Abstract

Generation of arbitrarily complex intensity profiles by using phase-only Fourier-domain pulse shaping has thus far been performed by using optimization algorithms to find the optimal phase profile. We present an alternative method based on the Gerchberg–Saxton (GS) algorithm that converges at least several hundred times faster and is independent of the number of phase points and gray levels. The numerical and experimental performance of the GS algorithm is characterized and compared against a genetic algorithm. An application of amplified GS-synthesized waveforms to large-amplitude coherent phonon generation and destruction is demonstrated.

© 2002 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
  35. 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]
  36. R. Bartels, S. Backus, I. P. Christov, H. C. Kapteyn, and M. M. Murnane, “Attosecond time-scale feedback control of coherent x ray generation,” Chem. Phys. 267, 277–289 (2001).
    [CrossRef]
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    [CrossRef]
  38. T. Brixner, N. H. Damrauer, P. Niklaus, and G. Gerber, “Photoselective adaptive femtosecond quantum control in the liquid phase,” Nature 414, 57–60 (2001).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]

2001 (6)

B. J. Pearson, J. L. White, T. C. Weinacht, and P. H. Bucksbaum, “Coherent control using adaptive learning algorithms,” Phys. Rev. A 63, 063412 (2001).
[CrossRef]

R. Bartels, S. Backus, I. P. Christov, H. C. Kapteyn, and M. M. Murnane, “Attosecond time-scale feedback control of coherent x ray generation,” Chem. Phys. 267, 277–289 (2001).
[CrossRef]

T. C. Weinacht, R. Bartels, S. Backus, P. H. Bucksbaum, B. Pearson, J. M. Geremia, H. Rabitz, H. C. Kapteyn, and M.M. Murnane, “Coherent learning control of vibrational motion in room temperature molecular gases,” Chem. Phys. Lett. 344, 333–338 (2001).
[CrossRef]

T. Brixner, N. H. Damrauer, P. Niklaus, and G. Gerber, “Photoselective adaptive femtosecond quantum control in the liquid phase,” Nature 414, 57–60 (2001).
[CrossRef] [PubMed]

F. G. Omenetto, A. J. Taylor, M. D. Moores, and D. H. Reitze, “Adaptive control of femtosecond pulse propagation in optical fibers,” Opt. Lett. 26, 938–40 (2001).
[CrossRef]

M. Hacker, G. Stobrawa, and T. Feurer, “Iterative Fourier transform algorithm for phase-only pulse shaping,” Opt. Express 9, 191–199 (2001).
[CrossRef] [PubMed]

2000 (5)

A. Efimov, M. D. Moores, B. Mei, J. L. Krause, C. W. Siders, and D. H. Reitze, “Minimization of phase distortion in an ultrafast chirped-pulse amplifier using adaptive learning,” Appl. Phys. B 70, S133–S141 (2000).
[CrossRef]

E. Zeek, R. Bartels, M. M. Murnane, H. C. Kapteyn, S. Backus, and G. Vdovin, “Adaptive pulse compression for transform-limited 15-fs high-energy pulse generation,” Opt. Lett. 25, 587–589 (2000).
[CrossRef]

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]

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71, 1929–1960 (2000).
[CrossRef]

T. Hornung, R. Meier, and M. Motzkus, “Optimal control of molecular states in a loop with a parameterization in frequency and time domain,” Chem. Phys. Lett. 326, 445–453 (2000).
[CrossRef]

1999 (1)

P. H. Bucksbaum and R. Merlin, “The phonon Bragg switch: a proposal to generate sub-picosecond x ray pulses,” Solid State Commun. 111, 535–539 (1999).
[CrossRef]

1998 (7)

P. Chen, A. Spitkovsky, T. Katsouleas, and W. Mori, “Transformer ratio and pulse shaping in laser wakefield acccelerators,” Nucl. Instrum. Methods Phys. Res. A 410, 488–492 (1998).
[CrossRef]

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

M. Hase, T. Itano, K. Mizoguchi, and S. I. Nakashima, “Selective enhancement of coherent optical phonons using THz-rate pulse train,” Jpn. J. Appl. Phys., 37, L281–L283 (1998).
[CrossRef]

J. Peatross and A. Rundquist, “Temporal decorrelation of short laser pulses,” J. Opt. Soc. Am. B 15, 216–222 (1998).
[CrossRef]

D. Meshulach, D. Yelin, and Y. Silberberg, “Adaptive real-time femtosecond pulse shaping,” J. Opt. Soc. Am. B 15, 1615–1619 (1998).
[CrossRef]

