Abstract

We describe generation of shaped femtosecond waveforms by using frequency-domain phase-only filters designed by numerical optimization techniques. The task of filter design for pulse shaping in the time domain is directly analogous to the design of phase-only filters for beam shaping and array generation in the spatial domain. We experimentally tested phase filters that were designed to produce ultrafast square and triangle pulses and femtosecond pulse sequences. Our results demonstrate the ability to generate high-quality terahertz-repetition-rate sequences of femtosecond pulses by means of low-loss phase-only filtering. On the other hand, experiments that tested generation of individual shaped pulses, such as square pulses, were less successful than previous experiments that used simultaneous phase and amplitude filtering. Our results indicate the importance of building increased robustness against variations in the input pulse shape into the phase-only filter design.

© 1993 Optical Society of America

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  1. D. Prongue, H. P. Herzig, “Design and fabrication of HOE for clock distribution in integrated circuits,” presented at the Institute of Electrical Engineers Conference on Holographic Systems, Components, and Applications, Bath, UK, 1989.
  2. M. C. Hutley, “Optical techniques for the generation of microlens arrays,” J. Mod. Opt. 37, 253–265 (1990).
    [CrossRef]
  3. K. M. Flood, J. M. Finlan, “Collimation of diode laser arrays using etched cylindrical computer generated holograms,” in Holographic Optics: Optically and Computer Generated, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1052, 186–190 (1989).
    [CrossRef]
  4. H. Dammann, K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
    [CrossRef]
  5. H. Dammann, E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
    [CrossRef]
  6. U. Killat, G. Rabe, W. Rave, “Binary phase gratings for star couplers with high splitting ratios,” Fiber Integr. Opt. 4, 159–167 (1982).
    [CrossRef]
  7. J. Turunen, A. Vasara, J. Westerholm, G. Jin, A. Salin, “Optimization and fabrication of grating beamsplitters,”J. Phys. D 21, S102–S105 (1988).
    [CrossRef]
  8. J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
    [CrossRef]
  9. M. P. Dames, R. J. Dowling, D. Wood, “Efficient optical elements to generate intensity weighted spot arrays: design and fabrication,” Appl. Opt. 30, 2685–2691 (1991).
    [CrossRef] [PubMed]
  10. A. M. Weiner, J. P. Heritage, “Picosecond and femtosecond Fourier pulse shape synthesis,” Rev. Phys. Appl. 22, 1619–1628 (1987).
    [CrossRef]
  11. A. M. Weiner, J. P. Heritage, E. M. Kirschner, “High resolution femtosecond pulse shaping,” J. Opt. Soc. Am. B 5, 1563–1572 (1988).
    [CrossRef]
  12. A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
    [CrossRef] [PubMed]
  13. A. M. Weiner, D. E. Leaird, G. P. Wiederrecht, K. A. Nelson, “Femtosecond pulse sequences used for optical manipulation of molecular motion,” Science 247, 1317–1319 (1990);“Femtosecond multiple-pulse impulsive stimulated Raman scattering spectroscopy,” J. Opt. Soc. Am. B 8, 1264–1275 (1991).
    [CrossRef] [PubMed]
  14. A. M. Weiner, D. E. Leaird, “Generation of terahertz-rate trains of femtosecond pulses by phase-only filtering,” Opt. Lett. 15, 51–53 (1990).
    [CrossRef] [PubMed]
  15. J. A. Valdmanis, R. L. Fork, J. P. Gordon, “Generation of optical pulses as short as 27 femtoseconds directly from a laser balancing self-phase modulation, group velocity dispersion, saturable absorption, and saturable gain,” Opt. Lett. 10, 131–133 (1985).
    [CrossRef] [PubMed]
  16. C. Froehly, B. Colombeau, M. Vampouille, “Shaping and analysis of picosecond light pulses,” in Progress in Optics XX, E. Wolf, ed. (North-Holland, Amsterdam, 1983), pp. 65–153.
  17. A. VanderLugt, “Signal detection by complex spatial filtering,”IEEE Trans. Inf. Theory IT-10, 139–145 (1964).
  18. R. N. Thurston, J. P. Heritage, A. M. Weiner, W. J. Tomlinson, “Analysis of picosecond pulse shape synthesis by spatial masking in a grating pulse compressor,” IEEE J. Quantum Electron. 22, 682–696 (1986).
    [CrossRef]
  19. A. M. Weiner, J. P. Heritage, J. A. Salehi, “Encoding and decoding of femtosecond pulses,” Opt. Lett. 13, 300–302 (1988).
    [CrossRef] [PubMed]
  20. A. M. Weiner, D. E. Leaird, J. S. Patel, J. R. Wullert, “Programmable femtosecond pulse shaping by use of a multi-element liquid-crystal phase modulator,” Opt. Lett. 15, 326–328 (1990).
    [CrossRef] [PubMed]
  21. A. M. Weiner, D. E. Leaird, J. S. Patel, J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of a 128-element liquid crystal phase modulator,” IEEE J. Quantum Electron. 28, 908–920 (1992).
    [CrossRef]
  22. A. M. Weiner, J. P. Heritage, R. N. Thurston, “Synthesis of phase-coherent, picosecond optical square pulses,” Opt. Lett. 11, 153–155 (1986).
    [CrossRef] [PubMed]
  23. K. Ema, F. Shimizu, “Optical pulse shaping using a Fourier-transformed hologram,” Jpn. J. Appl. Phys. 29, L631–L633 (1990).
    [CrossRef]
  24. A. M. Weiner, D. E. Leaird, D. H. Reitze, E. G. Paek, “Spectral holography of shaped femtosecond pulses,” Opt. Lett. 17, 224–226 (1992).
    [CrossRef] [PubMed]
  25. R. Skaug, J. F. Hjelmstad, Spread Spectrum in Communications (Peregrinus, London, 1985).
    [CrossRef]
  26. D. H. Reitze, A. M. Weiner, D. E. Leaird, “Shaping of wide-bandwidth, 20 femtosecond optical pulses,” Appl. Phys. Lett. 61, 1260–1262 (1992).
    [CrossRef]
  27. N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. H. Teller, E. Teller, “Equation of state calculations by fast computing machines,”J. Chem. Phys. 21, 1087–1092 (1953).
    [CrossRef]
  28. S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
    [CrossRef] [PubMed]
  29. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), pp. 326–334.
  30. A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25, 2648–2655 (1989).
    [CrossRef]
  31. J. L. A. Chilla, O. E. Martinez, “Direct determination of the amplitude and the phase of femtosecond light pulses,” Opt. Lett. 16, 39–41 (1991).
    [CrossRef] [PubMed]
  32. D. J. Kane, R. Trebino, “Measurement of the intensity and phase of femtosecond pulses using spectrally resolved self-diffraction,” presented at the Eighth International Conference on Ultrafast Phenomena, Juan-Les-Pins, France, June 8–12, 1992.

