K. R. Wilson, V. V. Yakovlev, and Y. Yan, “Quantum control of vibrational dynamics with tailored light pulses,” in Ultrafast Phenomena IX, G. A. Mourou, A. H. Zewail, P. F. Barbara, and W. H. Knox, eds. (Springer-Verlag, Berlin, 1994), p. 44.
[Crossref]

Leaird, D. E.

A. M. Weiner and D. E. Leaird, “Femtosecond signal processing by second-order spectral holography,” Opt. Lett. 19, 123 (1994).
[Crossref] [PubMed]

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. B 10, 1112 (1993).
[Crossref]

A. M. Weiner, D. E. Leaird, D. H. Reitze, and E. G. Paek, “Spectral holography of shaped femtosecond pulses,” Opt. Lett. 17, 224 (1992); “Femtosecond spectral holography,” IEEE J. Quantum Electron. 28, 2251 (1992).
[Crossref] [PubMed]

D. H. Reitze, A. M. Weiner, and D. E. Leaird, “Shaping of wide bandwidth, 20 fsec optical pulses,” Appl. Phys. Lett. 61, 1260 (1992).
[Crossref]

D. H. Reitze, A. M. Weiner, and D. E. Leaird, “Spatial soliton pulse compression,” Opt. Lett. 16, 1409 (1991).
[Crossref] [PubMed]

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, “Programmable femtosecond pulse shaping by use of a multielement liquid-crystal phase modulator,” Opt. Lett. 15, 326 (1990); “Programmable shaping of femtosecond optical pulses by use of 128-element liquid crystal phase modulator,” J. Quantum Electron. 28, 908 (1992).
[Crossref] [PubMed]

A. M. Weiner, D. E. Leaird, G. P. Wiederrecht, and K. A. Nelson, “Femtosecond pulse sequences used for optical control of molecular motion,” Science 247, 1317 (1990); “Femtosecond multiple-pulse impulsive stimulated Raman scattering spectroscopy,” J. Opt. Soc. Am. B 8, 1264 (1991).
[Crossref] [PubMed]

A. M. Weiner and D. E. Leaird, “Generation of terahertz-rate trains of femtosecond pulses by phase-only filtering,” Opt. Lett. 15, 51 (1990).
[Crossref] [PubMed]

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445 (1988).
[Crossref] [PubMed]

Lemoff, B. E.

Li, M.

Lou, M. S. C.

P. C. M. Planken, I. Brener, M. C. Nuss, M. S. C. Lou, and S. L. Chuang, “Coherent control of terahertz charge oscillations in a coupled quantum well using phase-locked optical pulses,” Phys. Rev. B 48, 4903 (1993).
[Crossref]

Macklin, J. J.

Martinez, O. E.

Mukamel, S.

Y. Yan, R. E. Gillilan, R. M. Whitnell, K. R. Wilson, and S. Mukamel, “Optical control of molecular dynamics: Liouville-space theory,” J. Chem. Phys. 97, 2320 (1993).
[Crossref]

Murnane, M. C.

J. Zhou, G. Taft, C. Shi, H. C. Kapteyn, and M. C. Murnane, “Sub-10 fs pulse generation in Ti:sapphire: capabilities and ultimate limits,” in Ultrafast Phenomena IX, G. A. Mourou, A. H. Zewail, P. F. Barbara, and W. H. Knox, eds. (Springer-Verlag, Berlin, 1994), p. 39.
[Crossref]

Murnane, M. M.

Nathel, H.

Nelson, K. A.

M. A. Wefers and K. A. Nelson, “Programmable phase and amplitude femtosecond pulse shaping,” Opt. Lett. 18, 2032 (1993).
[Crossref] [PubMed]

A. M. Weiner, D. E. Leaird, G. P. Wiederrecht, and K. A. Nelson, “Femtosecond pulse sequences used for optical control of molecular motion,” Science 247, 1317 (1990); “Femtosecond multiple-pulse impulsive stimulated Raman scattering spectroscopy,” J. Opt. Soc. Am. B 8, 1264 (1991).
[Crossref] [PubMed]

Nuss, M. C.

