Abstract

We describe a programmable spectral-phase, pulse-shaping system for femtosecond pulses based on a deformable membrane mirror. Accurate spectral phase design as well as pulse intensity modulation was achieved with direct control of the mirror surface by use of a negative-feedback, mirror-surface control mode. Convergence to the chosen spectral-phase design was typically achieved within several seconds. The pulses were measured with a real-time, second-harmonic-generation, frequency-resolved optical gating system.

© 2004 Optical Society of America

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References

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  1. A. 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]
  2. D. Meshulach, D. Yelin, and Y. Silberberg, “Adaptive real-time femtosecond pulse shaping,” J. Opt. Soc. Am. B 15, 1615–1619 (1998).
    [CrossRef]
  3. D. Yelin, D. Meshulach, and Y. Silberberg, “Adaptive femtosecond pulse compression,” Opt. Lett. 22, 1793–1795 (1997).
    [CrossRef]
  4. T. Brixner, A. Oehrlein, M. Strehle, and G. Gerber, “Feedback-controlled femtosecond pulse shaping,” Appl. Phys. B 70, S119–S124 (2000).
    [CrossRef]
  5. E. Zeek, K. Maginnis, S. Backus, U. Russek, M. Murnane, G. Mourou, H. Kapteyn, and G. Vdovin, “Pulse compression by use of deformable mirrors,” Opt. Lett. 24, 493–495 (1999).
    [CrossRef]
  6. D. Zeidler, S. Frey, K. L. Kompa, and M. Motzkus, “Evolutionary algorithms and their application to optimal control studies,” Phys. Rev. A 64, 023420 (2001).
    [CrossRef]
  7. K. Ohno, T. Tanabe, and F. Kannari, “Adaptive pulse shaping of phase and amplitude of an amplified femtosecond pulse laser by direct reference to frequency-resolved optical gating traces,” J. Opt. Soc. Am. B 19, 2781–2790 (2002).
    [CrossRef]
  8. C. Dorrer and F. Salin, “Characterization of spectral phasemodulation by classical and polarization spectral interferometry,” J. Opt. Soc. Am. B 15, 2331–2337 (1998).
    [CrossRef]
  9. F. Verluise, V. Laude, Z. Cheng, Ch. Spielmann, and P. Tournois, “Amplitude and phase control of ultrashort pulses by use of an acousto-optic programmable dispersive filter: pulse compression and shaping,” Opt. Lett. 25, 575–577 (2000).
    [CrossRef]
  10. OKO Technologies, P.O. Box 2600 AN Delft, The Netherlands.
  11. J. Garduño-Mejía, E. Ramsay, A. Greenaway, and D. T. Reid, “Real-time femtosecond optical pulse measurement using a video-rate, frequency-resolved optical gating system,” Rev. Sci. Instrum. 74, 3624–3627 (2003).
    [CrossRef]
  12. R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
    [CrossRef]
  13. P. M. Blanchard, D. J. Fisher, S. C. Woods, and A. H. Greenaway, “Phase-diversity wave-front sensing with a distorted diffraction grating,” Appl. Opt. 39, 6649–6655 (2000).
    [CrossRef]
  14. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe pattern analysis for computer-based tomography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [CrossRef]
  15. J. Goodman, Introduction to Fourier Optics, 1st ed. (McGraw-Hill, New York, 1968).
  16. G. W. Stewart, Introduction to Matrix Computations, Computer Science and Applied Mathematics Series (Academic, New York, 1973).
  17. W. H. Press, S. A. Teukolski, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University, Cambridge, UK, 1997).
  18. B. C. Walker, C. Toth, D. Fittinghoff, and T. Guo, “Theoretical and experimental spectral phase error analysis for pulsed laser fields,” J. Opt. Soc. Am. B 16, 1292–1299 (1999).
    [CrossRef]
  19. J. Garduño-Mejía, A. H. Greenaway, and D. T. Reid, “Designer femtosecond pulses using adaptive optics,” Opt. Express 11, 2030–2040 (2003).
    [CrossRef] [PubMed]
  20. Ultrafast Optics Group, Heriot-Watt University, http://www.phy.hw.ac.uk/resrev/ufast.
  21. M. Bergt, T. Brixner, B. Kiefer, M. Strehle, and G. Gerber, “Controlling the femtochemistry of Fe(CO)5,” J. Phys. Chem. A 103, 10381–10387 (1999).
    [CrossRef]
  22. C. Iaconis and I. A. Walmsley, “Spectral phase interferometry for direct electric-field reconstruction of ultrashort optical pulses,” Opt. Lett. 23, 792–794 (1998).
    [CrossRef]
  23. Timothy M. Shuman, Matthew E. Anderson, Jake Bromage, Chris Iaconis, Lean Waxer, and Ian A. Walmsley, “Real-time SPIDER: ultrashort pulse characterization at 20 Hz,” Opt. Express 5, 134–143 (1999).
    [CrossRef] [PubMed]

