Abstract

We demonstrate a new approach to laser control using binary phase shaping. We apply this method to the problem of spectrally narrowing multiphoton excitation using shaped laser pulses as required for selectivity in two-photon microscopy. The symmetry of the problem is analyzed from first principles and a rational solution is proposed. Successful experimental implementation and simulations are presented using 10 fs ultrashort pulses. The proposed solution is a factor of 6 better than the sinusoidal phase used previously by our group. An evolutionary learning algorithm was used to efficiently improve the solution by a further factor of 2.5 because of the greatly reduced search space afforded by binary phase shaping.

© 2004 Optical Society of America

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  1. R.S. Judson and H. Rabitz, “Teaching Lasers to Control Molecules,” Phys. Rev. Lett. 68, 1500–1503 (1992)
    [Crossref] [PubMed]
  2. 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]
  3. 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]
  4. D. Goswami, “Optical pulse shaping approaches to coherent control,” Phys. Rep. 374, 385–481 (2003)
    [Crossref]
  5. M. Shapiro and P. Brumer, “On the origin of pulse shaping control of molecular dynamics,” J. Phys. Chem. A 105, 2897–2902 (2001)
    [Crossref]
  6. I. Pastirk, J.M. Dela Cruz, K.A. Walowicz, V.V. Lozovoy, and M. Dantus, “Selective two-photon microscopy with shaped femtosecond pulses,” Opt. Express 11, 1695–1701 (2003)
    [Crossref] [PubMed]
  7. J.M. Dela Cruz, I. Pastirk, V.V. Lozovoy, K.A. Walowicz, and M. Dantus, “Multiphoton intrapulse interference 3: Probing microscopic chemical environments,” J. Phys. Chem. A 108, 53–58 (2004)
    [Crossref]
  8. V.V. Lozovoy, I. Pastirk, K.A. Walowicz, and M. Dantus, “Multiphoton intrapulse interference. 2. Control of two-and three-photon laser induced fluorescence with shaped pulses,” J. Chem. Phys. 118, 3187–3196 (2003)
    [Crossref]
  9. K.A. Walowicz, I. Pastirk, V.V. Lozovoy, and M. Dantus, “Multiphoton intrapulse interference. 1. Control of multiphoton processes in condensed phases,” J. Phys. Chem. A 106, 9369–9373 (2002)
    [Crossref]
  10. B. Broers, L.D. Noordam, and H.B.V. Vandenheuvell, “Diffraction and focusing of spectral energy in multiphoton processes,” Phys. Rev. A 46, 2749–2756 (1992)
    [Crossref] [PubMed]
  11. M. Hacker, R. Netz, M. Roth, G. Stobrawa, T. Feurer, and R. Sauerbrey, “Frequency doubling of phase-modulated, Ultrashort Laser Pulses,” Appl. Phys. B. 73, 273–277 (2001)
    [Crossref]
  12. V.V. Lozovoy, I. Pastirk, and M. Dantus, “Multiphoton intrapulse interference. 4. Characterization of the phase of ultrashort laser pulses,” Opt. Lett. 7, 775–777 (2004)
    [Crossref]
  13. Z. Zheng and A.M. Weiner, “Spectral phase correlation of coded femtosecond pulses by second-harmonic generation in thick nonlinear crystals,” Opt. Lett. 25, 984–986 (2000)
    [Crossref]
  14. Z. Zheng and A.M. Weiner, “Coherent control of second harmonic generation using spectrally phase coded femtosecond waveforms,” Chem. Phys. 267, 161–171 (2001)
    [Crossref]
  15. A.M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71, 1929–1960 (2000)
    [Crossref]
  16. L. Wang and A.M. Weiner, “Programmable spectral phase coding of an amplified spontaneous emission light source,” 167, 211–224 (1999)
  17. D. Meshulach and Y. Silberberg, “Coherent quantum control of multiphoton transitions by shaped ultrashort optical pulses,” Phys. Rev. A 60, 1287–1292 (1999)
    [Crossref]
  18. N. Dudovich, B. Dayan, S.M.G. Faeder, and Y. Silberberg, “Transform-limited pulses are not optimal for resonant multiphoton transitions,” Phys. Rev. Lett. 86, 47–50 (2001)
    [Crossref] [PubMed]
  19. J.L. Herek, W. Wohlleben, R.J. Cogdell, D. Zeidler, and M. Motzkus, “Quantum control of energy flow in light harvesting,” Nature 417, 533–535 (2002)
    [Crossref] [PubMed]
  20. 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]
  21. D. Zeidler, S. Frey, K.L. Kompa, and M. Motzkus, “Evolutionary algorithms and their application to optimal control studies,” Phys. Rev. A6402, art# 023420 (2001)