M. C. Nuss, M. Li, T. H. Chiu, A. M. Weiner, and A. Partovi, “Time-to-space mapping of femtosecond pulses,” Opt. Lett. 19, 664 (1994).
[Crossref] [PubMed]

P. C. M. Planken, I. Brener, M. C. Nuss, M. S. C. Lou, and S. L. Chuang, “Coherent control of terahertz charge oscillations in a coupled quantum well using phase-locked optical pulses,” Phys. Rev. B 48, 4903 (1993).
[Crossref]

Oudin, S.

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. B 10, 1112 (1993).
[Crossref]

Paek, E. G.

Partovi, A.

Patel, J. S.

Patterson, F. G.

Planken, P. C. M.

P. C. M. Planken, I. Brener, M. C. Nuss, M. S. C. Lou, and S. L. Chuang, “Coherent control of terahertz charge oscillations in a coupled quantum well using phase-locked optical pulses,” Phys. Rev. B 48, 4903 (1993).
[Crossref]

Press, W. H.

See, for example, W. H. Press, S. A. Teukolsky, W. T. Vettering, and B. P. Flannery, Numerical Recipes (Cambridge U. Press, Cambridge, 1992), Chap. 10.

Price, D. F.

Rabitz, H.

W. S. Warren, H. Rabitz, and Mohammed Dahleh, “Coherent control of quantum mechanics: the dream is alive,” Science 259, 1581 (1993).
[Crossref] [PubMed]

H. Rabitz and S. Shi, “Optimal control of molecular motion: making molecules dance,” in Vibrational Spectroscopy, J. Bowman, ed. (Jai, Greenwich, Conn., 1991), Vol. 1, Part A, p. 187.

Reitze, D. H.

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. B 10, 1112 (1993).
[Crossref]

D. H. Reitze, A. M. Weiner, and D. E. Leaird, “Shaping of wide bandwidth, 20 fsec optical pulses,” Appl. Phys. Lett. 61, 1260 (1992).
[Crossref]

A. M. Weiner, D. E. Leaird, D. H. Reitze, and E. G. Paek, “Spectral holography of shaped femtosecond pulses,” Opt. Lett. 17, 224 (1992); “Femtosecond spectral holography,” IEEE J. Quantum Electron. 28, 2251 (1992).
[Crossref] [PubMed]

D. H. Reitze, A. M. Weiner, and D. E. Leaird, “Spatial soliton pulse compression,” Opt. Lett. 16, 1409 (1991).
[Crossref] [PubMed]

P. Hyldgaard, G. D. Sanders, and D. H. Reitze, “Coherent optical control of electron dynamics in asymmetric double quantum wells in the nonimpulsive regime,” presented at the Annual Meeting of the Optical Society of America, Dallas, Tx., October 1994.

Rothenberg, J. E.

J. E. Rothenberg, D. Grischkowsky, and A. C. Balant, “Observation of the formation of the 0π pulse,” Phys. Rev. Lett. 53, 552 (1984).
[Crossref]

Sanders, G. D.

P. Hyldgaard, G. D. Sanders, and D. H. Reitze, “Coherent optical control of electron dynamics in asymmetric double quantum wells in the nonimpulsive regime,” presented at the Annual Meeting of the Optical Society of America, Dallas, Tx., October 1994.

Shank, C. V.

Shepherd, R. L.

Shi, C.

J. Zhou, G. Taft, C. Shi, H. C. Kapteyn, and M. C. Murnane, “Sub-10 fs pulse generation in Ti:sapphire: capabilities and ultimate limits,” in Ultrafast Phenomena IX, G. A. Mourou, A. H. Zewail, P. F. Barbara, and W. H. Knox, eds. (Springer-Verlag, Berlin, 1994), p. 39.
[Crossref]

Shi, C. Y.

Shi, S.

H. Rabitz and S. Shi, “Optimal control of molecular motion: making molecules dance,” in Vibrational Spectroscopy, J. Bowman, ed. (Jai, Greenwich, Conn., 1991), Vol. 1, Part A, p. 187.