1992 (3)

A. M. Weiner, D. E. Leaird, J. S. Patel, J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of a 128-element liquid crystal phase modulator,” IEEE J. Quantum Electron. 28, 908–920 (1992).
[CrossRef]

A. M. Weiner, D. E. Leaird, D. H. Reitze, E. G. Paek, “Spectral holography of shaped femtosecond pulses,” Opt. Lett. 17, 224–226 (1992).
[CrossRef] [PubMed]

D. H. Reitze, A. M. Weiner, D. E. Leaird, “Shaping of wide-bandwidth, 20 femtosecond optical pulses,” Appl. Phys. Lett. 61, 1260–1262 (1992).
[CrossRef]

1991 (2)

1990 (5)

M. C. Hutley, “Optical techniques for the generation of microlens arrays,” J. Mod. Opt. 37, 253–265 (1990).
[CrossRef]

A. M. Weiner, D. E. Leaird, G. P. Wiederrecht, K. A. Nelson, “Femtosecond pulse sequences used for optical manipulation of molecular motion,” Science 247, 1317–1319 (1990);“Femtosecond multiple-pulse impulsive stimulated Raman scattering spectroscopy,” J. Opt. Soc. Am. B 8, 1264–1275 (1991).
[CrossRef] [PubMed]

A. M. Weiner, D. E. Leaird, “Generation of terahertz-rate trains of femtosecond pulses by phase-only filtering,” Opt. Lett. 15, 51–53 (1990).
[CrossRef] [PubMed]

A. M. Weiner, D. E. Leaird, J. S. Patel, J. R. Wullert, “Programmable femtosecond pulse shaping by use of a multi-element liquid-crystal phase modulator,” Opt. Lett. 15, 326–328 (1990).
[CrossRef] [PubMed]

K. Ema, F. Shimizu, “Optical pulse shaping using a Fourier-transformed hologram,” Jpn. J. Appl. Phys. 29, L631–L633 (1990).
[CrossRef]

1989 (2)

A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25, 2648–2655 (1989).
[CrossRef]

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

1988 (4)

J. Turunen, A. Vasara, J. Westerholm, G. Jin, A. Salin, “Optimization and fabrication of grating beamsplitters,”J. Phys. D 21, S102–S105 (1988).
[CrossRef]

