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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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  8. V.V. Lozovoy, I. Pastirk, K.A. Walowicz, 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, 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, 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, R. Sauerbrey, "Frequency doubling of phase-modulated, Ultrashort Laser Pulses," Appl. Phys. B. 73, 273-277 (2001)
    [CrossRef]
  12. V.V. Lozovoy, I. Pastirk, M. Dantus, "Multiphoton intrapulse interference. 4. Characterization of the phase of ultrashort laser pulses," Opt. Lett. 7, 775-777 (2004)
    [CrossRef]
  13. Z. Zheng, 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, 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, A.M. Weiner, "Programmable spectral phase coding of an amplified spontaneous emission light source," 167, 211-224 (1999)
  17. D. Meshulach, 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, 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, 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, M.M. Murnane, "Coherent learning control of vibrational motion in room temperature molecular gases," Chem. Phys. Lett. 344, 333-338 (2001)
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  21. D. Zeidler, S. Frey, K.L. Kompa, M. Motzkus, "Evolutionary algorithms and their application to optimal control studies," Phys. Rev. A 6402, art# 023420 (2001)

Appl. Phys. B. (1)

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

Chem. Phys. (1)

Z. Zheng, 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)

T.C. Weinacht, R. Bartels, S. Backus, P.H. Bucksbaum, B. Pearson, J.M. Geremia, H. Rabitz, H.C. Kapteyn, 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, W.S. Warren, "Feedback quantum control of molecular electronic population transfer," Chem. Phys. Lett. 280, 151-158 (1997)
[CrossRef]

J. Chem. Phys. (1)

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

M. Shapiro, 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, 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, M. Motzkus, "Quantum control of energy flow in light harvesting," Nature 417, 533-535 (2002)
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Z. Zheng, 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]

V.V. Lozovoy, I. Pastirk, M. Dantus, "Multiphoton intrapulse interference. 4. Characterization of the phase of ultrashort laser pulses," Opt. Lett. 7, 775-777 (2004)
[CrossRef]

Phys. Rep. (1)

D. Goswami, "Optical pulse shaping approaches to coherent control," Phys. Rep. 374, 385-481 (2003)
[CrossRef]

Phys. Rev. A (3)

B. Broers, L.D. Noordam, H.B.V. Vandenheuvell, "Diffraction and focusing of spectral energy in multiphoton processes," Phys. Rev. A 46, 2749-2756 (1992
[CrossRef] [PubMed]

D. Zeidler, S. Frey, K.L. Kompa, M. Motzkus, "Evolutionary algorithms and their application to optimal control studies," Phys. Rev. A 6402, art# 023420 (2001)

D. Meshulach, Y. Silberberg, "Coherent quantum control of multiphoton transitions by shaped ultrashort optical pulses," Phys. Rev. A 60, 1287-1292 (1999)
[CrossRef]

Phys. Rev. Lett. (2)

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

R.S. Judson, H. Rabitz, "Teaching Lasers to Control Molecules," Phys. Rev. Lett. 68, 1500-1503 (1992)
[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, G. Gerber, "Control of chemical reactions by feedback-optimized phase- shaped femtosecond laser pulses," Science 282, 919-922 (1998)
[CrossRef] [PubMed]

Other (1)

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

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)

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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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