Abstract

We present an experimental study of the control of ultrafast semiconductor nonlinearities by adaptive feedback optical pulse shaping. In the feedback loop, an evolutionary algorithm directs the modulation of the spectral phase of 20-fs laser pulses. In this way, control is achieved over the broadband semiconductor continuum nonlinearity as measured in differential transmission experiments. Design guidelines are given for the implementation of the evolutionary algorithm. Our results demonstrate that a feedback loop with a carefully designed algorithm can serve as a new, sensitive tool in ultrafast semiconductor spectroscopy. Moreover, an optimized feedback loop allows for the substantial enhancement of ultrafast semiconductor nonlinearities.

© 2001 Optical Society of America

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  12. T. Hornung, R. Meier, D. Zeidler, K.-L. Kompa, D. Proch, and M. Motzkus, “Optimal control of one- and two-photon transitions with shaped femtosecond pulses and feedback,” Appl. Phys. B 71, 277–284 (2000).
    [CrossRef]
  13. T. C. Weinacht, J. Ahn, and P. H. Bucksbaum, “Controlling the shape of a quantum wavefunction,” Nature (London) 397, 233–235 (1999).
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    [CrossRef]
  25. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. Sweetser, M. A. Krumbügel, and B. Richman, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 1–19 (1997).
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  29. The ratio 100/15≈7 is chosen to guarantee a sufficiently low selection pressure.17
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    [CrossRef]
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  32. For the SI DT signal, we took the pump-induced transmission change ΔTav normalized to the transmission in absence of the pump T0, av. Both quantities ΔTav and T0, av are averaged individually over the probe spectrum.
  33. J.-P. Foing, D. Hulin, M. Joffre, M. K. Jackson, J.-L. Oudar, C. Tanguay, and M. Combescot, “Absorption edge singularities in highly excited semiconductors,” Phys. Rev. Lett. 68, 110–113 (1992).
    [CrossRef] [PubMed]
  34. K. El Sayed and C. J. Stanton, “Line-shape analysis of differential transmission spectra in the coherent regime,” Phys. Rev. B 55, 9671–9678 (1997).
    [CrossRef]
  35. B. Fluegel, N. Peyghambarian, G. Olbright, M. Lindberg, S. W. Koch, M. Joffre, D. Hulin, A. Migus, and A. Antonetti, “Femtosecond studies of coherent transients in semiconductors,” Phys. Rev. Lett. 59, 2588–2591 (1987).
    [CrossRef] [PubMed]

2000 (7)

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]

D. Zeidler, T. Hornung, D. Proch, and M. Motzkus, “Adaptive compression of tunable pulses from a non-collinear-type OPA to below 16 fs by feedback-controlled pulse shaping,” Appl. Phys. B 70, S125–S131 (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 (London) 406, 164–166 (2000).
[CrossRef]

T. Hornung, R. Meier, D. Zeidler, K.-L. Kompa, D. Proch, and M. Motzkus, “Optimal control of one- and two-photon transitions with shaped femtosecond pulses and feedback,” Appl. Phys. B 71, 277–284 (2000).
[CrossRef]

J. Kunde, B. Baumann, S. Arlt, F. Morier-Genoud, U. Siegner, and U. Keller, “Adaptive feedback control of ultrafast semiconductor nonlinearities,” Appl. Phys. Lett. 77, 924–926 (2000).
[CrossRef]

J. Kunde, S. Arlt, L. Gallmann, F. Morier-Genoud, U. Siegner, and U. Keller, “Sensitive characterization of phase and amplitude semiconductor nonlinearities for broadband 20 fs excitation,” J. Appl. Phys. 88, 1187–1189 (2000).
[CrossRef]

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

1999 (4)

1998 (3)

1997 (5)

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]

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

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, “Femtosecond pulse shaping by an evolutionary algorithm with feedback,” Appl. Phys. B 65, 779–782 (1997).
[CrossRef]

