Abstract

A femtosecond pulse shaping apparatus based on a thermo-optically driven spatial phase modulator is presented. The modulator cell is illuminated by a standard projector and is easily controllable with a computer. In principle the setup allows for two dimensional pulse shaping, however, all initial demonstrations reported here, such as feedback controlled dispersion compensation or pulse train generation, are performed in a one dimensional phase-only shaping geometry.

© 2007 Optical Society of America

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References

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    [Crossref]
  2. D. Yelin, M. Meshulach, and Y. Silberberg, “Adaptive femtosecond pulse compression,” Opt. Lett. 22,1793–17951997).
    [Crossref]
  3. 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]
  4. E. Zeek, K. Maginnis, S. Backus, U. Russek, M. Murnane, G. Mourou, H. Kapteyn, and G. Vdovin, “Pulse compression ,” Opt. Lett. 24,493–495 (1999).
    [Crossref]
  5. R. Stoian, M. Boyle, A. Thoss, A. Rosenfeld, G. Korn, I. V. Hertel, and E. E. B. Campbell, “Laser ablation of ,” Appl. Phys. Lett. 80,353–355 (2002).
    [Crossref]
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    [Crossref] [PubMed]
  11. D. Zeidler, S. Frey, K. L. Kompa, and M. Motzkus, “Evolutionary algorithms and their application to optimal control studies,” Phys. Rev. A 64, Art. No.023420 (2001).
    [Crossref]
  12. D. Meshulach and Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature (London) 396,239–242 (1998).
    [Crossref]
  13. D. Zeidler, S. Frey, W. Wohlleben, M. Motzkus, F. Busch, T. Chen, W. Kiefer, and A. Materny, “Optimal control of ground-state dynamics in polymers,” J. Chem. Phys. 116,5231–5235 (2002).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  23. K. DeLong, “Frog3 Program,”http://www.femtosoft.biz.
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    [Crossref]
  25. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++ (Cambridge University2002).
  26. T. Feurer, “Feedback-controlled optimization of soft-X-ray radiation from femtosecond laser-produced plasmas,“ Appl. Phys. B 68,55–60 (1999).
    [Crossref]
  27. A. M. Weiner, D. E. Leaird, G. P. Wiederrecht, and K. A. Nelson, “Femtosecond pulse sequences used for optical manipulation of molecular motion,” Science 247,1317–1319 (1990).
    [Crossref] [PubMed]
  28. B. Schmidt, M. Hacker, G. Stobrawa, and T. Feurer, “LAB2 - A virtual femtosecond laser lab,” http://www.lab2.de.

2006 (3)

2005 (1)

2004 (1)

F. Reinert and W. Lüthy, “Optically controlled adaptive mirror,” Laser Phys. Lett. 1,551–554 (2004).
[Crossref]

2002 (4)

T. Feurer, J. C. Vaughan, R. M. Koehl, and K. A. Nelson, “Multidimensional control of femtosecond pulses by use of a programmable liquid-crystal matrix,” Opt. Lett. 27,652–654 (2002).
[Crossref]

R. Stoian, M. Boyle, A. Thoss, A. Rosenfeld, G. Korn, I. V. Hertel, and E. E. B. Campbell, “Laser ablation of ,” Appl. Phys. Lett. 80,353–355 (2002).
[Crossref]

D. Zeidler, S. Frey, W. Wohlleben, M. Motzkus, F. Busch, T. Chen, W. Kiefer, and A. Materny, “Optimal control of ground-state dynamics in polymers,” J. Chem. Phys. 116,5231–5235 (2002).
[Crossref]

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature (London) 418,512–514 (2002).
[Crossref]

2001 (1)

D. Zeidler, S. Frey, K. L. Kompa, and M. Motzkus, “Evolutionary algorithms and their application to optimal control studies,” Phys. Rev. A 64, Art. No.023420 (2001).
[Crossref]

2000 (2)

1999 (2)

T. Feurer, “Feedback-controlled optimization of soft-X-ray radiation from femtosecond laser-produced plasmas,“ Appl. Phys. B 68,55–60 (1999).
[Crossref]

E. Zeek, K. Maginnis, S. Backus, U. Russek, M. Murnane, G. Mourou, H. Kapteyn, and G. Vdovin, “Pulse compression ,” Opt. Lett. 24,493–495 (1999).
[Crossref]

1998 (1)

D. Meshulach and Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature (London) 396,239–242 (1998).
[Crossref]

1997 (4)

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]

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]

T. Feurer, A. Glass, and R. Sauerbrey, “Two-photon photoconductivity in SiC photodiodes and its application to autocorrelation measurements of femtosecond optical pulses,” Appl. Phys. B 65,295–297 (1997).
[Crossref]

D. Yelin, M. Meshulach, and Y. Silberberg, “Adaptive femtosecond pulse compression,” Opt. Lett. 22,1793–17951997).
[Crossref]

1990 (1)

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

Backus, S.