A. M. Weiner, J. P. Heritage, E. M. Kirschner, “High resolution femtosecond pulse shaping,” J. Opt. Soc. Am. B 5, 1563–1572 (1988).
[CrossRef]

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

A. M. Weiner, J. P. Heritage, J. A. Salehi, “Encoding and decoding of femtosecond pulses,” Opt. Lett. 13, 300–302 (1988).
[CrossRef] [PubMed]

1987 (1)

A. M. Weiner, J. P. Heritage, “Picosecond and femtosecond Fourier pulse shape synthesis,” Rev. Phys. Appl. 22, 1619–1628 (1987).
[CrossRef]

1986 (2)

R. N. Thurston, J. P. Heritage, A. M. Weiner, W. J. Tomlinson, “Analysis of picosecond pulse shape synthesis by spatial masking in a grating pulse compressor,” IEEE J. Quantum Electron. 22, 682–696 (1986).
[CrossRef]

A. M. Weiner, J. P. Heritage, R. N. Thurston, “Synthesis of phase-coherent, picosecond optical square pulses,” Opt. Lett. 11, 153–155 (1986).
[CrossRef] [PubMed]

1985 (1)

1983 (1)

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

1982 (1)

U. Killat, G. Rabe, W. Rave, “Binary phase gratings for star couplers with high splitting ratios,” Fiber Integr. Opt. 4, 159–167 (1982).
[CrossRef]

1977 (1)

H. Dammann, E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

1971 (1)

H. Dammann, K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

1964 (1)

A. VanderLugt, “Signal detection by complex spatial filtering,”IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

1953 (1)

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. H. Teller, E. Teller, “Equation of state calculations by fast computing machines,”J. Chem. Phys. 21, 1087–1092 (1953).
[CrossRef]

Andrejco, M. J.

A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25, 2648–2655 (1989).
[CrossRef]

Chilla, J. L. A.

Colombeau, B.

C. Froehly, B. Colombeau, M. Vampouille, “Shaping and analysis of picosecond light pulses,” in Progress in Optics XX, E. Wolf, ed. (North-Holland, Amsterdam, 1983), pp. 65–153.

Dames, M. P.

Dammann, H.

H. Dammann, E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

H. Dammann, K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Dowling, R. J.

Downs, M. M.

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

Ema, K.

K. Ema, F. Shimizu, “Optical pulse shaping using a Fourier-transformed hologram,” Jpn. J. Appl. Phys. 29, L631–L633 (1990).
[CrossRef]

Finlan, J. M.

K. M. Flood, J. M. Finlan, “Collimation of diode laser arrays using etched cylindrical computer generated holograms,” in Holographic Optics: Optically and Computer Generated, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1052, 186–190 (1989).
[CrossRef]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), pp. 326–334.

Flood, K. M.

K. M. Flood, J. M. Finlan, “Collimation of diode laser arrays using etched cylindrical computer generated holograms,” in Holographic Optics: Optically and Computer Generated, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1052, 186–190 (1989).
[CrossRef]

Fork, R. L.

Fouckhardt, H.

A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25, 2648–2655 (1989).
[CrossRef]

Froehly, C.

C. Froehly, B. Colombeau, M. Vampouille, “Shaping and analysis of picosecond light pulses,” in Progress in Optics XX, E. Wolf, ed. (North-Holland, Amsterdam, 1983), pp. 65–153.

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Gordon, J. P.

Gortler, K.

H. Dammann, K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Hawkins, R. J.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

Heritage, J. P.

A. M. Weiner, J. P. Heritage, J. A. Salehi, “Encoding and decoding of femtosecond pulses,” Opt. Lett. 13, 300–302 (1988).
[CrossRef] [PubMed]

A. M. Weiner, J. P. Heritage, E. M. Kirschner, “High resolution femtosecond pulse shaping,” J. Opt. Soc. Am. B 5, 1563–1572 (1988).
[CrossRef]

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

A. M. Weiner, J. P. Heritage, “Picosecond and femtosecond Fourier pulse shape synthesis,” Rev. Phys. Appl. 22, 1619–1628 (1987).
[CrossRef]

A. M. Weiner, J. P. Heritage, R. N. Thurston, “Synthesis of phase-coherent, picosecond optical square pulses,” Opt. Lett. 11, 153–155 (1986).
[CrossRef] [PubMed]

R. N. Thurston, J. P. Heritage, A. M. Weiner, W. J. Tomlinson, “Analysis of picosecond pulse shape synthesis by spatial masking in a grating pulse compressor,” IEEE J. Quantum Electron. 22, 682–696 (1986).
[CrossRef]

Herzig, H. P.