K. El Sayed and C. J. Stanton, “Line-shape analysis of differential transmission spectra in the coherent regime,” Phys. Rev. B 55, 9671–9678 (1997).
[CrossRef]

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. Sweetser, M. A. Krumbügel, and B. Richman, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 1–19 (1997).
[CrossRef]

1996 (1)

M. M. Wefers and K. A. Nelson, “Space-time profiles of shaped ultrafast optical waveforms,” IEEE J. Quantum Electron. 32, 161–172 (1996).
[CrossRef]

1995 (2)

1992 (3)

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

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

J.-P. Foing, D. Hulin, M. Joffre, M. K. Jackson, J.-L. Oudar, C. Tanguay, and M. Combescot, “Absorption edge singularities in highly excited semiconductors,” Phys. Rev. Lett. 68, 110–113 (1992).
[CrossRef] [PubMed]

1990 (1)

1987 (1)

B. Fluegel, N. Peyghambarian, G. Olbright, M. Lindberg, S. W. Koch, M. Joffre, D. Hulin, A. Migus, and A. Antonetti, “Femtosecond studies of coherent transients in semiconductors,” Phys. Rev. Lett. 59, 2588–2591 (1987).
[CrossRef] [PubMed]

Ahn, J.

T. C. Weinacht, J. Ahn, and P. H. Bucksbaum, “Controlling the shape of a quantum wavefunction,” Nature (London) 397, 233–235 (1999).
[CrossRef]

Antonetti, A.

B. Fluegel, N. Peyghambarian, G. Olbright, M. Lindberg, S. W. Koch, M. Joffre, D. Hulin, A. Migus, and A. Antonetti, “Femtosecond studies of coherent transients in semiconductors,” Phys. Rev. Lett. 59, 2588–2591 (1987).
[CrossRef] [PubMed]

Arlt, S.

J. Kunde, B. Baumann, S. Arlt, F. Morier-Genoud, U. Siegner, and U. Keller, “Adaptive feedback control of ultrafast semiconductor nonlinearities,” Appl. Phys. Lett. 77, 924–926 (2000).
[CrossRef]

J. Kunde, S. Arlt, L. Gallmann, F. Morier-Genoud, U. Siegner, and U. Keller, “Sensitive characterization of phase and amplitude semiconductor nonlinearities for broadband 20 fs excitation,” J. Appl. Phys. 88, 1187–1189 (2000).
[CrossRef]

J. Kunde, U. Siegner, S. Arlt, G. Steinmeyer, F. Morier-Genoud, and U. Keller, “Potential of femtosecond chirp con-trol of ultrabroadband semiconductor continuum nonlinearities,” J. Opt. Soc. Am. B 16, 2285–2294 (1999).
[CrossRef]

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.

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 (London) 406, 164–166 (2000).
[CrossRef]

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, 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 (London) 406, 164–166 (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]

Baumann, B.

J. Kunde, B. Baumann, S. Arlt, F. Morier-Genoud, U. Siegner, and U. Keller, “Adaptive feedback control of ultrafast semiconductor nonlinearities,” Appl. Phys. Lett. 77, 924–926 (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]

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, “Femtosecond pulse shaping by an evolutionary algorithm with feedback,” Appl. Phys. B 65, 779–782 (1997).
[CrossRef]

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]

Brixner, T.

T. Brixner, M. Strehle, and G. Gerber, “Feedback-controlled optimization of amplified femtosecond laser pulses,” Appl. Phys. B 68, 281–284 (1999).
[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]

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, “Femtosecond pulse shaping by an evolutionary algorithm with feedback,” Appl. Phys. B 65, 779–782 (1997).
[CrossRef]

Bucksbaum, P. H.

T. C. Weinacht, J. Ahn, and P. H. Bucksbaum, “Controlling the shape of a quantum wavefunction,” Nature (London) 397, 233–235 (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]

Christov, I. P.