A. Efimov and D. H. Reitze, “Programmable dispersion compensation and pulse shaping in a 26-fs chirped-pulse amplifier,” Opt. Lett. 23, 1612–1614 (1998).
[CrossRef]

A. Efimov, M. D. Moores, N. M. Beach, J. L. Krause, and D. H. Reitze, “Adaptive control of pulse phase in a chirped-pulse amplifier,” Opt. Lett. 23, 1915–1917 (1998).
[CrossRef]

1997 (3)

D. Yelin, D. Meshulach, and Y. Silberberg, “Adaptive femtosecond pulse compression,” Opt. Lett. 22, 1793–1795 (1997).
[CrossRef]

C. J. Brennan and K. A. Nelson, “Direct time-resolved measurement of anharmonic lattice vibrations in ferroelectric crystals,” J. Chem. Phys. 107, 9691–9694 (1997).
[CrossRef]

C. J. Bardeen, V. V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

1995 (3)

1994 (2)

D. Umstadter, E. Esarey, and J. Kim, “Nonlinear plasma waves resonantly driven by optimized laser pulse trains,” Phys. Rev. Lett. 72, 1224–1227 (1994).
[CrossRef] [PubMed]

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, “A simple method for the determination of the intensity and phase of ultrashort optical pulses,” Opt. Commun. 113, 79–84 (1994).
[CrossRef]

1993 (2)

T. Dekorsy, W. Kutt, T. Pfeifer, and H. Kurz, “Coherent control of LO-phonon dynamics in opaque semiconductors by femtosecond laser pulses,” Europhys. Lett. 23, 223–228 (1993).
[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. A 10, 1112–1120 (1993).
[CrossRef]

1992 (1)

R. S. Judson and H. Rabitz, “Teaching lasers to control molecules,” Phys. Rev. Lett. 68, 1500–1503 (1992).
[CrossRef] [PubMed]

1990 (2)

A. M. Weiner, D. E. Leaird, Gary P. Wiederrecht, and Keith A. Nelson, “Femtosecond pulse sequences used for optical manipulation of molecular motion,” Science 247, 1317–1319 (1990).
[CrossRef] [PubMed]

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

1986 (1)

J. R. Fienup and C. C. Wackerman, “Phase-retrieval stagnation problems and solutions,” J. Opt. Soc. Am. B 3, 1897–1907 (1986).
[CrossRef]

1985 (1)

Yong-Xin Yan, E. B. Gamble, Jr., and K. A. Nelson, “Impulsive stimulated scattering: general importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83, 5391–5399 (1985).
[CrossRef]

1982 (1)

1973 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “Phase determination from image and diffraction plane pictures in the electron microscope,” Optik 35, 237–246 (1972).

Assion, A.

A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, 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.

T. C. Weinacht, R. Bartels, S. Backus, P. H. Bucksbaum, B. Pearson, J. M. Geremia, H. Rabitz, H. C. Kapteyn, and M.M. Murnane, “Coherent learning control of vibrational motion in room temperature molecular gases,” Chem. Phys. Lett. 344, 333–338 (2001).
[CrossRef]

R. Bartels, S. Backus, I. P. Christov, H. C. Kapteyn, and M. M. Murnane, “Attosecond time-scale feedback control of coherent x ray generation,” Chem. Phys. 267, 277–289 (2001).
[CrossRef]

E. Zeek, R. Bartels, M. M. Murnane, H. C. Kapteyn, S. Backus, and G. Vdovin, “Adaptive pulse compression for transform-limited 15-fs high-energy pulse generation,” Opt. Lett. 25, 587–589 (2000).
[CrossRef]

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]

Bardeen, C. J.

C. J. Bardeen, V. V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

Bartels, R.

R. Bartels, S. Backus, I. P. Christov, H. C. Kapteyn, and M. M. Murnane, “Attosecond time-scale feedback control of coherent x ray generation,” Chem. Phys. 267, 277–289 (2001).
[CrossRef]

T. C. Weinacht, R. Bartels, S. Backus, P. H. Bucksbaum, B. Pearson, J. M. Geremia, H. Rabitz, H. C. Kapteyn, and M.M. Murnane, “Coherent learning control of vibrational motion in room temperature molecular gases,” Chem. Phys. Lett. 344, 333–338 (2001).
[CrossRef]

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]

E. Zeek, R. Bartels, M. M. Murnane, H. C. Kapteyn, S. Backus, and G. Vdovin, “Adaptive pulse compression for transform-limited 15-fs high-energy pulse generation,” Opt. Lett. 25, 587–589 (2000).
[CrossRef]

Baumert, T.

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

Beach, N. M.

Bergt, M.

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

Brennan, C. J.