2004 (2)

J.M. Dela Cruz, I. Pastirk, V.V. Lozovoy, K.A. Walowicz, and M. Dantus, “Multiphoton intrapulse interference 3: Probing microscopic chemical environments,” J. Phys. Chem. A 108, 53–58 (2004)
[Crossref]

V.V. Lozovoy, I. Pastirk, and M. Dantus, “Multiphoton intrapulse interference. 4. Characterization of the phase of ultrashort laser pulses,” Opt. Lett. 7, 775–777 (2004)
[Crossref]

2003 (3)

I. Pastirk, J.M. Dela Cruz, K.A. Walowicz, V.V. Lozovoy, and M. Dantus, “Selective two-photon microscopy with shaped femtosecond pulses,” Opt. Express 11, 1695–1701 (2003)
[Crossref] [PubMed]

V.V. Lozovoy, I. Pastirk, K.A. Walowicz, and M. Dantus, “Multiphoton intrapulse interference. 2. Control of two-and three-photon laser induced fluorescence with shaped pulses,” J. Chem. Phys. 118, 3187–3196 (2003)
[Crossref]

D. Goswami, “Optical pulse shaping approaches to coherent control,” Phys. Rep. 374, 385–481 (2003)
[Crossref]

2002 (2)

K.A. Walowicz, I. Pastirk, V.V. Lozovoy, and M. Dantus, “Multiphoton intrapulse interference. 1. Control of multiphoton processes in condensed phases,” J. Phys. Chem. A 106, 9369–9373 (2002)
[Crossref]

J.L. Herek, W. Wohlleben, R.J. Cogdell, D. Zeidler, and M. Motzkus, “Quantum control of energy flow in light harvesting,” Nature 417, 533–535 (2002)
[Crossref] [PubMed]

2001 (5)

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]

M. Shapiro and P. Brumer, “On the origin of pulse shaping control of molecular dynamics,” J. Phys. Chem. A 105, 2897–2902 (2001)
[Crossref]

Z. Zheng and A.M. Weiner, “Coherent control of second harmonic generation using spectrally phase coded femtosecond waveforms,” Chem. Phys. 267, 161–171 (2001)
[Crossref]

M. Hacker, R. Netz, M. Roth, G. Stobrawa, T. Feurer, and R. Sauerbrey, “Frequency doubling of phase-modulated, Ultrashort Laser Pulses,” Appl. Phys. B. 73, 273–277 (2001)
[Crossref]

N. Dudovich, B. Dayan, S.M.G. Faeder, and Y. Silberberg, “Transform-limited pulses are not optimal for resonant multiphoton transitions,” Phys. Rev. Lett. 86, 47–50 (2001)
[Crossref] [PubMed]

2000 (2)

1999 (1)

D. Meshulach and Y. Silberberg, “Coherent quantum control of multiphoton transitions by shaped ultrashort optical pulses,” Phys. Rev. A 60, 1287–1292 (1999)
[Crossref]

1998 (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]

1997 (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]

1992 (2)

R.S. Judson and H. Rabitz, “Teaching Lasers to Control Molecules,” Phys. Rev. Lett. 68, 1500–1503 (1992)
[Crossref] [PubMed]

B. Broers, L.D. Noordam, and H.B.V. Vandenheuvell, “Diffraction and focusing of spectral energy in multiphoton processes,” Phys. Rev. A 46, 2749–2756 (1992)
[Crossref] [PubMed]

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]

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.