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

Combescot, M.

J.-P. Foing, D. Hulin, M. Joffre, M. K. Jackson, J.-L. Oudar, C. Tanguay, and M. Combescot, “Absorption edge singularities in highly excited semiconductors,” Phys. Rev. Lett. 68, 110–113 (1992).
[CrossRef] [PubMed]

DeLong, K. W.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. Sweetser, M. A. Krumbügel, and B. Richman, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 1–19 (1997).
[CrossRef]

Efimov, A.

El Sayed, K.

K. El Sayed and C. J. Stanton, “Line-shape analysis of differential transmission spectra in the coherent regime,” Phys. Rev. B 55, 9671–9678 (1997).
[CrossRef]

Fittinghoff, D. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. Sweetser, M. A. Krumbügel, and B. Richman, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 1–19 (1997).
[CrossRef]

Fluegel, B.

B. Fluegel, N. Peyghambarian, G. Olbright, M. Lindberg, S. W. Koch, M. Joffre, D. Hulin, A. Migus, and A. Antonetti, “Femtosecond studies of coherent transients in semiconductors,” Phys. Rev. Lett. 59, 2588–2591 (1987).
[CrossRef] [PubMed]

Foing, J.-P.

J.-P. Foing, D. Hulin, M. Joffre, M. K. Jackson, J.-L. Oudar, C. Tanguay, and M. Combescot, “Absorption edge singularities in highly excited semiconductors,” Phys. Rev. Lett. 68, 110–113 (1992).
[CrossRef] [PubMed]

Gallmann, L.

J. Kunde, S. Arlt, L. Gallmann, F. Morier-Genoud, U. Siegner, and U. Keller, “Sensitive characterization of phase and amplitude semiconductor nonlinearities for broadband 20 fs excitation,” J. Appl. Phys. 88, 1187–1189 (2000).
[CrossRef]

Gerber, G.

T. Brixner, M. Strehle, and G. Gerber, “Feedback-controlled optimization of amplified femtosecond laser pulses,” Appl. Phys. B 68, 281–284 (1999).
[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]

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, “Femtosecond pulse shaping by an evolutionary algorithm with feedback,” Appl. Phys. B 65, 779–782 (1997).
[CrossRef]

Hornung, T.

D. Zeidler, T. Hornung, D. Proch, and M. Motzkus, “Adaptive compression of tunable pulses from a non-collinear-type OPA to below 16 fs by feedback-controlled pulse shaping,” Appl. Phys. B 70, S125–S131 (2000).
[CrossRef]

T. Hornung, R. Meier, D. Zeidler, K.-L. Kompa, D. Proch, and M. Motzkus, “Optimal control of one- and two-photon transitions with shaped femtosecond pulses and feedback,” Appl. Phys. B 71, 277–284 (2000).
[CrossRef]

Hulin, D.

J.-P. Foing, D. Hulin, M. Joffre, M. K. Jackson, J.-L. Oudar, C. Tanguay, and M. Combescot, “Absorption edge singularities in highly excited semiconductors,” Phys. Rev. Lett. 68, 110–113 (1992).
[CrossRef] [PubMed]

B. Fluegel, N. Peyghambarian, G. Olbright, M. Lindberg, S. W. Koch, M. Joffre, D. Hulin, A. Migus, and A. Antonetti, “Femtosecond studies of coherent transients in semiconductors,” Phys. Rev. Lett. 59, 2588–2591 (1987).
[CrossRef] [PubMed]

Jackson, M. K.

J.-P. Foing, D. Hulin, M. Joffre, M. K. Jackson, J.-L. Oudar, C. Tanguay, and M. Combescot, “Absorption edge singularities in highly excited semiconductors,” Phys. Rev. Lett. 68, 110–113 (1992).
[CrossRef] [PubMed]

Joffre, M.