Stern, M.

M. Stern, J. P. Heritage, and E. W. Chase, “Grating compensation of 3rd-order fiber dispersion,” IEEE J. Quantum Electron. 28, 2742 (1992).
[Crossref]

Strickland, D.

Sullivan, A.

Taft, G.

J. Zhou, G. Taft, C. Shi, H. C. Kapteyn, and M. C. Murnane, “Sub-10 fs pulse generation in Ti:sapphire: capabilities and ultimate limits,” in Ultrafast Phenomena IX, G. A. Mourou, A. H. Zewail, P. F. Barbara, and W. H. Knox, eds. (Springer-Verlag, Berlin, 1994), p. 39.
[Crossref]

Teukolsky, S. A.

See, for example, W. H. Press, S. A. Teukolsky, W. T. Vettering, and B. P. Flannery, Numerical Recipes (Cambridge U. Press, Cambridge, 1992), Chap. 10.

Thurston, R. N.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445 (1988).
[Crossref] [PubMed]

Thurston, R. W.

R. W. Thurston, J. P. Heritage, A. M. Weiner, and W. J. Tomlinson, “Analysis of picosecond pulse shape synthesis by spectral masking in a grating pulse compressor,” IEEE J. Quantum Electron. 22, 682 (1986).
[Crossref]

Tomlinson, W. J.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445 (1988).
[Crossref] [PubMed]

R. W. Thurston, J. P. Heritage, A. M. Weiner, and W. J. Tomlinson, “Analysis of picosecond pulse shape synthesis by spectral masking in a grating pulse compressor,” IEEE J. Quantum Electron. 22, 682 (1986).
[Crossref]

Treacy, E. B.

E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. 5, 454 (1969).
[Crossref]

Tull, J. X.

Umstadter, D.

D. Umstadter, E. Esarey, and J. Kim, “Nonlinear plasma waves resonantly driven by optimized laser pulse trains,” Phys. Rev. Lett. 72, 1224 (1994).
[Crossref] [PubMed]

Vettering, W. T.

See, for example, W. H. Press, S. A. Teukolsky, W. T. Vettering, and B. P. Flannery, Numerical Recipes (Cambridge U. Press, Cambridge, 1992), Chap. 10.

Warren, W.

Warren, W. S.

W. S. Warren, H. Rabitz, and Mohammed Dahleh, “Coherent control of quantum mechanics: the dream is alive,” Science 259, 1581 (1993).
[Crossref] [PubMed]

Wefers, M. A.

Weiner, A. M.

A. M. Weiner and D. E. Leaird, “Femtosecond signal processing by second-order spectral holography,” Opt. Lett. 19, 123 (1994).
[Crossref] [PubMed]

M. C. Nuss, M. Li, T. H. Chiu, A. M. Weiner, and A. Partovi, “Time-to-space mapping of femtosecond pulses,” Opt. Lett. 19, 664 (1994).
[Crossref] [PubMed]

A. M. Weiner, “Enhancement of coherent charge oscillations in coupled quantum wells by femtosecond pulse shaping,” J. Opt. Soc. Am. B 11, 2480 (1994).
[Crossref]

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. B 10, 1112 (1993).
[Crossref]

D. H. Reitze, A. M. Weiner, and D. E. Leaird, “Shaping of wide bandwidth, 20 fsec optical pulses,” Appl. Phys. Lett. 61, 1260 (1992).
[Crossref]

A. M. Weiner, D. E. Leaird, D. H. Reitze, and E. G. Paek, “Spectral holography of shaped femtosecond pulses,” Opt. Lett. 17, 224 (1992); “Femtosecond spectral holography,” IEEE J. Quantum Electron. 28, 2251 (1992).
[Crossref] [PubMed]

D. H. Reitze, A. M. Weiner, and D. E. Leaird, “Spatial soliton pulse compression,” Opt. Lett. 16, 1409 (1991).
[Crossref] [PubMed]