D. Prongue, H. P. Herzig, “Design and fabrication of HOE for clock distribution in integrated circuits,” presented at the Institute of Electrical Engineers Conference on Holographic Systems, Components, and Applications, Bath, UK, 1989.

Hjelmstad, J. F.

R. Skaug, J. F. Hjelmstad, Spread Spectrum in Communications (Peregrinus, London, 1985).
[CrossRef]

Hutley, M. C.

M. C. Hutley, “Optical techniques for the generation of microlens arrays,” J. Mod. Opt. 37, 253–265 (1990).
[CrossRef]

Jahns, J.

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

Jin, G.

J. Turunen, A. Vasara, J. Westerholm, G. Jin, A. Salin, “Optimization and fabrication of grating beamsplitters,”J. Phys. D 21, S102–S105 (1988).
[CrossRef]

Kane, D. J.

D. J. Kane, R. Trebino, “Measurement of the intensity and phase of femtosecond pulses using spectrally resolved self-diffraction,” presented at the Eighth International Conference on Ultrafast Phenomena, Juan-Les-Pins, France, June 8–12, 1992.

Killat, U.

U. Killat, G. Rabe, W. Rave, “Binary phase gratings for star couplers with high splitting ratios,” Fiber Integr. Opt. 4, 159–167 (1982).
[CrossRef]

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Kirschner, E. M.

A. M. Weiner, J. P. Heritage, E. M. Kirschner, “High resolution femtosecond pulse shaping,” J. Opt. Soc. Am. B 5, 1563–1572 (1988).
[CrossRef]

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

Klotz, E.

H. Dammann, E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Leaird, D. E.

A. M. Weiner, D. E. Leaird, D. H. Reitze, E. G. Paek, “Spectral holography of shaped femtosecond pulses,” Opt. Lett. 17, 224–226 (1992).
[CrossRef] [PubMed]

A. M. Weiner, D. E. Leaird, J. S. Patel, J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of a 128-element liquid crystal phase modulator,” IEEE J. Quantum Electron. 28, 908–920 (1992).
[CrossRef]

D. H. Reitze, A. M. Weiner, D. E. Leaird, “Shaping of wide-bandwidth, 20 femtosecond optical pulses,” Appl. Phys. Lett. 61, 1260–1262 (1992).
[CrossRef]

A. M. Weiner, D. E. Leaird, J. S. Patel, J. R. Wullert, “Programmable femtosecond pulse shaping by use of a multi-element liquid-crystal phase modulator,” Opt. Lett. 15, 326–328 (1990).
[CrossRef] [PubMed]

A. M. Weiner, D. E. Leaird, G. P. Wiederrecht, K. A. Nelson, “Femtosecond pulse sequences used for optical manipulation of molecular motion,” Science 247, 1317–1319 (1990);“Femtosecond multiple-pulse impulsive stimulated Raman scattering spectroscopy,” J. Opt. Soc. Am. B 8, 1264–1275 (1991).
[CrossRef] [PubMed]

A. M. Weiner, D. E. Leaird, “Generation of terahertz-rate trains of femtosecond pulses by phase-only filtering,” Opt. Lett. 15, 51–53 (1990).
[CrossRef] [PubMed]

A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25, 2648–2655 (1989).
[CrossRef]

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

Martinez, O. E.

Metropolis, N.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. H. Teller, E. Teller, “Equation of state calculations by fast computing machines,”J. Chem. Phys. 21, 1087–1092 (1953).
[CrossRef]

Nelson, K. A.

A. M. Weiner, D. E. Leaird, G. P. Wiederrecht, K. A. Nelson, “Femtosecond pulse sequences used for optical manipulation of molecular motion,” Science 247, 1317–1319 (1990);“Femtosecond multiple-pulse impulsive stimulated Raman scattering spectroscopy,” J. Opt. Soc. Am. B 8, 1264–1275 (1991).
[CrossRef] [PubMed]

Paek, E. G.

Patel, J. S.

A. M. Weiner, D. E. Leaird, J. S. Patel, J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of a 128-element liquid crystal phase modulator,” IEEE J. Quantum Electron. 28, 908–920 (1992).
[CrossRef]

A. M. Weiner, D. E. Leaird, J. S. Patel, J. R. Wullert, “Programmable femtosecond pulse shaping by use of a multi-element liquid-crystal phase modulator,” Opt. Lett. 15, 326–328 (1990).
[CrossRef] [PubMed]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), pp. 326–334.

Prise, M. E.

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

Prongue, D.