J.-P. Foing, D. Hulin, M. Joffre, M. K. Jackson, J.-L. Oudar, C. Tanguay, and M. Combescot, “Absorption edge singularities in highly excited semiconductors,” Phys. Rev. Lett. 68, 110–113 (1992).
[CrossRef] [PubMed]

B. Fluegel, N. Peyghambarian, G. Olbright, M. Lindberg, S. W. Koch, M. Joffre, D. Hulin, A. Migus, and A. Antonetti, “Femtosecond studies of coherent transients in semiconductors,” Phys. Rev. Lett. 59, 2588–2591 (1987).
[CrossRef] [PubMed]

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.

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 (London) 406, 164–166 (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]

Keller, U.

J. Kunde, B. Baumann, S. Arlt, F. Morier-Genoud, U. Siegner, and U. Keller, “Adaptive feedback control of ultrafast semiconductor nonlinearities,” Appl. Phys. Lett. 77, 924–926 (2000).
[CrossRef]

J. Kunde, S. Arlt, L. Gallmann, F. Morier-Genoud, U. Siegner, and U. Keller, “Sensitive characterization of phase and amplitude semiconductor nonlinearities for broadband 20 fs excitation,” J. Appl. Phys. 88, 1187–1189 (2000).
[CrossRef]

J. Kunde, U. Siegner, S. Arlt, G. Steinmeyer, F. Morier-Genoud, and U. Keller, “Potential of femtosecond chirp con-trol of ultrabroadband semiconductor continuum nonlinearities,” J. Opt. Soc. Am. B 16, 2285–2294 (1999).
[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]

Koch, S. W.

B. Fluegel, N. Peyghambarian, G. Olbright, M. Lindberg, S. W. Koch, M. Joffre, D. Hulin, A. Migus, and A. Antonetti, “Femtosecond studies of coherent transients in semiconductors,” Phys. Rev. Lett. 59, 2588–2591 (1987).
[CrossRef] [PubMed]

Kompa, K.-L.

T. Hornung, R. Meier, D. Zeidler, K.-L. Kompa, D. Proch, and M. Motzkus, “Optimal control of one- and two-photon transitions with shaped femtosecond pulses and feedback,” Appl. Phys. B 71, 277–284 (2000).
[CrossRef]

Krause, J. L.

Krumbügel, M. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. Sweetser, M. A. Krumbügel, and B. Richman, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 1–19 (1997).
[CrossRef]

Kunde, J.

J. Kunde, S. Arlt, L. Gallmann, F. Morier-Genoud, U. Siegner, and U. Keller, “Sensitive characterization of phase and amplitude semiconductor nonlinearities for broadband 20 fs excitation,” J. Appl. Phys. 88, 1187–1189 (2000).
[CrossRef]

J. Kunde, B. Baumann, S. Arlt, F. Morier-Genoud, U. Siegner, and U. Keller, “Adaptive feedback control of ultrafast semiconductor nonlinearities,” Appl. Phys. Lett. 77, 924–926 (2000).
[CrossRef]

J. Kunde, U. Siegner, S. Arlt, G. Steinmeyer, F. Morier-Genoud, and U. Keller, “Potential of femtosecond chirp con-trol of ultrabroadband semiconductor continuum nonlinearities,” J. Opt. Soc. Am. B 16, 2285–2294 (1999).
[CrossRef]

Leaird, D. E.

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

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, 326–328 (1990).
[CrossRef] [PubMed]

Lindberg, M.

B. Fluegel, N. Peyghambarian, G. Olbright, M. Lindberg, S. W. Koch, M. Joffre, D. Hulin, A. Migus, and A. Antonetti, “Femtosecond studies of coherent transients in semiconductors,” Phys. Rev. Lett. 59, 2588–2591 (1987).
[CrossRef] [PubMed]

Luce, B. P.

Meier, R.

T. Hornung, R. Meier, D. Zeidler, K.-L. Kompa, D. Proch, and M. Motzkus, “Optimal control of one- and two-photon transitions with shaped femtosecond pulses and feedback,” Appl. Phys. B 71, 277–284 (2000).
[CrossRef]

Meshulach, D.