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, “Programmable femtosecond pulse shaping by use of a multielement liquid-crystal phase modulator,” Opt. Lett. 15, 326 (1990); “Programmable shaping of femtosecond optical pulses by use of 128-element liquid crystal phase modulator,” J. Quantum Electron. 28, 908 (1992).
[Crossref] [PubMed]

A. M. Weiner, D. E. Leaird, G. P. Wiederrecht, and K. A. Nelson, “Femtosecond pulse sequences used for optical control of molecular motion,” Science 247, 1317 (1990); “Femtosecond multiple-pulse impulsive stimulated Raman scattering spectroscopy,” J. Opt. Soc. Am. B 8, 1264 (1991).
[Crossref] [PubMed]

A. M. Weiner and D. E. Leaird, “Generation of terahertz-rate trains of femtosecond pulses by phase-only filtering,” Opt. Lett. 15, 51 (1990).
[Crossref] [PubMed]

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445 (1988).
[Crossref] [PubMed]

A. M. Weiner, J. P. Heritage, and E. M. Kirschner, “High-resolution femtosecond pulse shaping,” J. Opt. Soc. Am. B 5, 1563 (1988).
[Crossref]

R. W. Thurston, J. P. Heritage, A. M. Weiner, and W. J. Tomlinson, “Analysis of picosecond pulse shape synthesis by spectral masking in a grating pulse compressor,” IEEE J. Quantum Electron. 22, 682 (1986).
[Crossref]

White, W.

White, W. E.

Whitnell, R. M.

Y. Yan, R. E. Gillilan, R. M. Whitnell, K. R. Wilson, and S. Mukamel, “Optical control of molecular dynamics: Liouville-space theory,” J. Chem. Phys. 97, 2320 (1993).
[Crossref]

B. Kohler, J. L. Krause, R. M. Whitnell, K. R. Wilson, V. V. Yakovlev, and Y. Yan, “Quantum control of vibrational dynamics with tailored light pulses,” in Ultrafast Phenomena IX, G. A. Mourou, A. H. Zewail, P. F. Barbara, and W. H. Knox, eds. (Springer-Verlag, Berlin, 1994), p. 44.
[Crossref]

Wiederrecht, G. P.

A. M. Weiner, D. E. Leaird, G. P. Wiederrecht, and K. A. Nelson, “Femtosecond pulse sequences used for optical control of molecular motion,” Science 247, 1317 (1990); “Femtosecond multiple-pulse impulsive stimulated Raman scattering spectroscopy,” J. Opt. Soc. Am. B 8, 1264 (1991).
[Crossref] [PubMed]

Wilson, K. R.

Y. Yan, R. E. Gillilan, R. M. Whitnell, K. R. Wilson, and S. Mukamel, “Optical control of molecular dynamics: Liouville-space theory,” J. Chem. Phys. 97, 2320 (1993).
[Crossref]

B. Kohler, J. L. Krause, R. M. Whitnell, K. R. Wilson, V. V. Yakovlev, and Y. Yan, “Quantum control of vibrational dynamics with tailored light pulses,” in Ultrafast Phenomena IX, G. A. Mourou, A. H. Zewail, P. F. Barbara, and W. H. Knox, eds. (Springer-Verlag, Berlin, 1994), p. 44.
[Crossref]

Wullert, J. R.

Yakovlev, V. V.

B. Kohler, J. L. Krause, R. M. Whitnell, K. R. Wilson, V. V. Yakovlev, and Y. Yan, “Quantum control of vibrational dynamics with tailored light pulses,” in Ultrafast Phenomena IX, G. A. Mourou, A. H. Zewail, P. F. Barbara, and W. H. Knox, eds. (Springer-Verlag, Berlin, 1994), p. 44.
[Crossref]

Yan, Y.

Y. Yan, R. E. Gillilan, R. M. Whitnell, K. R. Wilson, and S. Mukamel, “Optical control of molecular dynamics: Liouville-space theory,” J. Chem. Phys. 97, 2320 (1993).
[Crossref]

B. Kohler, J. L. Krause, R. M. Whitnell, K. R. Wilson, V. V. Yakovlev, and Y. Yan, “Quantum control of vibrational dynamics with tailored light pulses,” in Ultrafast Phenomena IX, G. A. Mourou, A. H. Zewail, P. F. Barbara, and W. H. Knox, eds. (Springer-Verlag, Berlin, 1994), p. 44.
[Crossref]

Young, J. F.