C. J. Brennan and K. A. Nelson, “Direct time-resolved measurement of anharmonic lattice vibrations in ferroelectric crystals,” J. Chem. Phys. 107, 9691–9694 (1997).
[CrossRef]

Brixner, T.

T. Brixner, N. H. Damrauer, P. Niklaus, and G. Gerber, “Photoselective adaptive femtosecond quantum control in the liquid phase,” Nature 414, 57–60 (2001).
[CrossRef] [PubMed]

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

Bucksbaum, P. H.

T. C. Weinacht, R. Bartels, S. Backus, P. H. Bucksbaum, B. Pearson, J. M. Geremia, H. Rabitz, H. C. Kapteyn, and M.M. Murnane, “Coherent learning control of vibrational motion in room temperature molecular gases,” Chem. Phys. Lett. 344, 333–338 (2001).
[CrossRef]

B. J. Pearson, J. L. White, T. C. Weinacht, and P. H. Bucksbaum, “Coherent control using adaptive learning algorithms,” Phys. Rev. A 63, 063412 (2001).
[CrossRef]

P. H. Bucksbaum and R. Merlin, “The phonon Bragg switch: a proposal to generate sub-picosecond x ray pulses,” Solid State Commun. 111, 535–539 (1999).
[CrossRef]

Carpenter, S. D.

C. J. Bardeen, V. V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

Chen, P.

P. Chen, A. Spitkovsky, T. Katsouleas, and W. Mori, “Transformer ratio and pulse shaping in laser wakefield acccelerators,” Nucl. Instrum. Methods Phys. Res. A 410, 488–492 (1998).
[CrossRef]

Cheriaux, G.

Christov, I. P.

R. Bartels, S. Backus, I. P. Christov, H. C. Kapteyn, and M. M. Murnane, “Attosecond time-scale feedback control of coherent x ray generation,” Chem. Phys. 267, 277–289 (2001).
[CrossRef]

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]

Damrauer, N. H.

T. Brixner, N. H. Damrauer, P. Niklaus, and G. Gerber, “Photoselective adaptive femtosecond quantum control in the liquid phase,” Nature 414, 57–60 (2001).
[CrossRef] [PubMed]

Dekorsy, T.

T. Dekorsy, W. Kutt, T. Pfeifer, and H. Kurz, “Coherent control of LO-phonon dynamics in opaque semiconductors by femtosecond laser pulses,” Europhys. Lett. 23, 223–228 (1993).
[CrossRef]

Efimov, A.

Esarey, E.

D. Umstadter, E. Esarey, and J. Kim, “Nonlinear plasma waves resonantly driven by optimized laser pulse trains,” Phys. Rev. Lett. 72, 1224–1227 (1994).
[CrossRef] [PubMed]

Feurer, T.

Fienup, J. R.

J. R. Fienup and C. C. Wackerman, “Phase-retrieval stagnation problems and solutions,” J. Opt. Soc. Am. B 3, 1897–1907 (1986).
[CrossRef]

J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
[CrossRef] [PubMed]

Franco, M. A.

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, “A simple method for the determination of the intensity and phase of ultrashort optical pulses,” Opt. Commun. 113, 79–84 (1994).
[CrossRef]

Gallagher, N. C.

Gamble Jr., E. B.

Yong-Xin Yan, E. B. Gamble, Jr., and K. A. Nelson, “Impulsive stimulated scattering: general importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83, 5391–5399 (1985).
[CrossRef]

Gerber, G.

T. Brixner, N. H. Damrauer, P. Niklaus, and G. Gerber, “Photoselective adaptive femtosecond quantum control in the liquid phase,” Nature 414, 57–60 (2001).
[CrossRef] [PubMed]

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

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “Phase determination from image and diffraction plane pictures in the electron microscope,” Optik 35, 237–246 (1972).

Geremia, J. M.

T. C. Weinacht, R. Bartels, S. Backus, P. H. Bucksbaum, B. Pearson, J. M. Geremia, H. Rabitz, H. C. Kapteyn, and M.M. Murnane, “Coherent learning control of vibrational motion in room temperature molecular gases,” Chem. Phys. Lett. 344, 333–338 (2001).
[CrossRef]

Hacker, M.

Hase, M.

M. Hase, T. Itano, K. Mizoguchi, and S. I. Nakashima, “Selective enhancement of coherent optical phonons using THz-rate pulse train,” Jpn. J. Appl. Phys., 37, L281–L283 (1998).
[CrossRef]

Hornung, T.

T. Hornung, R. Meier, and M. Motzkus, “Optimal control of molecular states in a loop with a parameterization in frequency and time domain,” Chem. Phys. Lett. 326, 445–453 (2000).
[CrossRef]

Itano, T.