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]

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]

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.

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]

Broers, B.

B. Broers, L.D. Noordam, and H.B.V. Vandenheuvell, “Diffraction and focusing of spectral energy in multiphoton processes,” Phys. Rev. A 46, 2749–2756 (1992)
[Crossref] [PubMed]

Brumer, P.

M. Shapiro and P. Brumer, “On the origin of pulse shaping control of molecular dynamics,” J. Phys. Chem. A 105, 2897–2902 (2001)
[Crossref]

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]

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]

Cogdell, R.J.

J.L. Herek, W. Wohlleben, R.J. Cogdell, D. Zeidler, and M. Motzkus, “Quantum control of energy flow in light harvesting,” Nature 417, 533–535 (2002)
[Crossref] [PubMed]

Dantus, M.

V.V. Lozovoy, I. Pastirk, and M. Dantus, “Multiphoton intrapulse interference. 4. Characterization of the phase of ultrashort laser pulses,” Opt. Lett. 7, 775–777 (2004)
[Crossref]

J.M. Dela Cruz, I. Pastirk, V.V. Lozovoy, K.A. Walowicz, and M. Dantus, “Multiphoton intrapulse interference 3: Probing microscopic chemical environments,” J. Phys. Chem. A 108, 53–58 (2004)
[Crossref]

V.V. Lozovoy, I. Pastirk, K.A. Walowicz, and M. Dantus, “Multiphoton intrapulse interference. 2. Control of two-and three-photon laser induced fluorescence with shaped pulses,” J. Chem. Phys. 118, 3187–3196 (2003)
[Crossref]

I. Pastirk, J.M. Dela Cruz, K.A. Walowicz, V.V. Lozovoy, and M. Dantus, “Selective two-photon microscopy with shaped femtosecond pulses,” Opt. Express 11, 1695–1701 (2003)
[Crossref] [PubMed]

K.A. Walowicz, I. Pastirk, V.V. Lozovoy, and M. Dantus, “Multiphoton intrapulse interference. 1. Control of multiphoton processes in condensed phases,” J. Phys. Chem. A 106, 9369–9373 (2002)
[Crossref]

Dayan, B.

N. Dudovich, B. Dayan, S.M.G. Faeder, and Y. Silberberg, “Transform-limited pulses are not optimal for resonant multiphoton transitions,” Phys. Rev. Lett. 86, 47–50 (2001)
[Crossref] [PubMed]

Dela Cruz, J.M.

J.M. Dela Cruz, I. Pastirk, V.V. Lozovoy, K.A. Walowicz, and M. Dantus, “Multiphoton intrapulse interference 3: Probing microscopic chemical environments,” J. Phys. Chem. A 108, 53–58 (2004)
[Crossref]

I. Pastirk, J.M. Dela Cruz, K.A. Walowicz, V.V. Lozovoy, and M. Dantus, “Selective two-photon microscopy with shaped femtosecond pulses,” Opt. Express 11, 1695–1701 (2003)
[Crossref] [PubMed]

Dudovich, N.

N. Dudovich, B. Dayan, S.M.G. Faeder, and Y. Silberberg, “Transform-limited pulses are not optimal for resonant multiphoton transitions,” Phys. Rev. Lett. 86, 47–50 (2001)
[Crossref] [PubMed]

Faeder, S.M.G.

N. Dudovich, B. Dayan, S.M.G. Faeder, and Y. Silberberg, “Transform-limited pulses are not optimal for resonant multiphoton transitions,” Phys. Rev. Lett. 86, 47–50 (2001)
[Crossref] [PubMed]

Feurer, T.