Zajac, A.

See, for example, E. Hecht and A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1976), p. 323.

Zhou, J.

J. Zhou, G. Taft, C. Shi, H. C. Kapteyn, and M. C. Murnane, “Sub-10 fs pulse generation in Ti:sapphire: capabilities and ultimate limits,” in Ultrafast Phenomena IX, G. A. Mourou, A. H. Zewail, P. F. Barbara, and W. H. Knox, eds. (Springer-Verlag, Berlin, 1994), p. 39.
[Crossref]

Zhou, J. P.

Appl. Phys. Lett. (1)

D. H. Reitze, A. M. Weiner, and D. E. Leaird, “Shaping of wide bandwidth, 20 fsec optical pulses,” Appl. Phys. Lett. 61, 1260 (1992).
[Crossref]

IEEE J. Quantum Electron. (3)

E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. 5, 454 (1969).
[Crossref]

M. Stern, J. P. Heritage, and E. W. Chase, “Grating compensation of 3rd-order fiber dispersion,” IEEE J. Quantum Electron. 28, 2742 (1992).
[Crossref]

R. W. Thurston, J. P. Heritage, A. M. Weiner, and W. J. Tomlinson, “Analysis of picosecond pulse shape synthesis by spectral masking in a grating pulse compressor,” IEEE J. Quantum Electron. 22, 682 (1986).
[Crossref]

J. Chem. Phys. (1)

Y. Yan, R. E. Gillilan, R. M. Whitnell, K. R. Wilson, and S. Mukamel, “Optical control of molecular dynamics: Liouville-space theory,” J. Chem. Phys. 97, 2320 (1993).
[Crossref]

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

Opt. Lett. (18)

D. H. Reitze, A. M. Weiner, and D. E. Leaird, “Spatial soliton pulse compression,” Opt. Lett. 16, 1409 (1991).
[Crossref] [PubMed]

A. M. Weiner, D. E. Leaird, J. S. Patel, and J. R. Wullert, “Programmable femtosecond pulse shaping by use of a multielement liquid-crystal phase modulator,” Opt. Lett. 15, 326 (1990); “Programmable shaping of femtosecond optical pulses by use of 128-element liquid crystal phase modulator,” J. Quantum Electron. 28, 908 (1992).
[Crossref] [PubMed]

M. A. Wefers and K. A. Nelson, “Programmable phase and amplitude femtosecond pulse shaping,” Opt. Lett. 18, 2032 (1993).
[Crossref] [PubMed]

C. W. Hillegas, J. X. Tull, D. Goswami, D. Strickland, and W. Warren, “Femtosecond laser pulse shaping by use of microsecond radio-frequency pulses,” Opt. Lett. 19, 737 (1994).
[Crossref] [PubMed]

A. M. Weiner, D. E. Leaird, D. H. Reitze, and E. G. Paek, “Spectral holography of shaped femtosecond pulses,” Opt. Lett. 17, 224 (1992); “Femtosecond spectral holography,” IEEE J. Quantum Electron. 28, 2251 (1992).
[Crossref] [PubMed]

A. M. Weiner and D. E. Leaird, “Femtosecond signal processing by second-order spectral holography,” Opt. Lett. 19, 123 (1994).
[Crossref] [PubMed]

M. C. Nuss, M. Li, T. H. Chiu, A. M. Weiner, and A. Partovi, “Time-to-space mapping of femtosecond pulses,” Opt. Lett. 19, 664 (1994).
[Crossref] [PubMed]

R. L. Fork, O. E. Martinez, and J. P. Gordon, “Negative dispersion using pairs of prisms,” Opt. Lett. 9, 150 (1984).
[Crossref] [PubMed]

R. L. Fork, C. H. Brito-Cruz, P. C. Becker, and C. V. Shank, “Compression of optical pulses to six femtoseconds using cubic phase compensation,” Opt. Lett. 12, 483 (1987).
[Crossref] [PubMed]