2003

J. Garduño-Mejía, E. Ramsay, A. Greenaway, and D. T. Reid, “Real-time femtosecond optical pulse measurement using a video-rate, frequency-resolved optical gating system,” Rev. Sci. Instrum. 74, 3624–3627 (2003).
[CrossRef]

J. Garduño-Mejía, A. H. Greenaway, and D. T. Reid, “Designer femtosecond pulses using adaptive optics,” Opt. Express 11, 2030–2040 (2003).
[CrossRef] [PubMed]

2002

2001

D. Zeidler, S. Frey, K. L. Kompa, and M. Motzkus, “Evolutionary algorithms and their application to optimal control studies,” Phys. Rev. A 64, 023420 (2001).
[CrossRef]

2000

1999

1998

1997

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

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

1992

A. 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]

1982

Anderson, Matthew E.

Backus, S.

Bergt, M.

M. Bergt, T. Brixner, B. Kiefer, M. Strehle, and G. Gerber, “Controlling the femtochemistry of Fe(CO)5,” J. Phys. Chem. A 103, 10381–10387 (1999).
[CrossRef]

Blanchard, P. M.

Brixner, T.

T. Brixner, A. Oehrlein, M. Strehle, and G. Gerber, “Feedback-controlled femtosecond pulse shaping,” Appl. Phys. B 70, S119–S124 (2000).
[CrossRef]

M. Bergt, T. Brixner, B. Kiefer, M. Strehle, and G. Gerber, “Controlling the femtochemistry of Fe(CO)5,” J. Phys. Chem. A 103, 10381–10387 (1999).
[CrossRef]

Bromage, Jake

Cheng, Z.

DeLong, K. W.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Dorrer, C.

Fisher, D. J.

Fittinghoff, D.

Fittinghoff, D. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Frey, S.

D. Zeidler, S. Frey, K. L. Kompa, and M. Motzkus, “Evolutionary algorithms and their application to optimal control studies,” Phys. Rev. A 64, 023420 (2001).
[CrossRef]

Garduño-Mejía, J.

J. Garduño-Mejía, A. H. Greenaway, and D. T. Reid, “Designer femtosecond pulses using adaptive optics,” Opt. Express 11, 2030–2040 (2003).
[CrossRef] [PubMed]

J. Garduño-Mejía, E. Ramsay, A. Greenaway, and D. T. Reid, “Real-time femtosecond optical pulse measurement using a video-rate, frequency-resolved optical gating system,” Rev. Sci. Instrum. 74, 3624–3627 (2003).
[CrossRef]

Gerber, G.

T. Brixner, A. Oehrlein, M. Strehle, and G. Gerber, “Feedback-controlled femtosecond pulse shaping,” Appl. Phys. B 70, S119–S124 (2000).
[CrossRef]

M. Bergt, T. Brixner, B. Kiefer, M. Strehle, and G. Gerber, “Controlling the femtochemistry of Fe(CO)5,” J. Phys. Chem. A 103, 10381–10387 (1999).
[CrossRef]

Greenaway, A.

J. Garduño-Mejía, E. Ramsay, A. Greenaway, and D. T. Reid, “Real-time femtosecond optical pulse measurement using a video-rate, frequency-resolved optical gating system,” Rev. Sci. Instrum. 74, 3624–3627 (2003).
[CrossRef]

Greenaway, A. H.

Guo, T.

Iaconis, C.

Iaconis, Chris

Ina, H.

Kane, D. J.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Kannari, F.

Kapteyn, H.

Kiefer, B.

M. Bergt, T. Brixner, B. Kiefer, M. Strehle, and G. Gerber, “Controlling the femtochemistry of Fe(CO)5,” J. Phys. Chem. A 103, 10381–10387 (1999).
[CrossRef]

Kobayashi, S.

Kompa, K. L.

D. Zeidler, S. Frey, K. L. Kompa, and M. Motzkus, “Evolutionary algorithms and their application to optimal control studies,” Phys. Rev. A 64, 023420 (2001).
[CrossRef]

Krumbugel, M. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Laude, V.