M. Hacker, R. Netz, M. Roth, G. Stobrawa, T. Feurer, and R. Sauerbrey, “Frequency doubling of phase-modulated, Ultrashort Laser Pulses,” Appl. Phys. B. 73, 273–277 (2001)
[Crossref]

Frey, S.

D. Zeidler, S. Frey, K.L. Kompa, and M. Motzkus, “Evolutionary algorithms and their application to optimal control studies,” Phys. Rev. A6402, art# 023420 (2001)

Gerber, G.

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]

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]

Goswami, D.

D. Goswami, “Optical pulse shaping approaches to coherent control,” Phys. Rep. 374, 385–481 (2003)
[Crossref]

Hacker, M.

M. Hacker, R. Netz, M. Roth, G. Stobrawa, T. Feurer, and R. Sauerbrey, “Frequency doubling of phase-modulated, Ultrashort Laser Pulses,” Appl. Phys. B. 73, 273–277 (2001)
[Crossref]

Herek, J.L.

J.L. Herek, W. Wohlleben, R.J. Cogdell, D. Zeidler, and M. Motzkus, “Quantum control of energy flow in light harvesting,” Nature 417, 533–535 (2002)
[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.

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]

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]

Kompa, K.L.

D. Zeidler, S. Frey, K.L. Kompa, and M. Motzkus, “Evolutionary algorithms and their application to optimal control studies,” Phys. Rev. A6402, art# 023420 (2001)

Lozovoy, V.V.

V.V. Lozovoy, I. Pastirk, and M. Dantus, “Multiphoton intrapulse interference. 4. Characterization of the phase of ultrashort laser pulses,” Opt. Lett. 7, 775–777 (2004)
[Crossref]

J.M. Dela Cruz, I. Pastirk, V.V. Lozovoy, K.A. Walowicz, and M. Dantus, “Multiphoton intrapulse interference 3: Probing microscopic chemical environments,” J. Phys. Chem. A 108, 53–58 (2004)
[Crossref]

V.V. Lozovoy, I. Pastirk, K.A. Walowicz, and M. Dantus, “Multiphoton intrapulse interference. 2. Control of two-and three-photon laser induced fluorescence with shaped pulses,” J. Chem. Phys. 118, 3187–3196 (2003)
[Crossref]

I. Pastirk, J.M. Dela Cruz, K.A. Walowicz, V.V. Lozovoy, and M. Dantus, “Selective two-photon microscopy with shaped femtosecond pulses,” Opt. Express 11, 1695–1701 (2003)
[Crossref] [PubMed]

K.A. Walowicz, I. Pastirk, V.V. Lozovoy, and M. Dantus, “Multiphoton intrapulse interference. 1. Control of multiphoton processes in condensed phases,” J. Phys. Chem. A 106, 9369–9373 (2002)
[Crossref]

Meshulach, D.

D. Meshulach and Y. Silberberg, “Coherent quantum control of multiphoton transitions by shaped ultrashort optical pulses,” Phys. Rev. A 60, 1287–1292 (1999)
[Crossref]

Motzkus, M.

J.L. Herek, W. Wohlleben, R.J. Cogdell, D. Zeidler, and M. Motzkus, “Quantum control of energy flow in light harvesting,” Nature 417, 533–535 (2002)
[Crossref] [PubMed]

D. Zeidler, S. Frey, K.L. Kompa, and M. Motzkus, “Evolutionary algorithms and their application to optimal control studies,” Phys. Rev. A6402, art# 023420 (2001)

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]

Netz, R.

M. Hacker, R. Netz, M. Roth, G. Stobrawa, T. Feurer, and R. Sauerbrey, “Frequency doubling of phase-modulated, Ultrashort Laser Pulses,” Appl. Phys. B. 73, 273–277 (2001)
[Crossref]

Noordam, L.D.

B. Broers, L.D. Noordam, and H.B.V. Vandenheuvell, “Diffraction and focusing of spectral energy in multiphoton processes,” Phys. Rev. A 46, 2749–2756 (1992)
[Crossref] [PubMed]

Pastirk, I.