J. P. Zhou, C. P. Huang, C. Y. Shi, M. M. Murnane, and H. C. Kapteyn, “Generation of 21-fs millijoule-energy pulses by use of Ti-sapphire,” Opt. Lett. 19, 126 (1994).
[Crossref] [PubMed]

A. M. Weiner and D. E. Leaird, “Generation of terahertz-rate trains of femtosecond pulses by phase-only filtering,” Opt. Lett. 15, 51 (1990).
[Crossref] [PubMed]

I. P. Christov, M. M. Murnane, H. C. Kapteyn, J. P. Zhou, and C. P. Huang, “Fourth-order dispersion-limited solitary pulses,” Opt. Lett. 19, 1465 (1994).
[Crossref] [PubMed]

J. D. Kmetec, J. J. Macklin, and J. F. Young, “0.5-TW, 125-fs Ti:sapphire laser,” Opt. Lett. 16, 1001 (1991).
[Crossref] [PubMed]

A. Sullivan, H. Hamster, H. C. Kapteyn, S. Gordon, W. White, H. Nathel, R. J. Blair, and R. W. Falcone, “Multiterawatt, 100-fs laser,” Opt. Lett. 16, 1406 (1991).
[Crossref] [PubMed]

C. P. Barty, C. L. Gordon, and B. E. Lemoff, “Multiterawatt 30-fs ti-sapphire laser system,” Opt. Lett. 18, 1442 (1994).
[Crossref]

W. E. White, F. G. Patterson, R. L. Combs, D. F. Price, and R. L. Shepherd, “Compensation of higher-order frequency-dependent phase terms in chirped-pulse amplification systems,” Opt. Lett. 18, 1343 (1993).
[Crossref] [PubMed]

B. E. Lemoff and C. P. J. Barty, “Quintic-phase-limited, spatially uniform expansion and recompression of ultrashort optical pulses,” Opt. Lett. 18, 1651 (1993).
[Crossref] [PubMed]

M. T. Asaki, C. P. Huang, D. Garvey, J. P. Zhou, H. C. Kapteyn, and M. M. Murnane, “Generation of 11-fs pulses from a self-mode-locked Ti-sapphire laser,” Opt. Lett. 18, 977 (1993).
[Crossref] [PubMed]

Phys. Rev. B (1)

P. C. M. Planken, I. Brener, M. C. Nuss, M. S. C. Lou, and S. L. Chuang, “Coherent control of terahertz charge oscillations in a coupled quantum well using phase-locked optical pulses,” Phys. Rev. B 48, 4903 (1993).
[Crossref]

Phys. Rev. Lett. (3)

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, and W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445 (1988).
[Crossref] [PubMed]

D. Umstadter, E. Esarey, and J. Kim, “Nonlinear plasma waves resonantly driven by optimized laser pulse trains,” Phys. Rev. Lett. 72, 1224 (1994).
[Crossref] [PubMed]

J. E. Rothenberg, D. Grischkowsky, and A. C. Balant, “Observation of the formation of the 0π pulse,” Phys. Rev. Lett. 53, 552 (1984).
[Crossref]

Science (2)

A. M. Weiner, D. E. Leaird, G. P. Wiederrecht, and K. A. Nelson, “Femtosecond pulse sequences used for optical control of molecular motion,” Science 247, 1317 (1990); “Femtosecond multiple-pulse impulsive stimulated Raman scattering spectroscopy,” J. Opt. Soc. Am. B 8, 1264 (1991).
[Crossref] [PubMed]

W. S. Warren, H. Rabitz, and Mohammed Dahleh, “Coherent control of quantum mechanics: the dream is alive,” Science 259, 1581 (1993).
[Crossref] [PubMed]

Other (7)

B. Kohler, J. L. Krause, R. M. Whitnell, K. R. Wilson, V. V. Yakovlev, and Y. Yan, “Quantum control of vibrational dynamics with tailored light pulses,” in Ultrafast Phenomena IX, G. A. Mourou, A. H. Zewail, P. F. Barbara, and W. H. Knox, eds. (Springer-Verlag, Berlin, 1994), p. 44.
[Crossref]

H. Rabitz and S. Shi, “Optimal control of molecular motion: making molecules dance,” in Vibrational Spectroscopy, J. Bowman, ed. (Jai, Greenwich, Conn., 1991), Vol. 1, Part A, p. 187.