Baumert, T.

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]

Boyle, M.

R. Stoian, M. Boyle, A. Thoss, A. Rosenfeld, G. Korn, I. V. Hertel, and E. E. B. Campbell, “Laser ablation of ,” Appl. Phys. Lett. 80,353–355 (2002).
[Crossref]

Brixner, T.

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]

Brumer, P.

M. Shapiro and P. Brumer, Principles of the quantum control of molecular processes (Wiley-Interscience, 2003).

Busch, F.

D. Zeidler, S. Frey, W. Wohlleben, M. Motzkus, F. Busch, T. Chen, W. Kiefer, and A. Materny, “Optimal control of ground-state dynamics in polymers,” J. Chem. Phys. 116,5231–5235 (2002).
[Crossref]

Campbell, E. E. B.

R. Stoian, M. Boyle, A. Thoss, A. Rosenfeld, G. Korn, I. V. Hertel, and E. E. B. Campbell, “Laser ablation of ,” Appl. Phys. Lett. 80,353–355 (2002).
[Crossref]

Chen, T.

D. Zeidler, S. Frey, W. Wohlleben, M. Motzkus, F. Busch, T. Chen, W. Kiefer, and A. Materny, “Optimal control of ground-state dynamics in polymers,” J. Chem. Phys. 116,5231–5235 (2002).
[Crossref]

Cheng, Z.

Cruz, J. M. Dela

Dantus, M.

DeLong, K.

K. DeLong, “Frog3 Program,”http://www.femtosoft.biz.

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]

Dudovich, N.

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature (London) 418,512–514 (2002).
[Crossref]

Feurer, T.

J. C. Vaughan, T. Feurer, K. W. Stone, and K. A. Nelson, “Analysis of replica pulses in femtosecond pulse shaping with pixelated devices,” Opt. Express 14,1314–1328 (2006).
[Crossref] [PubMed]

T. Feurer, J. C. Vaughan, R. M. Koehl, and K. A. Nelson, “Multidimensional control of femtosecond pulses by use of a programmable liquid-crystal matrix,” Opt. Lett. 27,652–654 (2002).
[Crossref]

T. Feurer, “Feedback-controlled optimization of soft-X-ray radiation from femtosecond laser-produced plasmas,“ Appl. Phys. B 68,55–60 (1999).
[Crossref]

T. Feurer, A. Glass, and R. Sauerbrey, “Two-photon photoconductivity in SiC photodiodes and its application to autocorrelation measurements of femtosecond optical pulses,” Appl. Phys. B 65,295–297 (1997).
[Crossref]

B. Schmidt, M. Hacker, G. Stobrawa, and T. Feurer, “LAB2 - A virtual femtosecond laser lab,” http://www.lab2.de.

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]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++ (Cambridge University2002).

Frey, S.

D. Zeidler, S. Frey, W. Wohlleben, M. Motzkus, F. Busch, T. Chen, W. Kiefer, and A. Materny, “Optimal control of ground-state dynamics in polymers,” J. Chem. Phys. 116,5231–5235 (2002).
[Crossref]

D. Zeidler, S. Frey, K. L. Kompa, and M. Motzkus, “Evolutionary algorithms and their application to optimal control studies,” Phys. Rev. A 64, Art. No.023420 (2001).
[Crossref]

Gerber, G.

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]

Glass, A.

T. Feurer, A. Glass, and R. Sauerbrey, “Two-photon photoconductivity in SiC photodiodes and its application to autocorrelation measurements of femtosecond optical pulses,” Appl. Phys. B 65,295–297 (1997).
[Crossref]

Gunn, J. M.

Hacker, M.

B. Schmidt, M. Hacker, G. Stobrawa, and T. Feurer, “LAB2 - A virtual femtosecond laser lab,” http://www.lab2.de.

Hertel, I. V.

R. Stoian, M. Boyle, A. Thoss, A. Rosenfeld, G. Korn, I. V. Hertel, and E. E. B. Campbell, “Laser ablation of ,” Appl. Phys. Lett. 80,353–355 (2002).
[Crossref]

J. S., Radzewicz

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]

Kapteyn, H.