J.M. Dela Cruz, I. Pastirk, V.V. Lozovoy, K.A. Walowicz, and M. Dantus, “Multiphoton intrapulse interference 3: Probing microscopic chemical environments,” J. Phys. Chem. A 108, 53–58 (2004)
[Crossref]

V.V. Lozovoy, I. Pastirk, and M. Dantus, “Multiphoton intrapulse interference. 4. Characterization of the phase of ultrashort laser pulses,” Opt. Lett. 7, 775–777 (2004)
[Crossref]

V.V. Lozovoy, I. Pastirk, K.A. Walowicz, and M. Dantus, “Multiphoton intrapulse interference. 2. Control of two-and three-photon laser induced fluorescence with shaped pulses,” J. Chem. Phys. 118, 3187–3196 (2003)
[Crossref]

I. Pastirk, J.M. Dela Cruz, K.A. Walowicz, V.V. Lozovoy, and M. Dantus, “Selective two-photon microscopy with shaped femtosecond pulses,” Opt. Express 11, 1695–1701 (2003)
[Crossref] [PubMed]

K.A. Walowicz, I. Pastirk, V.V. Lozovoy, and M. Dantus, “Multiphoton intrapulse interference. 1. Control of multiphoton processes in condensed phases,” J. Phys. Chem. A 106, 9369–9373 (2002)
[Crossref]

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]

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]

Roth, M.

M. Hacker, R. Netz, M. Roth, G. Stobrawa, T. Feurer, and R. Sauerbrey, “Frequency doubling of phase-modulated, Ultrashort Laser Pulses,” Appl. Phys. B. 73, 273–277 (2001)
[Crossref]

Sauerbrey, R.

M. Hacker, R. Netz, M. Roth, G. Stobrawa, T. Feurer, and R. Sauerbrey, “Frequency doubling of phase-modulated, Ultrashort Laser Pulses,” Appl. Phys. B. 73, 273–277 (2001)
[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]

Shapiro, M.

M. Shapiro and P. Brumer, “On the origin of pulse shaping control of molecular dynamics,” J. Phys. Chem. A 105, 2897–2902 (2001)
[Crossref]

Silberberg, Y.

N. Dudovich, B. Dayan, S.M.G. Faeder, and Y. Silberberg, “Transform-limited pulses are not optimal for resonant multiphoton transitions,” Phys. Rev. Lett. 86, 47–50 (2001)
[Crossref] [PubMed]

D. Meshulach and Y. Silberberg, “Coherent quantum control of multiphoton transitions by shaped ultrashort optical pulses,” Phys. Rev. A 60, 1287–1292 (1999)
[Crossref]

Stobrawa, G.

M. Hacker, R. Netz, M. Roth, G. Stobrawa, T. Feurer, and R. Sauerbrey, “Frequency doubling of phase-modulated, Ultrashort Laser Pulses,” Appl. Phys. B. 73, 273–277 (2001)
[Crossref]

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]

Vandenheuvell, H.B.V.

B. Broers, L.D. Noordam, and H.B.V. Vandenheuvell, “Diffraction and focusing of spectral energy in multiphoton processes,” Phys. Rev. A 46, 2749–2756 (1992)
[Crossref] [PubMed]

Walowicz, K.A.

J.M. Dela Cruz, I. Pastirk, V.V. Lozovoy, K.A. Walowicz, and M. Dantus, “Multiphoton intrapulse interference 3: Probing microscopic chemical environments,” J. Phys. Chem. A 108, 53–58 (2004)
[Crossref]

V.V. Lozovoy, I. Pastirk, K.A. Walowicz, and M. Dantus, “Multiphoton intrapulse interference. 2. Control of two-and three-photon laser induced fluorescence with shaped pulses,” J. Chem. Phys. 118, 3187–3196 (2003)
[Crossref]

I. Pastirk, J.M. Dela Cruz, K.A. Walowicz, V.V. Lozovoy, and M. Dantus, “Selective two-photon microscopy with shaped femtosecond pulses,” Opt. Express 11, 1695–1701 (2003)
[Crossref] [PubMed]

K.A. Walowicz, I. Pastirk, V.V. Lozovoy, and M. Dantus, “Multiphoton intrapulse interference. 1. Control of multiphoton processes in condensed phases,” J. Phys. Chem. A 106, 9369–9373 (2002)
[Crossref]

Wang, L.