J. Zhou, G. Taft, C. Shi, H. C. Kapteyn, and M. C. Murnane, “Sub-10 fs pulse generation in Ti:sapphire: capabilities and ultimate limits,” in Ultrafast Phenomena IX, G. A. Mourou, A. H. Zewail, P. F. Barbara, and W. H. Knox, eds. (Springer-Verlag, Berlin, 1994), p. 39.
[Crossref]

P. Hyldgaard, G. D. Sanders, and D. H. Reitze, “Coherent optical control of electron dynamics in asymmetric double quantum wells in the nonimpulsive regime,” presented at the Annual Meeting of the Optical Society of America, Dallas, Tx., October 1994.

See, for example, W. H. Press, S. A. Teukolsky, W. T. Vettering, and B. P. Flannery, Numerical Recipes (Cambridge U. Press, Cambridge, 1992), Chap. 10.

See, for example, G. P. Agrawal, “Nonlinear Fiber Optics (Academic, Boston, 1989), Chap. 1.

See, for example, E. Hecht and A. Zajac, Optics (Addison-Wesley, Reading, Mass., 1976), p. 323.

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Figures (15)

Fig. 1
Fig. 1

Schematic of the ultrabroad-bandwidth pulse-shaping apparatus.

Fig. 2
Fig. 2

Phase versus voltage calibration for the liquid-crystal SLM for 750 nm (solid curve), 800 nm (dashed curve), 850 nm (short-and-long-dashed curve). Phase shifts in excess of 2π can be obtained at all wavelengths.

Fig. 3
Fig. 3

Cross correlation (solid curve) of an unshaped pulse after it propagates through the shaper. The (sech2) deconvolved pulse width is 13.0 fs. For comparison, an autocorrelation directly from the oscillator is displayed (dashed curve).

Fig. 4
Fig. 4

Cross correlation of a 13-fs odd pulse. The high fidelity of this pulse is characterized by the depth of central minimum of the pulse.

Fig. 5
Fig. 5

Cross correlations of phase-filtered terahertz-rate pulse trains generated by length 7 M-sequences: (a) 8.8-THz train, (b) 16.0-THz train, (c) 23.6-THz train.

Fig. 6
Fig. 6

Cross correlations of asymmetric, chirped trains of femtosecond pulses generated by 64 gray-level phase masks designed with simulated annealing. Each panel shows the target (dashed curve), the numerical results (dotted-dashed curve), and the experimental cross correlation (solid curve).

Fig. 7
Fig. 7

Experimental cross correlations (solid curves) and numerical simulations (dashed curves) of a pulse with a cubic-phase modulation of (a) Φ(3) = 6 × 104 fs3 (12π), (b) Φ(3) = 6.0 × 105 fs3 (122π). The effects of aliasing are clearly seen in (b).

Fig. 8
Fig. 8

(a) Cross correlation of a pulse with a cubic-phase modulation of Φ(3) = 3.0 × 105 fs3, (b) semilog plot of the same pulse. Oscillations are clearly visible over the entire pulse (~1.4 ps).

Fig. 9
Fig. 9

Experimental cross correlations (solid curve) and numerical simulations (dashed curve) of a pulse with a quartic-phase modulation of (a) Φ(4) = 1.1 × 105 fs4 (40π), (b) Φ(4) = 1.1 × 106 fs4 (400π). The slightly asymmetric profiles are caused by residual cubic-phase dispersion.

Fig. 10
Fig. 10

Geometry for calculating the effects of higher-order spatial dispersion in the masking plane.

Fig. 11
Fig. 11

Spatial wavelength dispersion in the masking plane of the shaper, showing linear dispersion (dashed curve) and third-order dispersion (solid curve). The exact position of the wavelength in the masking plane is identical to the third-order result over this wavelength.