Migus, A.

B. Fluegel, N. Peyghambarian, G. Olbright, M. Lindberg, S. W. Koch, M. Joffre, D. Hulin, A. Migus, and A. Antonetti, “Femtosecond studies of coherent transients in semiconductors,” Phys. Rev. Lett. 59, 2588–2591 (1987).
[CrossRef] [PubMed]

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 (London) 406, 164–166 (2000).
[CrossRef]

Moores, M. D.

Morier-Genoud, F.

J. Kunde, B. Baumann, S. Arlt, F. Morier-Genoud, U. Siegner, and U. Keller, “Adaptive feedback control of ultrafast semiconductor nonlinearities,” Appl. Phys. Lett. 77, 924–926 (2000).
[CrossRef]

J. Kunde, S. Arlt, L. Gallmann, F. Morier-Genoud, U. Siegner, and U. Keller, “Sensitive characterization of phase and amplitude semiconductor nonlinearities for broadband 20 fs excitation,” J. Appl. Phys. 88, 1187–1189 (2000).
[CrossRef]

J. Kunde, U. Siegner, S. Arlt, G. Steinmeyer, F. Morier-Genoud, and U. Keller, “Potential of femtosecond chirp con-trol of ultrabroadband semiconductor continuum nonlinearities,” J. Opt. Soc. Am. B 16, 2285–2294 (1999).
[CrossRef]

Motzkus, M.

T. Hornung, R. Meier, D. Zeidler, K.-L. Kompa, D. Proch, and M. Motzkus, “Optimal control of one- and two-photon transitions with shaped femtosecond pulses and feedback,” Appl. Phys. B 71, 277–284 (2000).
[CrossRef]

D. Zeidler, T. Hornung, D. Proch, and M. Motzkus, “Adaptive compression of tunable pulses from a non-collinear-type OPA to below 16 fs by feedback-controlled pulse shaping,” Appl. Phys. B 70, S125–S131 (2000).
[CrossRef]

Murnane, M. M.

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 (London) 406, 164–166 (2000).
[CrossRef]

Nelson, K. A.

Olbright, G.

B. Fluegel, N. Peyghambarian, G. Olbright, M. Lindberg, S. W. Koch, M. Joffre, D. Hulin, A. Migus, and A. Antonetti, “Femtosecond studies of coherent transients in semiconductors,” Phys. Rev. Lett. 59, 2588–2591 (1987).
[CrossRef] [PubMed]

Omenetto, F. G.

Oudar, J.-L.

J.-P. Foing, D. Hulin, M. Joffre, M. K. Jackson, J.-L. Oudar, C. Tanguay, and M. Combescot, “Absorption edge singularities in highly excited semiconductors,” Phys. Rev. Lett. 68, 110–113 (1992).
[CrossRef] [PubMed]

Patel, J. S.

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

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, 326–328 (1990).
[CrossRef] [PubMed]

Peyghambarian, N.

B. Fluegel, N. Peyghambarian, G. Olbright, M. Lindberg, S. W. Koch, M. Joffre, D. Hulin, A. Migus, and A. Antonetti, “Femtosecond studies of coherent transients in semiconductors,” Phys. Rev. Lett. 59, 2588–2591 (1987).
[CrossRef] [PubMed]

Proch, D.

D. Zeidler, T. Hornung, D. Proch, and M. Motzkus, “Adaptive compression of tunable pulses from a non-collinear-type OPA to below 16 fs by feedback-controlled pulse shaping,” Appl. Phys. B 70, S125–S131 (2000).
[CrossRef]

T. Hornung, R. Meier, D. Zeidler, K.-L. Kompa, D. Proch, and M. Motzkus, “Optimal control of one- and two-photon transitions with shaped femtosecond pulses and feedback,” Appl. Phys. B 71, 277–284 (2000).
[CrossRef]

Rabitz, H.