M. Hase, T. Itano, K. Mizoguchi, and S. I. Nakashima, “Selective enhancement of coherent optical phonons using THz-rate pulse train,” Jpn. J. Appl. Phys., 37, L281–L283 (1998).
[CrossRef]

Joffre, M.

Judson, R. S.

R. S. Judson and H. Rabitz, “Teaching lasers to control molecules,” Phys. Rev. Lett. 68, 1500–1503 (1992).
[CrossRef] [PubMed]

Kapteyn, H. C.

T. C. Weinacht, R. Bartels, S. Backus, P. H. Bucksbaum, B. Pearson, J. M. Geremia, H. Rabitz, H. C. Kapteyn, and M.M. Murnane, “Coherent learning control of vibrational motion in room temperature molecular gases,” Chem. Phys. Lett. 344, 333–338 (2001).
[CrossRef]

R. Bartels, S. Backus, I. P. Christov, H. C. Kapteyn, and M. M. Murnane, “Attosecond time-scale feedback control of coherent x ray generation,” Chem. Phys. 267, 277–289 (2001).
[CrossRef]

E. Zeek, R. Bartels, M. M. Murnane, H. C. Kapteyn, S. Backus, and G. Vdovin, “Adaptive pulse compression for transform-limited 15-fs high-energy pulse generation,” Opt. Lett. 25, 587–589 (2000).
[CrossRef]

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]

Katsouleas, T.

P. Chen, A. Spitkovsky, T. Katsouleas, and W. Mori, “Transformer ratio and pulse shaping in laser wakefield acccelerators,” Nucl. Instrum. Methods Phys. Res. A 410, 488–492 (1998).
[CrossRef]

Kiefer, B.

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

Kim, J.

D. Umstadter, E. Esarey, and J. Kim, “Nonlinear plasma waves resonantly driven by optimized laser pulse trains,” Phys. Rev. Lett. 72, 1224–1227 (1994).
[CrossRef] [PubMed]

Krause, J. L.

A. Efimov, M. D. Moores, B. Mei, J. L. Krause, C. W. Siders, and D. H. Reitze, “Minimization of phase distortion in an ultrafast chirped-pulse amplifier using adaptive learning,” Appl. Phys. B 70, S133–S141 (2000).
[CrossRef]

A. Efimov, M. D. Moores, N. M. Beach, J. L. Krause, and D. H. Reitze, “Adaptive control of pulse phase in a chirped-pulse amplifier,” Opt. Lett. 23, 1915–1917 (1998).
[CrossRef]

Kurz, H.

T. Dekorsy, W. Kutt, T. Pfeifer, and H. Kurz, “Coherent control of LO-phonon dynamics in opaque semiconductors by femtosecond laser pulses,” Europhys. Lett. 23, 223–228 (1993).
[CrossRef]

Kutt, W.

T. Dekorsy, W. Kutt, T. Pfeifer, and H. Kurz, “Coherent control of LO-phonon dynamics in opaque semiconductors by femtosecond laser pulses,” Europhys. Lett. 23, 223–228 (1993).
[CrossRef]

Leaird, D. E.

Lepetit, L.

Liu, B.

Mei, B.

A. Efimov, M. D. Moores, B. Mei, J. L. Krause, C. W. Siders, and D. H. Reitze, “Minimization of phase distortion in an ultrafast chirped-pulse amplifier using adaptive learning,” Appl. Phys. B 70, S133–S141 (2000).
[CrossRef]

Meier, R.

T. Hornung, R. Meier, and M. Motzkus, “Optimal control of molecular states in a loop with a parameterization in frequency and time domain,” Chem. Phys. Lett. 326, 445–453 (2000).
[CrossRef]

Merlin, R.

P. H. Bucksbaum and R. Merlin, “The phonon Bragg switch: a proposal to generate sub-picosecond x ray pulses,” Solid State Commun. 111, 535–539 (1999).
[CrossRef]

Meshulach, D.

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]

Mizoguchi, K.

M. Hase, T. Itano, K. Mizoguchi, and S. I. Nakashima, “Selective enhancement of coherent optical phonons using THz-rate pulse train,” Jpn. J. Appl. Phys., 37, L281–L283 (1998).
[CrossRef]

Moores, M. D.

Mori, W.

P. Chen, A. Spitkovsky, T. Katsouleas, and W. Mori, “Transformer ratio and pulse shaping in laser wakefield acccelerators,” Nucl. Instrum. Methods Phys. Res. A 410, 488–492 (1998).
[CrossRef]

Motzkus, M.