Fig. 12
Fig. 12

Spatial frequency dispersion in the masking plane of the shaper, plotted in angular terahertz, obtained from the third-order wavelength result. FWHM bandwidths for 21, 10, and 5 fs are shown for reference.

Fig. 13
Fig. 13

Numerical simulations of (a) 66.8-THz, (b) 138.1-THz pulse trains that incorporate the effects of higher-order spatial dispersion, assuming a transform-limited 5-fs input pulse. These trains were synthesized by the use of an amplitude mask that consisted of two slits of equal spatial dimension centered about x = 0 in the masking plane.

Fig. 14
Fig. 14

Numerical simulation of a 62.5-THz pulse train (solid curve) that shows the effects of higher-order spatial dispersion, synthesized with a length 7 M-sequence phase mask. The fidelity of this train is significantly degraded with respect to a train synthesized assuming only linear frequency dispersion in the masking plane (dashed curve).

Fig. 15
Fig. 15

Numerical simulations of (a) 50-fs, (b) 100-fs, (c) 300-fs square pulses (solid curve) synthesized with sin(πx/x0)/(πx/x0) phase and amplitude filters. For comparison, ideal square pulses (dashed curve) synthesized assuming linear frequency dispersion are also displayed.

Equations (18)

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Δ ϕ ( V p ) = cos - 1 [ 1 - 2 I trans ( V p ) I in ] ,
E target ( t ) = u ( t ) * k = - N N A k exp [ i α k ( 2 ) t 2 ] δ ( t - k T ) ,
J [ Φ ( ω ) ] = j = 1 1024 E guess 2 ( t j ) - E target 2 ( t j ) ,
Φ ( ω ) = Φ ( ω 0 ) + Φ ( 1 ) ( ω ) ( ω - ω 0 ) + 1 2 ! Φ ( 2 ) ( ω ) ( ω - ω 0 ) 2 + 1 3 ! Φ ( 3 ) ( ω ) ( ω - ω 0 ) 3 + 1 4 ! Φ ( 4 ) ( ω ) ( ω - ω 0 ) 4 + ,
β ( 2 ) ( ω ) = λ 3 2 π c 2 d 2 n d λ 2 ,
β ( 3 ) ( ω ) = - λ 4 4 π 2 c 3 ( 3 d 2 n d λ 2 + λ d 3 n d λ 3 ) ,
β ( 4 ) ( ω ) = λ 5 π 3 c 4 ( 3 4 d 2 n d λ 2 + λ d 3 n d λ 3 + λ 2 4 d 4 n d λ 4 ) .
λ ( x ) = λ 0 + λ ( 1 ) ( x ) Δ x + 1 2 ! λ ( 2 ) ( x ) ( Δ x ) 2 + 1 3 ! λ ( 3 ) ( x ) ( Δ x ) 3 ,
x = f tan Ω .
d [ sin θ i + sin ( Ω + θ d , 0 ) ] = λ .
( d λ d x ) λ 0 = d cos θ d , 0 f ,
( d 2 λ d x 2 ) λ 0 = - d sin θ d , 0 f 2 ,
( d 3 λ d x 3 ) λ 0 = - 3 d cos θ d , 0 f 3 .
M ( ω ) = ( 2 π w 0 2 ) 1 / 2 d x M ( x ) exp { - 2 ( x - f [ ω ] ) w 0 2 } ,
f ( ω ) = d x d ω ω + 1 2 ! d 2 x d ω 2 ω 2 + 1 3 ! d 3 x d ω 3 ω 3 + .
M ( x ) = [ C ( x ) n = - N / 2 N / 2 - 1 δ ( x - n δ x ) ] * rect ( x δ x ) ,
M ( ω ) = { C [ f ( ω ) ] n = - N / 2 N / 2 - 1 δ [ f ( ω ) - n δ x ] } * rect [ f ( ω ) δ x ] .
I ( t ) = 1 ( 2 π ) 2 d ω exp ( i ω t ) d ω E out ( ω ) * × E out ( ω + ω ) ,

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