Kiefer, W.

D. Zeidler, S. Frey, W. Wohlleben, M. Motzkus, F. Busch, T. Chen, W. Kiefer, and A. Materny, “Optimal control of ground-state dynamics in polymers,” J. Chem. Phys. 116,5231–5235 (2002).
[Crossref]

Koehl, R. M.

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, Art. No.023420 (2001).
[Crossref]

Korn, G.

R. Stoian, M. Boyle, A. Thoss, A. Rosenfeld, G. Korn, I. V. Hertel, and E. E. B. Campbell, “Laser ablation of ,” Appl. Phys. Lett. 80,353–355 (2002).
[Crossref]

Kovacs, A. P.

K. Osvay, K. Varju, A. P. Kovacs, and G. Kurdi, “Higher order dispersion control in CPA lasers,” in Conference on Lasers and Electro-Optics, 2001 Technical Digest, paper CTuM10.

Krasinski, J.S.

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]

Kurdi, G.

K. Osvay, K. Varju, A. P. Kovacs, and G. Kurdi, “Higher order dispersion control in CPA lasers,” in Conference on Lasers and Electro-Optics, 2001 Technical Digest, paper CTuM10.

Laude, V.

Leaird, D. E.

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

Lide, D. R.

D. R. Lide, CRC Handbook of Chemistry and Physics (Boca Raton CRC Press, 1998) p. 10-218.

Lozovoy, V. V.

Lüthy, W.

F. Reinert and W. Lüthy, “Optically controlled adaptive mirror,” Laser Phys. Lett. 1,551–554 (2004).
[Crossref]

Lüuthy, W.

F. Reinert and W. Lüuthy, “Thermo-optically driven adaptive mirror,” in Laser Beam Control and Applications IX, A.V. Kudryashov et al. eds., Proc. SPIE 6101,52–58 (2006).

Maginnis, K.

Materny, A.

D. Zeidler, S. Frey, W. Wohlleben, M. Motzkus, F. Busch, T. Chen, W. Kiefer, and A. Materny, “Optimal control of ground-state dynamics in polymers,” J. Chem. Phys. 116,5231–5235 (2002).
[Crossref]

Meshulach, D.

D. Meshulach and Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature (London) 396,239–242 (1998).
[Crossref]

Meshulach, M.

Motzkus, M.

D. Zeidler, S. Frey, W. Wohlleben, M. Motzkus, F. Busch, T. Chen, W. Kiefer, and A. Materny, “Optimal control of ground-state dynamics in polymers,” J. Chem. Phys. 116,5231–5235 (2002).
[Crossref]

D. Zeidler, S. Frey, K. L. Kompa, and M. Motzkus, “Evolutionary algorithms and their application to optimal control studies,” Phys. Rev. A 64, Art. No.023420 (2001).
[Crossref]

Mourou, G.

Murnane, M.

Nelson, K. A.

Oron, D.

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature (London) 418,512–514 (2002).
[Crossref]

Osvay, K.

K. Osvay, K. Varju, A. P. Kovacs, and G. Kurdi, “Higher order dispersion control in CPA lasers,” in Conference on Lasers and Electro-Optics, 2001 Technical Digest, paper CTuM10.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++ (Cambridge University2002).

Reinert, F.

F. Reinert and W. Lüuthy, “Thermo-optically driven adaptive mirror,” in Laser Beam Control and Applications IX, A.V. Kudryashov et al. eds., Proc. SPIE 6101,52–58 (2006).

F. Reinert and W. Lüthy, “Optically controlled adaptive mirror,” Laser Phys. Lett. 1,551–554 (2004).
[Crossref]

Rice, S. A.

S. A. Rice and M. Zhao, Optical Control of Molecular Dynamics, (John Wiley and Sons, 2000).

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]

Rosenfeld, A.

R. Stoian, M. Boyle, A. Thoss, A. Rosenfeld, G. Korn, I. V. Hertel, and E. E. B. Campbell, “Laser ablation of ,” Appl. Phys. Lett. 80,353–355 (2002).
[Crossref]

Russek, U.

Sauerbrey, R.

T. Feurer, A. Glass, and R. Sauerbrey, “Two-photon photoconductivity in SiC photodiodes and its application to autocorrelation measurements of femtosecond optical pulses,” Appl. Phys. B 65,295–297 (1997).
[Crossref]

Schmidt, B.

B. Schmidt, M. Hacker, G. Stobrawa, and T. Feurer, “LAB2 - A virtual femtosecond laser lab,” http://www.lab2.de.

Seyfried, V.