D. Prongue, H. P. Herzig, “Design and fabrication of HOE for clock distribution in integrated circuits,” presented at the Institute of Electrical Engineers Conference on Holographic Systems, Components, and Applications, Bath, UK, 1989.

Rabe, G.

U. Killat, G. Rabe, W. Rave, “Binary phase gratings for star couplers with high splitting ratios,” Fiber Integr. Opt. 4, 159–167 (1982).
[CrossRef]

Rave, W.

U. Killat, G. Rabe, W. Rave, “Binary phase gratings for star couplers with high splitting ratios,” Fiber Integr. Opt. 4, 159–167 (1982).
[CrossRef]

Reitze, D. H.

A. M. Weiner, D. E. Leaird, D. H. Reitze, E. G. Paek, “Spectral holography of shaped femtosecond pulses,” Opt. Lett. 17, 224–226 (1992).
[CrossRef] [PubMed]

D. H. Reitze, A. M. Weiner, D. E. Leaird, “Shaping of wide-bandwidth, 20 femtosecond optical pulses,” Appl. Phys. Lett. 61, 1260–1262 (1992).
[CrossRef]

Rosenbluth, A.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. H. Teller, E. Teller, “Equation of state calculations by fast computing machines,”J. Chem. Phys. 21, 1087–1092 (1953).
[CrossRef]

Rosenbluth, M.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. H. Teller, E. Teller, “Equation of state calculations by fast computing machines,”J. Chem. Phys. 21, 1087–1092 (1953).
[CrossRef]

Saifi, M. A.

A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25, 2648–2655 (1989).
[CrossRef]

Salehi, J. A.

Salin, A.

J. Turunen, A. Vasara, J. Westerholm, G. Jin, A. Salin, “Optimization and fabrication of grating beamsplitters,”J. Phys. D 21, S102–S105 (1988).
[CrossRef]

Shimizu, F.

K. Ema, F. Shimizu, “Optical pulse shaping using a Fourier-transformed hologram,” Jpn. J. Appl. Phys. 29, L631–L633 (1990).
[CrossRef]

Silberberg, Y.

A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25, 2648–2655 (1989).
[CrossRef]

Skaug, R.

R. Skaug, J. F. Hjelmstad, Spread Spectrum in Communications (Peregrinus, London, 1985).
[CrossRef]

Smith, P. W.

A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25, 2648–2655 (1989).
[CrossRef]

Streibl, N.

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

Teller, A. H.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. H. Teller, E. Teller, “Equation of state calculations by fast computing machines,”J. Chem. Phys. 21, 1087–1092 (1953).
[CrossRef]

Teller, E.

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. H. Teller, E. Teller, “Equation of state calculations by fast computing machines,”J. Chem. Phys. 21, 1087–1092 (1953).
[CrossRef]

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), pp. 326–334.

Thurston, R. N.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

R. N. Thurston, J. P. Heritage, A. M. Weiner, W. J. Tomlinson, “Analysis of picosecond pulse shape synthesis by spatial masking in a grating pulse compressor,” IEEE J. Quantum Electron. 22, 682–696 (1986).
[CrossRef]

A. M. Weiner, J. P. Heritage, R. N. Thurston, “Synthesis of phase-coherent, picosecond optical square pulses,” Opt. Lett. 11, 153–155 (1986).
[CrossRef] [PubMed]

Tomlinson, W. J.

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

R. N. Thurston, J. P. Heritage, A. M. Weiner, W. J. Tomlinson, “Analysis of picosecond pulse shape synthesis by spatial masking in a grating pulse compressor,” IEEE J. Quantum Electron. 22, 682–696 (1986).
[CrossRef]

Trebino, R.

D. J. Kane, R. Trebino, “Measurement of the intensity and phase of femtosecond pulses using spectrally resolved self-diffraction,” presented at the Eighth International Conference on Ultrafast Phenomena, Juan-Les-Pins, France, June 8–12, 1992.

Turunen, J.

J. Turunen, A. Vasara, J. Westerholm, G. Jin, A. Salin, “Optimization and fabrication of grating beamsplitters,”J. Phys. D 21, S102–S105 (1988).
[CrossRef]

Valdmanis, J. A.

Vampouille, M.

C. Froehly, B. Colombeau, M. Vampouille, “Shaping and analysis of picosecond light pulses,” in Progress in Optics XX, E. Wolf, ed. (North-Holland, Amsterdam, 1983), pp. 65–153.

VanderLugt, A.

A. VanderLugt, “Signal detection by complex spatial filtering,”IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

Vasara, A.

J. Turunen, A. Vasara, J. Westerholm, G. Jin, A. Salin, “Optimization and fabrication of grating beamsplitters,”J. Phys. D 21, S102–S105 (1988).
[CrossRef]

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), pp. 326–334.