Leaird, D. E.

A. 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]

Maginnis, K.

Meshulach, D.

Motzkus, M.

D. Zeidler, S. Frey, K. L. Kompa, and M. Motzkus, “Evolutionary algorithms and their application to optimal control studies,” Phys. Rev. A 64, 023420 (2001).
[CrossRef]

Mourou, G.

Murnane, M.

Oehrlein, A.

T. Brixner, A. Oehrlein, M. Strehle, and G. Gerber, “Feedback-controlled femtosecond pulse shaping,” Appl. Phys. B 70, S119–S124 (2000).
[CrossRef]

Ohno, K.

Patel, J. S.

A. 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]

Ramsay, E.

J. Garduño-Mejía, E. Ramsay, A. Greenaway, and D. T. Reid, “Real-time femtosecond optical pulse measurement using a video-rate, frequency-resolved optical gating system,” Rev. Sci. Instrum. 74, 3624–3627 (2003).
[CrossRef]

Reid, D. T.

J. Garduño-Mejía, E. Ramsay, A. Greenaway, and D. T. Reid, “Real-time femtosecond optical pulse measurement using a video-rate, frequency-resolved optical gating system,” Rev. Sci. Instrum. 74, 3624–3627 (2003).
[CrossRef]

J. Garduño-Mejía, A. H. Greenaway, and D. T. Reid, “Designer femtosecond pulses using adaptive optics,” Opt. Express 11, 2030–2040 (2003).
[CrossRef] [PubMed]

Richman, B. A.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Russek, U.

Salin, F.

Shuman, Timothy M.

Silberberg, Y.

Spielmann, Ch.

Strehle, M.

T. Brixner, A. Oehrlein, M. Strehle, and G. Gerber, “Feedback-controlled femtosecond pulse shaping,” Appl. Phys. B 70, S119–S124 (2000).
[CrossRef]

M. Bergt, T. Brixner, B. Kiefer, M. Strehle, and G. Gerber, “Controlling the femtochemistry of Fe(CO)5,” J. Phys. Chem. A 103, 10381–10387 (1999).
[CrossRef]

Sweetser, J. N.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Takeda, M.

Tanabe, T.

Toth, C.

Tournois, P.

Trebino, R.

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Vdovin, G.

Verluise, F.

Walker, B. C.

Walmsley, I. A.

Walmsley, Ian A.

Waxer, Lean

Weiner, A.

A. 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]

Woods, S. C.

Wullert, J. R.

A. 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]

Yelin, D.

Zeek, E.

Zeidler, D.

D. Zeidler, S. Frey, K. L. Kompa, and M. Motzkus, “Evolutionary algorithms and their application to optimal control studies,” Phys. Rev. A 64, 023420 (2001).
[CrossRef]

Appl. Opt.

Appl. Phys. B

T. Brixner, A. Oehrlein, M. Strehle, and G. Gerber, “Feedback-controlled femtosecond pulse shaping,” Appl. Phys. B 70, S119–S124 (2000).
[CrossRef]

IEEE J. Quantum Electron.

A. 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. Opt. Soc. Am.

J. Opt. Soc. Am. B

J. Phys. Chem. A

M. Bergt, T. Brixner, B. Kiefer, M. Strehle, and G. Gerber, “Controlling the femtochemistry of Fe(CO)5,” J. Phys. Chem. A 103, 10381–10387 (1999).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. A

D. Zeidler, S. Frey, K. L. Kompa, and M. Motzkus, “Evolutionary algorithms and their application to optimal control studies,” Phys. Rev. A 64, 023420 (2001).
[CrossRef]

Rev. Sci. Instrum.

J. Garduño-Mejía, E. Ramsay, A. Greenaway, and D. T. Reid, “Real-time femtosecond optical pulse measurement using a video-rate, frequency-resolved optical gating system,” Rev. Sci. Instrum. 74, 3624–3627 (2003).
[CrossRef]

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time-frequency domain using frequency-resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Other

J. Goodman, Introduction to Fourier Optics, 1st ed. (McGraw-Hill, New York, 1968).

G. W. Stewart, Introduction to Matrix Computations, Computer Science and Applied Mathematics Series (Academic, New York, 1973).

W. H. Press, S. A. Teukolski, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge University, Cambridge, UK, 1997).

Ultrafast Optics Group, Heriot-Watt University, http://www.phy.hw.ac.uk/resrev/ufast.