T. Hornung, R. Meier, and M. Motzkus, “Optimal control of molecular states in a loop with a parameterization in frequency and time domain,” Chem. Phys. Lett. 326, 445–453 (2000).
[CrossRef]

Murnane, M. M.

R. Bartels, S. Backus, I. P. Christov, H. C. Kapteyn, and M. M. Murnane, “Attosecond time-scale feedback control of coherent x ray generation,” Chem. Phys. 267, 277–289 (2001).
[CrossRef]

E. Zeek, R. Bartels, M. M. Murnane, H. C. Kapteyn, S. Backus, and G. Vdovin, “Adaptive pulse compression for transform-limited 15-fs high-energy pulse generation,” Opt. Lett. 25, 587–589 (2000).
[CrossRef]

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]

Murnane, M.M.

T. C. Weinacht, R. Bartels, S. Backus, P. H. Bucksbaum, B. Pearson, J. M. Geremia, H. Rabitz, H. C. Kapteyn, and M.M. Murnane, “Coherent learning control of vibrational motion in room temperature molecular gases,” Chem. Phys. Lett. 344, 333–338 (2001).
[CrossRef]

Mysyrowicz, A.

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, “A simple method for the determination of the intensity and phase of ultrashort optical pulses,” Opt. Commun. 113, 79–84 (1994).
[CrossRef]

Nakashima, S. I.

M. Hase, T. Itano, K. Mizoguchi, and S. I. Nakashima, “Selective enhancement of coherent optical phonons using THz-rate pulse train,” Jpn. J. Appl. Phys., 37, L281–L283 (1998).
[CrossRef]

Nelson, K. A.

C. J. Brennan and K. A. Nelson, “Direct time-resolved measurement of anharmonic lattice vibrations in ferroelectric crystals,” J. Chem. Phys. 107, 9691–9694 (1997).
[CrossRef]

M. M. Wefers and K. A. Nelson, “Analysis of programmable ultrashort waveform generation using liquid-crystal spatial light modulators,” J. Opt. Soc. Am. B 12, 1343–1362 (1995).
[CrossRef]

Yong-Xin Yan, E. B. Gamble, Jr., and K. A. Nelson, “Impulsive stimulated scattering: general importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83, 5391–5399 (1985).
[CrossRef]

Nelson, Keith A.

A. M. Weiner, D. E. Leaird, Gary P. Wiederrecht, and Keith A. Nelson, “Femtosecond pulse sequences used for optical manipulation of molecular motion,” Science 247, 1317–1319 (1990).
[CrossRef] [PubMed]

Nibbering, E. T. J.

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, “A simple method for the determination of the intensity and phase of ultrashort optical pulses,” Opt. Commun. 113, 79–84 (1994).
[CrossRef]

Niklaus, P.

T. Brixner, N. H. Damrauer, P. Niklaus, and G. Gerber, “Photoselective adaptive femtosecond quantum control in the liquid phase,” Nature 414, 57–60 (2001).
[CrossRef] [PubMed]

Omenetto, F. G.

Oudin, S.

Pearson, B.

T. C. Weinacht, R. Bartels, S. Backus, P. H. Bucksbaum, B. Pearson, J. M. Geremia, H. Rabitz, H. C. Kapteyn, and M.M. Murnane, “Coherent learning control of vibrational motion in room temperature molecular gases,” Chem. Phys. Lett. 344, 333–338 (2001).
[CrossRef]

Pearson, B. J.

B. J. Pearson, J. L. White, T. C. Weinacht, and P. H. Bucksbaum, “Coherent control using adaptive learning algorithms,” Phys. Rev. A 63, 063412 (2001).
[CrossRef]

Peatross, J.

Pfeifer, T.

T. Dekorsy, W. Kutt, T. Pfeifer, and H. Kurz, “Coherent control of LO-phonon dynamics in opaque semiconductors by femtosecond laser pulses,” Europhys. Lett. 23, 223–228 (1993).
[CrossRef]

Prade, B. S.

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, “A simple method for the determination of the intensity and phase of ultrashort optical pulses,” Opt. Commun. 113, 79–84 (1994).
[CrossRef]

Rabitz, H.

T. C. Weinacht, R. Bartels, S. Backus, P. H. Bucksbaum, B. Pearson, J. M. Geremia, H. Rabitz, H. C. Kapteyn, and M.M. Murnane, “Coherent learning control of vibrational motion in room temperature molecular gases,” Chem. Phys. Lett. 344, 333–338 (2001).
[CrossRef]

R. S. Judson and H. Rabitz, “Teaching lasers to control molecules,” Phys. Rev. Lett. 68, 1500–1503 (1992).
[CrossRef] [PubMed]

Reitze, D. H.