L. Wang and A.M. Weiner, “Programmable spectral phase coding of an amplified spontaneous emission light source,” 167, 211–224 (1999)

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]

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]

Weiner, A.M.

Z. Zheng and A.M. Weiner, “Coherent control of second harmonic generation using spectrally phase coded femtosecond waveforms,” Chem. Phys. 267, 161–171 (2001)
[Crossref]

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

Z. Zheng and A.M. Weiner, “Spectral phase correlation of coded femtosecond pulses by second-harmonic generation in thick nonlinear crystals,” Opt. Lett. 25, 984–986 (2000)
[Crossref]

L. Wang and A.M. Weiner, “Programmable spectral phase coding of an amplified spontaneous emission light source,” 167, 211–224 (1999)

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]

Wohlleben, W.

J.L. Herek, W. Wohlleben, R.J. Cogdell, D. Zeidler, and M. Motzkus, “Quantum control of energy flow in light harvesting,” Nature 417, 533–535 (2002)
[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]

Zeidler, D.

J.L. Herek, W. Wohlleben, R.J. Cogdell, D. Zeidler, and M. Motzkus, “Quantum control of energy flow in light harvesting,” Nature 417, 533–535 (2002)
[Crossref] [PubMed]

D. Zeidler, S. Frey, K.L. Kompa, and M. Motzkus, “Evolutionary algorithms and their application to optimal control studies,” Phys. Rev. A6402, art# 023420 (2001)

Zheng, Z.

Z. Zheng and A.M. Weiner, “Coherent control of second harmonic generation using spectrally phase coded femtosecond waveforms,” Chem. Phys. 267, 161–171 (2001)
[Crossref]

Z. Zheng and A.M. Weiner, “Spectral phase correlation of coded femtosecond pulses by second-harmonic generation in thick nonlinear crystals,” Opt. Lett. 25, 984–986 (2000)
[Crossref]

Appl. Phys. B. (1)

M. Hacker, R. Netz, M. Roth, G. Stobrawa, T. Feurer, and R. Sauerbrey, “Frequency doubling of phase-modulated, Ultrashort Laser Pulses,” Appl. Phys. B. 73, 273–277 (2001)
[Crossref]

Chem. Phys. (1)

Z. Zheng and A.M. Weiner, “Coherent control of second harmonic generation using spectrally phase coded femtosecond waveforms,” Chem. Phys. 267, 161–171 (2001)
[Crossref]

Chem. Phys. Lett. (2)

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.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]

J. Chem. Phys. (1)

V.V. Lozovoy, I. Pastirk, K.A. Walowicz, and M. Dantus, “Multiphoton intrapulse interference. 2. Control of two-and three-photon laser induced fluorescence with shaped pulses,” J. Chem. Phys. 118, 3187–3196 (2003)
[Crossref]

J. Phys. Chem. A (3)

K.A. Walowicz, I. Pastirk, V.V. Lozovoy, and M. Dantus, “Multiphoton intrapulse interference. 1. Control of multiphoton processes in condensed phases,” J. Phys. Chem. A 106, 9369–9373 (2002)
[Crossref]

M. Shapiro and P. Brumer, “On the origin of pulse shaping control of molecular dynamics,” J. Phys. Chem. A 105, 2897–2902 (2001)
[Crossref]