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]

Shapiro, M.

M. Shapiro and P. Brumer, Principles of the quantum control of molecular processes (Wiley-Interscience, 2003).

Silberberg, Y.

N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature (London) 418,512–514 (2002).
[Crossref]

D. Meshulach and Y. Silberberg, “Coherent quantum control of two-photon transitions by a femtosecond laser pulse,” Nature (London) 396,239–242 (1998).
[Crossref]

D. Yelin, M. Meshulach, and Y. Silberberg, “Adaptive femtosecond pulse compression,” Opt. Lett. 22,1793–17951997).
[Crossref]

Spielmann, Ch.

Stobrawa, G.

B. Schmidt, M. Hacker, G. Stobrawa, and T. Feurer, “LAB2 - A virtual femtosecond laser lab,” http://www.lab2.de.

Stoian, R.

R. Stoian, M. Boyle, A. Thoss, A. Rosenfeld, G. Korn, I. V. Hertel, and E. E. B. Campbell, “Laser ablation of ,” Appl. Phys. Lett. 80,353–355 (2002).
[Crossref]

Stone, K. W.

Strehle, M.

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. 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]

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++ (Cambridge University2002).

Thoss, A.

R. Stoian, M. Boyle, A. Thoss, A. Rosenfeld, G. Korn, I. V. Hertel, and E. E. B. Campbell, “Laser ablation of ,” Appl. Phys. Lett. 80,353–355 (2002).
[Crossref]

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]

Varju, K.

K. Osvay, K. Varju, A. P. Kovacs, and G. Kurdi, “Higher order dispersion control in CPA lasers,” in Conference on Lasers and Electro-Optics, 2001 Technical Digest, paper CTuM10.

Vaughan, J. C.

Vdovin, G.

Verluise, F.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++ (Cambridge University2002).

Weiner, A. M.

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

Weiner, A.M.

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

Wiederrecht, G. P.

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

Wnuk, P.

Wohlleben, W.

D. Zeidler, S. Frey, W. Wohlleben, M. Motzkus, F. Busch, T. Chen, W. Kiefer, and A. Materny, “Optimal control of ground-state dynamics in polymers,” J. Chem. Phys. 116,5231–5235 (2002).
[Crossref]

Xu, B.

Yelin, D.

Zeek, E.

Zeidler, D.

D. Zeidler, S. Frey, W. Wohlleben, M. Motzkus, F. Busch, T. Chen, W. Kiefer, and A. Materny, “Optimal control of ground-state dynamics in polymers,” J. Chem. Phys. 116,5231–5235 (2002).
[Crossref]

D. Zeidler, S. Frey, K. L. Kompa, and M. Motzkus, “Evolutionary algorithms and their application to optimal control studies,” Phys. Rev. A 64, Art. No.023420 (2001).
[Crossref]

Zhao, M.

S. A. Rice and M. Zhao, Optical Control of Molecular Dynamics, (John Wiley and Sons, 2000).

Appl. Phys. B (3)

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. Feurer, A. Glass, and R. Sauerbrey, “Two-photon photoconductivity in SiC photodiodes and its application to autocorrelation measurements of femtosecond optical pulses,” Appl. Phys. B 65,295–297 (1997).
[Crossref]

T. Feurer, “Feedback-controlled optimization of soft-X-ray radiation from femtosecond laser-produced plasmas,“ Appl. Phys. B 68,55–60 (1999).
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Figures (5)

Fig. 1.
Fig. 1.

Experimental arrangement with details of the spatial phase modulator (left side) and its integration into the femtosecond pulse shaping setup.

Fig. 2.
Fig. 2.

(a). Phase response to a 5 modulator pixel wide stripe with a spatial width of 2.2 mm and a grey scale value of 255. (b) Phase shift as a function of grey scale value. Here, the whole active area of the modulator was homogeneously illuminated.

Fig. 3.
Fig. 3.

(a) Oscillator spectrum and (b) intensity profile (dash-dotted line) applied to the TO-SLM. The dots represent the measured phase and the solid line a polynomial fit.

Fig. 4.
Fig. 4.

FROG traces of (a). the original oscillator pulse, (b) the pulse broadened by 47 mm of BK7 glass, and (c) the optimized pulse.

Fig. 5.
Fig. 5.

Sinusoidal phase modulation: Measured FROG traces (top row) for (a) 13 periods with ∆t = 213 fs and (c) 8 periods with ∆t = 137 fs. Simulated FROG traces (bottom row) for (b) 13 periods and (d) 8 periods.

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