Walker, S. J.

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

Weiner, A. M.

A. M. Weiner, D. E. Leaird, J. S. Patel, J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of a 128-element liquid crystal phase modulator,” IEEE J. Quantum Electron. 28, 908–920 (1992).
[CrossRef]

A. M. Weiner, D. E. Leaird, D. H. Reitze, E. G. Paek, “Spectral holography of shaped femtosecond pulses,” Opt. Lett. 17, 224–226 (1992).
[CrossRef] [PubMed]

D. H. Reitze, A. M. Weiner, D. E. Leaird, “Shaping of wide-bandwidth, 20 femtosecond optical pulses,” Appl. Phys. Lett. 61, 1260–1262 (1992).
[CrossRef]

A. M. Weiner, D. E. Leaird, J. S. Patel, J. R. Wullert, “Programmable femtosecond pulse shaping by use of a multi-element liquid-crystal phase modulator,” Opt. Lett. 15, 326–328 (1990).
[CrossRef] [PubMed]

A. M. Weiner, D. E. Leaird, “Generation of terahertz-rate trains of femtosecond pulses by phase-only filtering,” Opt. Lett. 15, 51–53 (1990).
[CrossRef] [PubMed]

A. M. Weiner, D. E. Leaird, G. P. Wiederrecht, K. A. Nelson, “Femtosecond pulse sequences used for optical manipulation of molecular motion,” Science 247, 1317–1319 (1990);“Femtosecond multiple-pulse impulsive stimulated Raman scattering spectroscopy,” J. Opt. Soc. Am. B 8, 1264–1275 (1991).
[CrossRef] [PubMed]

A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25, 2648–2655 (1989).
[CrossRef]

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

A. M. Weiner, J. P. Heritage, E. M. Kirschner, “High resolution femtosecond pulse shaping,” J. Opt. Soc. Am. B 5, 1563–1572 (1988).
[CrossRef]

A. M. Weiner, J. P. Heritage, J. A. Salehi, “Encoding and decoding of femtosecond pulses,” Opt. Lett. 13, 300–302 (1988).
[CrossRef] [PubMed]

A. M. Weiner, J. P. Heritage, “Picosecond and femtosecond Fourier pulse shape synthesis,” Rev. Phys. Appl. 22, 1619–1628 (1987).
[CrossRef]

A. M. Weiner, J. P. Heritage, R. N. Thurston, “Synthesis of phase-coherent, picosecond optical square pulses,” Opt. Lett. 11, 153–155 (1986).
[CrossRef] [PubMed]

R. N. Thurston, J. P. Heritage, A. M. Weiner, W. J. Tomlinson, “Analysis of picosecond pulse shape synthesis by spatial masking in a grating pulse compressor,” IEEE J. Quantum Electron. 22, 682–696 (1986).
[CrossRef]

Westerholm, J.

J. Turunen, A. Vasara, J. Westerholm, G. Jin, A. Salin, “Optimization and fabrication of grating beamsplitters,”J. Phys. D 21, S102–S105 (1988).
[CrossRef]

Wiederrecht, G. P.

A. M. Weiner, D. E. Leaird, G. P. Wiederrecht, K. A. Nelson, “Femtosecond pulse sequences used for optical manipulation of molecular motion,” Science 247, 1317–1319 (1990);“Femtosecond multiple-pulse impulsive stimulated Raman scattering spectroscopy,” J. Opt. Soc. Am. B 8, 1264–1275 (1991).
[CrossRef] [PubMed]

Wood, D.

Wullert, J. R.

A. M. Weiner, D. E. Leaird, J. S. Patel, J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of a 128-element liquid crystal phase modulator,” IEEE J. Quantum Electron. 28, 908–920 (1992).
[CrossRef]

A. M. Weiner, D. E. Leaird, J. S. Patel, J. R. Wullert, “Programmable femtosecond pulse shaping by use of a multi-element liquid-crystal phase modulator,” Opt. Lett. 15, 326–328 (1990).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

D. H. Reitze, A. M. Weiner, D. E. Leaird, “Shaping of wide-bandwidth, 20 femtosecond optical pulses,” Appl. Phys. Lett. 61, 1260–1262 (1992).
[CrossRef]

Fiber Integr. Opt. (1)

U. Killat, G. Rabe, W. Rave, “Binary phase gratings for star couplers with high splitting ratios,” Fiber Integr. Opt. 4, 159–167 (1982).
[CrossRef]

IEEE J. Quantum Electron. (3)