OKO Technologies, P.O. Box 2600 AN Delft, The Netherlands.

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Figures (14)

Fig. 1
Fig. 1

Schematic of adaptive-optical femtosecond pulse shaper: DG, diffraction grating; CM, concave mirror; DM, deformable mirror; PC, personal computer.

Fig. 2
Fig. 2

Pulse shaping by direct control of deformable mirror surface. First row, mirror set for zero spectral phase; second row, mirror adjusted for pulse compression; third row, mirror set for a near-sinusoidal surface shape. First column, measured or calculated mirror surface profile; second column, measured pulse spectral phase; third column, measured pulse temporal intensity. The gray lines below the curves in the first column (corresponding to the mirror distortion profile) represent the line spectrum position with respect to the mirror aperture.

Fig. 3
Fig. 3

Illustration of the procedure used for the mirror surface analysis. After Fourier transforming the image, the mirror distortion is retrieved by applying an inverse Fourier transform and by a phase recovery process on the positive side band (inset square).

Fig. 4
Fig. 4

(a) Actuator voltage profiles and (b) the resulting mirror surface distortions for the 19 data sets used to construct the influence matrix (see text).

Fig. 5
Fig. 5

Normalized influence matrix data elements.

Fig. 6
Fig. 6

Deformable mirror surface characterization by use of the influence matrix transformation. (a) Mirror surface distortion determined by the interferometric method (squares) and calculated directly by the influence matrix transformation method (circles); (b) actuator voltages applied to the mirror.

Fig. 7
Fig. 7

Flow chart showing the simulated annealing algorithm used to determine the actuator voltages necessary for producing a target mirror deformation profile.

Fig. 8
Fig. 8

(a) Target mirror profile (squares) and the profile resulting from the voltages determined by the simulated annealing algorithm (circles); (b) experimental voltages corresponding to the target mirror profile (squares), the voltages determined by the simulated annealing algorithm (circles), and the initial guess voltages (triangles).

Fig. 9
Fig. 9

Flow chart illustrating the negative-feedback, pulse-shaping scheme.

Fig. 10
Fig. 10

Image of the pulse shaper interface windows.

Fig. 11
Fig. 11

Pulse compression. Before shaping, the pulse incident on the pulse shaper was substantially chirped (top left panel, circles), but after shaping to a flat target spectral phase (top left panel, stars) the pulse was compressed. After shaping (bottom left panel), the spectral phase of the compressed pulse matched the target phase with a rms difference of 1.04×10-3. Corresponding pulse intensity (middle panels) and FROG traces (right panels), before (top) and after shaping (bottom) are also shown.

Fig. 12
Fig. 12

Near-quadratic spectral-phase design. Shaping begins from an arbitrary pulse with a small amount of spectral phase distortion (top left panel, circles) and converges on a near-quadratic target phase (top left panel, stars). After shaping (bottom left panel), the spectral phase of the pulse matched the target phase with a rms difference of 3.35×10-2. Corresponding pulse intensity (middle panels) and FROG traces (right panels), before (top) and after shaping (bottom) are also shown.

Fig. 13
Fig. 13

Nonlinear chirp pulse design. The target spectral phase (top left panel, stars) has a sinusoidal form corresponding to a double pulse. For comparison the initial pulse before shaping is also shown (top middle panel, circles). After (bottom left panel, circles) shaping, the spectral phase of the pulse matched the target phase (bottom left panel, stars) with a RMS difference of 5.94×10-1. Corresponding FROG traces, before (right panel, top) and after shaping (right panel, bottom) are also shown.

Fig. 14
Fig. 14

Near-cubic spectral-phase design. The target phase has an approximately cubic form (top left panel, stars) that leads to an asymmetrical temporal profile with one extended edge (middle panel, bottom row). For comparison the initial pulse before shaping is also shown (middle panel, top row). After shaping, the spectral phase of the pulse matched the target phase with a rms difference of 3.27×10-1. Corresponding retrieved FROG traces, before (right panel, top row) and after shaping (right panel, bottom row) are also shown.

Equations (6)

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

YSet=MInfluence·VSet,
YSet=y1ay1by1sy2ay2by2sy19ay19by19s,
VSet=v1a2v1b2v1s2v2a2v2b2v2s2v19a2v19b2v19s2,
MInfluence=(VSet)-1·YSet.
y1y2y19=MInfluence·v12v22v192.
ΔV(ω)=KΔϕ(ω).

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