J.M. Dela Cruz, I. Pastirk, V.V. Lozovoy, K.A. Walowicz, and M. Dantus, “Multiphoton intrapulse interference 3: Probing microscopic chemical environments,” J. Phys. Chem. A 108, 53–58 (2004)
[Crossref]

Nature (1)

J.L. Herek, W. Wohlleben, R.J. Cogdell, D. Zeidler, and M. Motzkus, “Quantum control of energy flow in light harvesting,” Nature 417, 533–535 (2002)
[Crossref] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

V.V. Lozovoy, I. Pastirk, and M. Dantus, “Multiphoton intrapulse interference. 4. Characterization of the phase of ultrashort laser pulses,” Opt. Lett. 7, 775–777 (2004)
[Crossref]

Z. Zheng and A.M. Weiner, “Spectral phase correlation of coded femtosecond pulses by second-harmonic generation in thick nonlinear crystals,” Opt. Lett. 25, 984–986 (2000)
[Crossref]

Phys. Rep. (1)

D. Goswami, “Optical pulse shaping approaches to coherent control,” Phys. Rep. 374, 385–481 (2003)
[Crossref]

Phys. Rev. A (2)

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[Crossref]

Phys. Rev. Lett. (2)

N. Dudovich, B. Dayan, S.M.G. Faeder, and Y. Silberberg, “Transform-limited pulses are not optimal for resonant multiphoton transitions,” Phys. Rev. Lett. 86, 47–50 (2001)
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[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 (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 (2)

L. Wang and A.M. Weiner, “Programmable spectral phase coding of an amplified spontaneous emission light source,” 167, 211–224 (1999)

D. Zeidler, S. Frey, K.L. Kompa, and M. Motzkus, “Evolutionary algorithms and their application to optimal control studies,” Phys. Rev. A6402, art# 023420 (2001)

Supplementary Material (1)

» Media 1: AVI (210 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

Cartoon representation of the problem. The broad bandwidth second harmonic spectrum from transform-limited pulses is represented by a Gaussian (thin line). The objective is to introduce phase modulation to cause the two-photon spectrum to be intense only inside the window defined by frequency 2ωc and width W, and to minimize the background B outside the window. The contrast ratio C is defined as the integrated intensity inside W divided by the integrated intensity of light outside the window.

Fig. 2.
Fig. 2.

Phase mask proposed based on the symmetry requirements of the problem, using the quasi randomness of prime numbers. This mask is reflected about pixel 64, and is designed to obtain a narrow second harmonic signal at the center of the spectrum.

Fig. 3.
Fig. 3.

Effect of spectral amplitude restriction on SHG. (a) Experimental spectrum of the laser before (black) and after filtering with windows of width 40 (red), 20 (blue), and 10 (green) nm. (b) Experimental (points) and simulation (continuous lines) for the second harmonic spectrum of TL and spectrally filtered pulses as indicated in panel (a).

Fig. 4.
Fig. 4.

Experimental results with binary phase shaping. (a) The spectrum of the laser (dashed lines) and the binary phase mask (0 or π) are shown as a function of wavelength. (b) The second harmonic spectrum of the TL pulses (dashed line) and second harmonic spectrum of the shaped pulses according to panel (a). The movie (428 kB) shows how translation of the binary phase mask across the spectrum tunes the frequency where the second harmonic is focused.

Fig. 5.
Fig. 5.

Comparison of a prime number inspired phase mask (black) with a mask that was optimized using a computer based learning algorithm(red). The insets on the left depict the phase masks for each case. The inset on the right shows the improvement in the contrast ratio, as defined in Fig. 1, as the learning algorithm finds the best solution starting from the prime number phase mask.

Equations (4)

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

E ( t ) = E ( ω ) exp [ i ϕ ( ω ) ] exp ( i ω t ) d ω ,
I SHG ( ω ) = E ( t ) 2 exp ( i ω t ) d t 2 .
I SHG ( 2 ω c ) = E ( ω c ω ) E ( ω c + ω ) d ω 2
S k = j b k j b k + j 2

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