Rundquist, A.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “Phase determination from image and diffraction plane pictures in the electron microscope,” Optik 35, 237–246 (1972).

Schaffer, C.

Schins, J. M.

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, “A simple method for the determination of the intensity and phase of ultrashort optical pulses,” Opt. Commun. 113, 79–84 (1994).
[CrossRef]

Seyfried, V.

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

Siders, C. W.

A. Efimov, M. D. Moores, B. Mei, J. L. Krause, C. W. Siders, and D. H. Reitze, “Minimization of phase distortion in an ultrafast chirped-pulse amplifier using adaptive learning,” Appl. Phys. B 70, S133–S141 (2000).
[CrossRef]

Silberberg, Y.

Spitkovsky, A.

P. Chen, A. Spitkovsky, T. Katsouleas, and W. Mori, “Transformer ratio and pulse shaping in laser wakefield acccelerators,” Nucl. Instrum. Methods Phys. Res. A 410, 488–492 (1998).
[CrossRef]

Stobrawa, G.

Strehle, M.

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

Taylor, A. J.

Umstadter, D.

D. Umstadter, E. Esarey, and J. Kim, “Nonlinear plasma waves resonantly driven by optimized laser pulse trains,” Phys. Rev. Lett. 72, 1224–1227 (1994).
[CrossRef] [PubMed]

Vdovin, G.

E. Zeek, R. Bartels, M. M. Murnane, H. C. Kapteyn, S. Backus, and G. Vdovin, “Adaptive pulse compression for transform-limited 15-fs high-energy pulse generation,” Opt. Lett. 25, 587–589 (2000).
[CrossRef]

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]

Wackerman, C. C.

J. R. Fienup and C. C. Wackerman, “Phase-retrieval stagnation problems and solutions,” J. Opt. Soc. Am. B 3, 1897–1907 (1986).
[CrossRef]

Warren, W. S.

C. J. Bardeen, V. V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

Weber, P. M.

C. J. Bardeen, V. V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

Wefers, M. M.

Weinacht, T. C.

T. C. Weinacht, R. Bartels, S. Backus, P. H. Bucksbaum, B. Pearson, J. M. Geremia, H. Rabitz, H. C. Kapteyn, and M.M. Murnane, “Coherent learning control of vibrational motion in room temperature molecular gases,” Chem. Phys. Lett. 344, 333–338 (2001).
[CrossRef]

B. J. Pearson, J. L. White, T. C. Weinacht, and P. H. Bucksbaum, “Coherent control using adaptive learning algorithms,” Phys. Rev. A 63, 063412 (2001).
[CrossRef]

Weiner, A. M.

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71, 1929–1960 (2000).
[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. A 10, 1112–1120 (1993).
[CrossRef]

A. M. Weiner, D. E. Leaird, Gary P. Wiederrecht, and Keith A. Nelson, “Femtosecond pulse sequences used for optical manipulation of molecular motion,” Science 247, 1317–1319 (1990).
[CrossRef] [PubMed]

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

White, J. L.

B. J. Pearson, J. L. White, T. C. Weinacht, and P. H. Bucksbaum, “Coherent control using adaptive learning algorithms,” Phys. Rev. A 63, 063412 (2001).
[CrossRef]

Wiederrecht, Gary P.

A. M. Weiner, D. E. Leaird, Gary P. Wiederrecht, and Keith A. Nelson, “Femtosecond pulse sequences used for optical manipulation of molecular motion,” Science 247, 1317–1319 (1990).
[CrossRef] [PubMed]

Wilson, K. R.

C. J. Bardeen, V. V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

Yakovlev, V. V.

C. J. Bardeen, V. V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

Yan, Yong-Xin

Yong-Xin Yan, E. B. Gamble, Jr., and K. A. Nelson, “Impulsive stimulated scattering: general importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83, 5391–5399 (1985).
[CrossRef]

Yelin, D.

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]

E. Zeek, R. Bartels, M. M. Murnane, H. C. Kapteyn, S. Backus, and G. Vdovin, “Adaptive pulse compression for transform-limited 15-fs high-energy pulse generation,” Opt. Lett. 25, 587–589 (2000).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. B (1)

A. Efimov, M. D. Moores, B. Mei, J. L. Krause, C. W. Siders, and D. H. Reitze, “Minimization of phase distortion in an ultrafast chirped-pulse amplifier using adaptive learning,” Appl. Phys. B 70, S133–S141 (2000).
[CrossRef]

Chem. Phys. (1)

R. Bartels, S. Backus, I. P. Christov, H. C. Kapteyn, and M. M. Murnane, “Attosecond time-scale feedback control of coherent x ray generation,” Chem. Phys. 267, 277–289 (2001).
[CrossRef]