R. N. Thurston, J. P. Heritage, A. M. Weiner, W. J. Tomlinson, “Analysis of picosecond pulse shape synthesis by spatial masking in a grating pulse compressor,” IEEE J. Quantum Electron. 22, 682–696 (1986).
[CrossRef]

A. M. Weiner, D. E. Leaird, J. S. Patel, J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of a 128-element liquid crystal phase modulator,” IEEE J. Quantum Electron. 28, 908–920 (1992).
[CrossRef]

A. M. Weiner, Y. Silberberg, H. Fouckhardt, D. E. Leaird, M. A. Saifi, M. J. Andrejco, P. W. Smith, “Use of femtosecond square pulses to avoid pulse breakup in all-optical switching,” IEEE J. Quantum Electron. 25, 2648–2655 (1989).
[CrossRef]

IEEE Trans. Inf. Theory (1)

A. VanderLugt, “Signal detection by complex spatial filtering,”IEEE Trans. Inf. Theory IT-10, 139–145 (1964).

J. Chem. Phys. (1)

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. H. Teller, E. Teller, “Equation of state calculations by fast computing machines,”J. Chem. Phys. 21, 1087–1092 (1953).
[CrossRef]

J. Mod. Opt. (1)

M. C. Hutley, “Optical techniques for the generation of microlens arrays,” J. Mod. Opt. 37, 253–265 (1990).
[CrossRef]

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

J. Phys. D (1)

J. Turunen, A. Vasara, J. Westerholm, G. Jin, A. Salin, “Optimization and fabrication of grating beamsplitters,”J. Phys. D 21, S102–S105 (1988).
[CrossRef]

Jpn. J. Appl. Phys. (1)

K. Ema, F. Shimizu, “Optical pulse shaping using a Fourier-transformed hologram,” Jpn. J. Appl. Phys. 29, L631–L633 (1990).
[CrossRef]

Opt. Acta (1)

H. Dammann, E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Opt. Commun. (1)

H. Dammann, K. Gortler, “High-efficiency in-line multiple imaging by means of multiple phase holograms,” Opt. Commun. 3, 312–315 (1971).
[CrossRef]

Opt. Eng. (1)

J. Jahns, M. M. Downs, M. E. Prise, N. Streibl, S. J. Walker, “Dammann gratings for laser beam shaping,” Opt. Eng. 28, 1267–1275 (1989).
[CrossRef]

Opt. Lett. (7)

Phys. Rev. Lett. (1)

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, “Experimental observation of the fundamental dark soliton in optical fibers,” Phys. Rev. Lett. 61, 2445–2448 (1988).
[CrossRef] [PubMed]

Rev. Phys. Appl. (1)

A. M. Weiner, J. P. Heritage, “Picosecond and femtosecond Fourier pulse shape synthesis,” Rev. Phys. Appl. 22, 1619–1628 (1987).
[CrossRef]

Science (2)

A. M. Weiner, D. E. Leaird, G. P. Wiederrecht, K. A. Nelson, “Femtosecond pulse sequences used for optical manipulation of molecular motion,” Science 247, 1317–1319 (1990);“Femtosecond multiple-pulse impulsive stimulated Raman scattering spectroscopy,” J. Opt. Soc. Am. B 8, 1264–1275 (1991).
[CrossRef] [PubMed]

S. Kirkpatrick, C. D. Gelatt, M. P. Vecchi, “Optimization by simulated annealing,” Science 220, 671–680 (1983).
[CrossRef] [PubMed]

Other (6)

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes (Cambridge U. Press, Cambridge, 1986), pp. 326–334.

R. Skaug, J. F. Hjelmstad, Spread Spectrum in Communications (Peregrinus, London, 1985).
[CrossRef]

D. J. Kane, R. Trebino, “Measurement of the intensity and phase of femtosecond pulses using spectrally resolved self-diffraction,” presented at the Eighth International Conference on Ultrafast Phenomena, Juan-Les-Pins, France, June 8–12, 1992.

C. Froehly, B. Colombeau, M. Vampouille, “Shaping and analysis of picosecond light pulses,” in Progress in Optics XX, E. Wolf, ed. (North-Holland, Amsterdam, 1983), pp. 65–153.

D. Prongue, H. P. Herzig, “Design and fabrication of HOE for clock distribution in integrated circuits,” presented at the Institute of Electrical Engineers Conference on Holographic Systems, Components, and Applications, Bath, UK, 1989.

K. M. Flood, J. M. Finlan, “Collimation of diode laser arrays using etched cylindrical computer generated holograms,” in Holographic Optics: Optically and Computer Generated, I. Cindrich, S. H. Lee, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1052, 186–190 (1989).
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

Apparatus for shaping of femtosecond optical pulses.