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

Reitze, D. H.

Richman, B.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. Sweetser, M. A. Krumbügel, and B. Richman, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 1–19 (1997).
[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]

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, “Femtosecond pulse shaping by an evolutionary algorithm with feedback,” Appl. Phys. B 65, 779–782 (1997).
[CrossRef]

Siegner, U.

J. Kunde, S. Arlt, L. Gallmann, F. Morier-Genoud, U. Siegner, and U. Keller, “Sensitive characterization of phase and amplitude semiconductor nonlinearities for broadband 20 fs excitation,” J. Appl. Phys. 88, 1187–1189 (2000).
[CrossRef]

J. Kunde, B. Baumann, S. Arlt, F. Morier-Genoud, U. Siegner, and U. Keller, “Adaptive feedback control of ultrafast semiconductor nonlinearities,” Appl. Phys. Lett. 77, 924–926 (2000).
[CrossRef]

J. Kunde, U. Siegner, S. Arlt, G. Steinmeyer, F. Morier-Genoud, and U. Keller, “Potential of femtosecond chirp con-trol of ultrabroadband semiconductor continuum nonlinearities,” J. Opt. Soc. Am. B 16, 2285–2294 (1999).
[CrossRef]

Silberberg, Y.

Stanton, C. J.

K. El Sayed and C. J. Stanton, “Line-shape analysis of differential transmission spectra in the coherent regime,” Phys. Rev. B 55, 9671–9678 (1997).
[CrossRef]

Steinmeyer, G.

Strehle, M.

T. Brixner, M. Strehle, and G. Gerber, “Feedback-controlled optimization of amplified femtosecond laser pulses,” Appl. Phys. B 68, 281–284 (1999).
[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]

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, “Femtosecond pulse shaping by an evolutionary algorithm with feedback,” Appl. Phys. B 65, 779–782 (1997).
[CrossRef]

Sweetser, J.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. Sweetser, M. A. Krumbügel, and B. Richman, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 1–19 (1997).
[CrossRef]

Tanguay, C.

J.-P. Foing, D. Hulin, M. Joffre, M. K. Jackson, J.-L. Oudar, C. Tanguay, and M. Combescot, “Absorption edge singularities in highly excited semiconductors,” Phys. Rev. Lett. 68, 110–113 (1992).
[CrossRef] [PubMed]

Taylor, A. J.

Trebino, R.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. Sweetser, M. A. Krumbügel, and B. Richman, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 1–19 (1997).
[CrossRef]

Vdovin, G.

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

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, J. Ahn, and P. H. Bucksbaum, “Controlling the shape of a quantum wavefunction,” Nature (London) 397, 233–235 (1999).
[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, D. E. Leaird, J. S. Patel, and J. R. Wullert, “Programmable shaping of femtosecond optical pulses by use of 128-element liquid crystal phase modulator,” IEEE J. Quantum Electron. 28, 908–920 (1992).
[CrossRef]

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, 326–328 (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]

Wullert, J. R.

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

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, 326–328 (1990).
[CrossRef] [PubMed]

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]

Yelin, D.

Zeek, E.

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 (London) 406, 164–166 (2000).
[CrossRef]

Zeidler, D.

D. Zeidler, T. Hornung, D. Proch, and M. Motzkus, “Adaptive compression of tunable pulses from a non-collinear-type OPA to below 16 fs by feedback-controlled pulse shaping,” Appl. Phys. B 70, S125–S131 (2000).
[CrossRef]

T. Hornung, R. Meier, D. Zeidler, K.-L. Kompa, D. Proch, and M. Motzkus, “Optimal control of one- and two-photon transitions with shaped femtosecond pulses and feedback,” Appl. Phys. B 71, 277–284 (2000).
[CrossRef]

Appl. Phys. B (4)