Chem. Phys. Lett. (3)

T. C. Weinacht, R. Bartels, S. Backus, P. H. Bucksbaum, B. Pearson, J. M. Geremia, H. Rabitz, H. C. Kapteyn, and M.M. Murnane, “Coherent learning control of vibrational motion in room temperature molecular gases,” Chem. Phys. Lett. 344, 333–338 (2001).
[CrossRef]

C. J. Bardeen, V. V. Yakovlev, K. R. Wilson, S. D. Carpenter, P. M. Weber, and W. S. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

T. Hornung, R. Meier, and M. Motzkus, “Optimal control of molecular states in a loop with a parameterization in frequency and time domain,” Chem. Phys. Lett. 326, 445–453 (2000).
[CrossRef]

Europhys. Lett. (1)

T. Dekorsy, W. Kutt, T. Pfeifer, and H. Kurz, “Coherent control of LO-phonon dynamics in opaque semiconductors by femtosecond laser pulses,” Europhys. Lett. 23, 223–228 (1993).
[CrossRef]

J. Chem. Phys. (2)

Yong-Xin Yan, E. B. Gamble, Jr., and K. A. Nelson, “Impulsive stimulated scattering: general importance in femtosecond laser pulse interactions with matter, and spectroscopic applications,” J. Chem. Phys. 83, 5391–5399 (1985).
[CrossRef]

C. J. Brennan and K. A. Nelson, “Direct time-resolved measurement of anharmonic lattice vibrations in ferroelectric crystals,” J. Chem. Phys. 107, 9691–9694 (1997).
[CrossRef]

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

J. Opt. Soc. Am. B (6)

Jpn. J. Appl. Phys. (1)

M. Hase, T. Itano, K. Mizoguchi, and S. I. Nakashima, “Selective enhancement of coherent optical phonons using THz-rate pulse train,” Jpn. J. Appl. Phys., 37, L281–L283 (1998).
[CrossRef]

Nature (2)

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]

T. Brixner, N. H. Damrauer, P. Niklaus, and G. Gerber, “Photoselective adaptive femtosecond quantum control in the liquid phase,” Nature 414, 57–60 (2001).
[CrossRef] [PubMed]

Nucl. Instrum. Methods Phys. Res. A (1)

P. Chen, A. Spitkovsky, T. Katsouleas, and W. Mori, “Transformer ratio and pulse shaping in laser wakefield acccelerators,” Nucl. Instrum. Methods Phys. Res. A 410, 488–492 (1998).
[CrossRef]

Opt. Commun. (1)

B. S. Prade, J. M. Schins, E. T. J. Nibbering, M. A. Franco, and A. Mysyrowicz, “A simple method for the determination of the intensity and phase of ultrashort optical pulses,” Opt. Commun. 113, 79–84 (1994).
[CrossRef]

Opt. Express (1)

Opt. Lett. (6)

Optik (1)

R. W. Gerchberg and W. O. Saxton, “Phase determination from image and diffraction plane pictures in the electron microscope,” Optik 35, 237–246 (1972).

Phys. Rev. A (1)

B. J. Pearson, J. L. White, T. C. Weinacht, and P. H. Bucksbaum, “Coherent control using adaptive learning algorithms,” Phys. Rev. A 63, 063412 (2001).
[CrossRef]

Phys. Rev. Lett. (2)

R. S. Judson and H. Rabitz, “Teaching lasers to control molecules,” Phys. Rev. Lett. 68, 1500–1503 (1992).
[CrossRef] [PubMed]

D. Umstadter, E. Esarey, and J. Kim, “Nonlinear plasma waves resonantly driven by optimized laser pulse trains,” Phys. Rev. Lett. 72, 1224–1227 (1994).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71, 1929–1960 (2000).
[CrossRef]

Science (2)

A. M. Weiner, D. E. Leaird, Gary P. Wiederrecht, and Keith A. Nelson, “Femtosecond pulse sequences used for optical manipulation of molecular motion,” Science 247, 1317–1319 (1990).
[CrossRef] [PubMed]

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

Solid State Commun. (1)

P. H. Bucksbaum and R. Merlin, “The phonon Bragg switch: a proposal to generate sub-picosecond x ray pulses,” Solid State Commun. 111, 535–539 (1999).
[CrossRef]

Other (3)

T. Dekorsy, G. C. Cho, and H. Kurz, Coherent Phonons in Condensed Media (Springer-Verlag, Berlin, 2000).

J. D. Grefenstette, GENESIS 5.0, available at http://www.aic.nrl.navy.mil/galist/src/

A. Rundquist, A. Efimov, D. H. Reitze, and M. C. Downer, “Real-time phase mask synthesis for generation of arbitrarily complex waveforms using Gerberg-Saxton algorithm,” in Conference on Lasers and Electro-Optics, Vol. 56 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C. 2001), p. 437.