Fig. 2
Fig. 2

Generation of high-rate pulse trains by spectral filtering: (A) input spectrum, (B) amplitude filter, (C) phase filter. For the phase filter, the various shaded rectangles denote different phases.

Fig. 3
Fig. 3

Intensity cross-correlation measurements of (A) 4.0-THz, (B) 5.85-THz pulse trains produced by phase-only filtering. The phase difference was Δφ = 0.84π for both traces.

Fig. 4
Fig. 4

Flat-topped pulse trains at a 2.5-THz repetition rate, produced by phase-only filters based on Dammann gratings. The phase difference was (A), (C) Δφ = π and (B), (D) Δφ = 0.857π.

Fig. 5
Fig. 5

Design of a phase-only filter for producing a 1.0-ps square pulse: (A) target intensity profile, (B) calculated intensity profile resulting from the phase-only filter, (C) phase filter designed by simulated annealing (top) and assumed input power spectrum (bottom). The phase filter was assumed to consist of 400 independent pixels.

Fig. 6
Fig. 6

Design of a phase-only filter for producing a 2.5-ps square pulse: (A) target intensity profile, (B) calculated intensity profile resulting from the phase-only filter, (C) phase filter designed by simulated annealing (top) and assumed input power spectrum (bottom). The phase filter was assumed to consist of 400 independent pixels.

Fig. 7
Fig. 7

Calculated phase profile of the square pulse from Fig. 5.

Fig. 8
Fig. 8

Design of a phase-only filter for producing a femtosecond pulse sequence: (A) target intensity profile corresponding to an = {11001110011}, (B) calculated intensity profile resulting from the phase-only filter. (C) Phase filter designed by simulated annealing (top) and assumed input power spectrum (bottom). The phase filter was assumed to consist of 128 independent pixels, and the hard edge at 612.5 nm in the input power spectrum corresponds to the edge of the clear spectral window transmitted through the liquid-crystal modulator.

Fig. 9
Fig. 9

Design of a phase-only filter for producing a femtosecond pulse sequence: (A) target intensity profile corresponding to an = {10011011001}, (B) calculated intensity profile resulting from the phase-only filter, (C) phase filter designed by simulated annealing (top) and assumed input power spectrum (bottom). The phase filter was assumed to consist of 128 independent pixels.

Fig. 10
Fig. 10

(A) Calculated intensity profile resulting from a phase-only filter designed to transform a symmetric, sech(t) input pulse into a 0.5-ps square pulse, (B) calculated intensity profile resulting when the same phase-only filter is used with an actual laser spectrum, (C) measured intensity profile obtained by passing a femtosecond pulse through the pulse-shaping apparatus.

Fig. 11
Fig. 11

Experimental tests of three different phase-only filters designed to produce 0.5-ps square pulses: (A), (C), (E) measured intensity profiles, (B), (D), (F) corresponding calculated intensity profiles. The phase filter consisted of (B), (D) 128 pixels, (F) 316 pixels. An actual laser power spectrum was used for (B), (F); a symmetric spectrum corresponding to sech(t) was used for (D).

Fig. 12
Fig. 12

Experimental tests of phase-only filters designed to produce ultrafast square pulses: (A) measured intensity profile for a 1-ps square pulse, (B) calculated intensity profile, (C) measured intensity profile for a 2-ps square pulse, (D) calculated intensity profile. The phase filters consisted of 316 pixels, and an actual laser power spectrum was used for the filter design.

Fig. 13
Fig. 13

Measured intensity profiles of ultrafast square pulses obtained by simultaneous phase and amplitude filtering: (A) 0.5-ps duration, (B) 1.5-ps duration. The smoothness of these intensity profiles is in contrast to those obtained by phase-only filtering.

Equations (9)

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E out ( ω ) = E in ( ω ) M eff ( ω ) ,
M eff ( ω ) = d x M ( x ) exp [ - 2 ( x - α ω 2 / w 0 2 ) ] .
α = ( d ω d x ) - 1 = - λ 2 2 π c ( d λ d x ) - 1 .
M eff ( ω ) ~ M ( x / α ) .
I ( t ) = ( 1 / 2 π ) 2 d Ω exp ( i Ω t ) d ω E * ( ω ) E ( ω + Ω ) .
C i = Max | e ( t ) 2 - e target ( t ) 2 | ,             t < T 0 .
e ( t ) = 1 2 π d ω E in ( ω ) M ( ω ) exp ( i ω t ) ,
C = w i C i .
e target ( t ) = n a n u ( t - n T ) ,

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