D. Zeidler, T. Hornung, D. Proch, and M. Motzkus, “Adaptive compression of tunable pulses from a non-collinear-type OPA to below 16 fs by feedback-controlled pulse shaping,” Appl. Phys. B 70, S125–S131 (2000).
[CrossRef]

T. Baumert, T. Brixner, V. Seyfried, M. Strehle, and G. Gerber, “Femtosecond pulse shaping by an evolutionary algorithm with feedback,” Appl. Phys. B 65, 779–782 (1997).
[CrossRef]

T. Hornung, R. Meier, D. Zeidler, K.-L. Kompa, D. Proch, and M. Motzkus, “Optimal control of one- and two-photon transitions with shaped femtosecond pulses and feedback,” Appl. Phys. B 71, 277–284 (2000).
[CrossRef]

T. Brixner, M. Strehle, and G. Gerber, “Feedback-controlled optimization of amplified femtosecond laser pulses,” Appl. Phys. B 68, 281–284 (1999).
[CrossRef]

Appl. Phys. Lett. (1)

J. Kunde, B. Baumann, S. Arlt, F. Morier-Genoud, U. Siegner, and U. Keller, “Adaptive feedback control of ultrafast semiconductor nonlinearities,” Appl. Phys. Lett. 77, 924–926 (2000).
[CrossRef]

Chem. Phys. Lett. (1)

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]

IEEE J. Quantum Electron. (2)

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

M. M. Wefers and K. A. Nelson, “Space-time profiles of shaped ultrafast optical waveforms,” IEEE J. Quantum Electron. 32, 161–172 (1996).
[CrossRef]

J. Appl. Phys. (1)

J. Kunde, S. Arlt, L. Gallmann, F. Morier-Genoud, U. Siegner, and U. Keller, “Sensitive characterization of phase and amplitude semiconductor nonlinearities for broadband 20 fs excitation,” J. Appl. Phys. 88, 1187–1189 (2000).
[CrossRef]

J. Opt. Soc. Am. B (4)

Nature (London) (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 (London) 406, 164–166 (2000).
[CrossRef]

T. C. Weinacht, J. Ahn, and P. H. Bucksbaum, “Controlling the shape of a quantum wavefunction,” Nature (London) 397, 233–235 (1999).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. B (1)

K. El Sayed and C. J. Stanton, “Line-shape analysis of differential transmission spectra in the coherent regime,” Phys. Rev. B 55, 9671–9678 (1997).
[CrossRef]

Phys. Rev. Lett. (3)

B. Fluegel, N. Peyghambarian, G. Olbright, M. Lindberg, S. W. Koch, M. Joffre, D. Hulin, A. Migus, and A. Antonetti, “Femtosecond studies of coherent transients in semiconductors,” Phys. Rev. Lett. 59, 2588–2591 (1987).
[CrossRef] [PubMed]

J.-P. Foing, D. Hulin, M. Joffre, M. K. Jackson, J.-L. Oudar, C. Tanguay, and M. Combescot, “Absorption edge singularities in highly excited semiconductors,” Phys. Rev. Lett. 68, 110–113 (1992).
[CrossRef] [PubMed]

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

Rev. Sci. Instrum. (2)

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

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. Sweetser, M. A. Krumbügel, and B. Richman, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 1–19 (1997).
[CrossRef]

Science (1)

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]

Other (8)

J. Shah, Ultrafast Spectroscopy of Semiconductors and Semiconductor Nanostructures, 2nd ed. (Springer-Verlag, Berlin, 1999).

H. Haug and A.-P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors (Springer-Verlag, Berlin, 1996).

H. P. Schwefel, Evolution and Optimum Seeking (Wiley, New York, 1995).

A. Efimov and D. H. Reitze, “FROG characterization of complex SLM-shaped amplified waveforms,” in Conference on Lasers and Electro-Optics, Vol. 39 of 2000 OSA Technical Digest Series (Optical Society of America, Washington D.C., 2000), pp. 621–622.