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Figures (16)

Fig. 1
Fig. 1

Operation of the GS algorithm. The two constraints of the problem are applied sequentially in time and frequency domains.

Fig. 2
Fig. 2

Results obtained with the GA and GS algorithms in temporal (left-hand side) and spectral (right-hand side) domains. The target is a transform-limited pulse at (a) zero delay, (b) -100 fs, (c) +300 fs. Left-hand side, target (dashed curve) and resultant intensity (solid curve). Right-hand side, intensity spectrum (dashed curve) and resultant phase (solid curve). Final values of the cost function are shown on the left.

Fig. 3
Fig. 3

Results for the stretched pulse target. Target durations are (a) 100 fs, (b) 300 fs, (c) 100 fs shifted in time to +200 fs.

Fig. 4
Fig. 4

Results of the GA and GS runs for the five-pulse targets. (a) Equally spaced pulses of transform-limited duration, (b) unequally spaced pulses of transform-limited duration, (c) unequally spaced pulses with increasing duration.

Fig. 5
Fig. 5

Results for the train of two pulse pairs used to control the duration of the A1g coherent phonon mode in sapphire; see Section 4. The separation between inner pulses is (a) 120 fs (b) 200 fs.

Fig. 6
Fig. 6

Triangular pulses with (a) 55 fs and (b) 135 fs duration. In the time domain, although GA results appear to be more robust in the main part of the pulse, they exhibit much more pronounced wing structure than do GS-generated pulses.

Fig. 7
Fig. 7

Computational results for 200-fs square-pulse target. Temporal intensities are shown on linear (top) and log (bottom) scales to highlight differences in the wing structure between the (a) GA and (b) GS results.

Fig. 8
Fig. 8

Cross correlation between the signal and reference pulses (solid curve), and autocorrelation of the signal (dotted–dashed curve) and reference (dashed curve) pulses. Inset, initial and corrected phase difference superimposed on the signal (solid curve) and reference (dashed curve) pulse spectra.

Fig. 9
Fig. 9

Experimental cross correlation of the square pulse (solid curve) compared with the numerical result (dashed curve) shaped with the GA- (top) and GS-generated (bottom) phase masks. Inset, phase difference between the SLM-shaped signal and reference pulses (circles) compared with the phase mask sent to the SLM (solid curve). Circle size corresponds to the estimated measured phase error. Superimposed (dashed curve) is the signal pulse intensity spectrum.

Fig. 10
Fig. 10

Cross correlations (solid curves) and numerical results (dashed curves) for the triangular pulse produced by the GA and GS masks.

Fig. 11
Fig. 11

Pulse train of five unequally spaced pulses of equal duration.

Fig. 12
Fig. 12

Asymmetric pulse train of five pulses of increasing duration.

Fig. 13
Fig. 13

Cross correlations of the resonant pulse trains with 1–17 pulses. Left-hand side, odd, and right-hand side, even number of pulses in each train. To avoid clutter, numerical target is not shown.

Fig. 14
Fig. 14

Left-hand side, cross correlations of the double-pulse sequences with variable interpulse delays produced with the phase masks generated by the GS algorithm; pulse spacing is τ=n×80 fs and is in phase with the A1g mode of sapphire. Right-hand side, in-phase four-pulse sequences with variable spacing between pulse pairs.

Fig. 15
Fig. 15

Time-resolved relative transmittance for in-phase multiple-pulse-train-CP excitation in sapphire. Number of pulses and pump energy increase toward the top. Electronic response is clipped to show the oscillations.

Fig. 16
Fig. 16

CP excitation with four pulses (cross correlations are shown in the insets) The second pair is (a) in phase with the vibration and (b) out of phase with the phonon mode. Nearly complete extinction is evident in the second case.

Tables (1)

Tables Icon

Table 1 Comparison of Final Error Values for GA and GS Algorithms

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

Ek(t)=|Ek(t)|exp[iψk(t)]=FFT-1{E˜k(ω)},
Ek(t)=|Etar(t)|exp[iψk(t)],
E˜k(ω)=|E˜k(ω)exp[iϕk(ψ)]=FFT{Ek(t)},
E˜k+1(ω)=|E˜meas(ω)|exp[iϕk+1(ω)],
|Ek(t)|=|Etar(t)|-αΔEk,
J[ϕ(ω)]=1Ni=1N|Ishape(ti)-Itarg(ti)|,

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