T. Bäck, Evolutionary Algorithms in Theory and Practice (Oxford U. Press, New York, 1996).

The ratio 100/15≈7 is chosen to guarantee a sufficiently low selection pressure.17

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, Pa., 1993).

For the SI DT signal, we took the pump-induced transmission change ΔTav normalized to the transmission in absence of the pump T0, av. Both quantities ΔTav and T0, av are averaged individually over the probe spectrum.

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Figures (11)

Fig. 1
Fig. 1

(a) Experimental setup for adaptive feedback control of the SI DT and the DT in narrow spectral windows. Solid lines indicate the optical beam path. The dashed lines illustrate how the feedback loop is closed between the experiment and the pulse shaper. The ES also directs the pump–probe (PP) delay. For pulse compression experiments, the semiconductor sample is replaced with a 10-µm-thick β barium borate crystal, and the time-integrated second-harmonic generation signal of the pump or the probe pulse serves as merit function. (b) The absorption spectrum of the Al0.06Ga0.94As sample (solid curve) and the excitation pulse spectrum (shaded area) are shown.

Fig. 2
Fig. 2

Average mutation step length σav and root-mean-square phase deviation Δφrms for a pulse compression experiment.

Fig. 3
Fig. 3

Optimized phase shapes for pulse compression experiments for a chirp expansion up to third-order dispersion (dashed curve), up to sixth-order dispersion (solid curve), and for the optimization of the spectral phase differences between all pixels independently (dotted curve). The shaded area is the excitation pulse spectrum.

Fig. 4
Fig. 4

Comparison of three different crossover operators that can be used to produce one offspring from parents 1 and 2.

Fig. 5
Fig. 5

Pulse compression experiments. Comparison of the convergence speed with a one-point crossover (dashed curves), discrete crossover (solid curves), and without crossover operator (dotted curves). (a) A chirp expansion up to sixth-order dispersion was used, and (b) the spectral phase differences between all pixels were optimized independently.

Fig. 6
Fig. 6

DT experiments. Comparison of the convergence speed with a one-point crossover (dashed curve), discrete crossover (solid curve), and without a crossover operator (dotted curve) for the maximization of the DT at 1.625 eV. The spectral phase differences between all pixels were optimized independently.

Fig. 7
Fig. 7

SI DT for the optimized phase φSI,max and for the optimization of only the slope of a linear chirp. Temperature is 300 K; Nexc3×1017 cm-3.

Fig. 8
Fig. 8

(a) Average of several optimization runs (dotted curves) yields the optimum phase φSI,max (solid curve), which maximizes the SI DT. Shown for comparison is the phase corresponding to a linear chirp (dashed curve). The shaded area is the excitation pulse spectrum. Temperature is 300 K; Nexc3×1017 cm-3. (b) Group delay (dφ/dω) obtained from φSI,max (solid curve) as compared with a linear chirp (dashed curve).

Fig. 9
Fig. 9

Calculated SI DT in arbitrary units for the optimized phase φSI,max and for the optimization of only the slope of a linear chirp.

Fig. 10
Fig. 10

DT at 1.625 eV for unchirped pulses (dotted curve) and after the positive DT (solid curve) or the negative DT (dashed curve) is maximized. Temperature 300 K; Nexc3×1017 cm-3.

Fig. 11
Fig. 11

Optimum phases φ (solid curves) that maximize the (a) positive or (b) negative DT (shown in Fig. 10) at 1.625 eV. Also shown are the corresponding DT spectra (dotted curves) and the excitation pulse spectrum (shaded area). Temperature 300 K; Nexc3×1017 cm-3.

Equations (2)

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φ(ω)=12d2φ/dω2|ω=ω0(ω-ω0)2+16d3φ/dω3|ω=ω0(ω-ω0)3+..
=GDD(ω-ω0)2+TOD(ω-ω0)3+..

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