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

1. Introduction

Pulse shaping [1] has found numerous applications from relatively simple tasks, such as dispersion compensation [2, 3, 4], to more complex challenges, such as controlling material processing [5] or chemistry [6, 7]. Frequently, pulse shaping is combined with a feedback loop and the pulse shaper’s transfer function is adaptively optimized until the desired goal is reached [2, 3, 4, 8]. Pulse shaping is a technique which heavily relies on the performance of the modulator used. To date, a wide range of modulators is available and they are usually classified in pix-elated and non-pixelated devices. Non-pixelated devices are ideally suited whenever smoothly varying phase modulations without any discontinuities [1, 4, 8, 9] are required; partly to avoid unwanted replica pulses [10]. Examples are the residual dispersion compensation or the application of a sinusoidal phase pattern [11] to control two- or multi-photon transitions [6, 7, 12], to enhance the selectivity in nonlinear spectroscopy [13, 14], or for in-situ pulse characterization [15] to name but a few.

Recently, a thermo-optically driven spatial phase modulator has been described [16, 17]. It is based on the variation of the refractive index of a fluid with temperature. A standard projector is used to deposit radiation energy in a user-defined pattern, causing a temperature and thus a refractive index modulation. On a theoretical basis, thermally induced dispersion control has been discussed earlier [18], but the only phase modulation considered had a parabolic shape with adjustable amplitude. Here, we report on a programmable thermo-optically driven spatial light modulator (TO-SLM: non-pixelated device) for femtosecond pulse shaping.

2. Experimental

Figure 1 (left side) shows a schematic diagram of the TO-SLM. The display of a standard computer-controlled projector was imaged onto the modulator, which consisted of a dye-doped liquid sandwiched in between two glass slides. The type of dye molecules and their concentration were chosen such that they efficiently absorb part of the projector’s spectrum. The absorbed energy is then transferred to the solvent and, where heated, the solvent changes its index of refraction due to thermal dispersion. For thin liquid layers with negligible in-plane heat transfer but sufficiently good thermal coupling to the supporting glass plates the illumination pattern yields a stationary phase pattern. This pattern is then exploited to modulate the frequency spectrum of a short laser pulse (see below).

 figure: Fig. 1.

Fig. 1. Experimental arrangement with details of the spatial phase modulator (left side) and its integration into the femtosecond pulse shaping setup.

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The liquid, a 1.4 ∙ 10-2 molar aqueous solution of Rhodamine B, was filled in a 1 mm thin gap between two 6 mm thick BK7 windows. The outer side of the front window had a broadband antireflection coating and the outer side of the back window was highly reflective for the laser spectrum around 808 nm, but had a larger than 60% transmission between 400 nm and 650 nm. The average thermal dispersion of H2O between 20 °C and 70 °C at 808 nm is -1.5-10-4 °C-1 [19], that is, the index of refraction decreases with temperature. When compared to the liquid, the glass windows have a positive thermal dispersion which is about two orders of magnitude lower [20] but their thickness is 12 times higher. Even if the glass windows are in thermal equilibrium with the liquid, the optical path variation is dominated by the liquid. The projector was operated with its original optics removed and the 14 mm × 10.5 mm large digital light processing chip with 1024 × 768 pixels was imaged onto a 45 mm × 5 mm large area at a mid-layer in the liquid by a suitable combination of cylindrical lenses. Only grey scale values between 0 and 255 were used. Although the projector has 1024 horizontal pixels, all experiments were performed with 100 ’modulator’ pixels, each approximately ten display pixels wide. In principle, the modulator allows for 2D pulse shaping [21]; here, it was used as a one-dimensional phase-only pulse shaper. The TO-SLM was inserted into a folded 4f zero-dispersion compressor and the total active area corresponded to a spectral width of about 130 nm. The laser pulses were reflected at the dielectric coating of the back glass window and thus passed twice through the liquid layer. Given the relatively moderate transmission of the TO-SLM of 60%, the total transmission of the shaper was 30%. The emission spectrum of the Ti:sapphire oscillator (KML Inc.) was centered at 808 nm and had an almost Gaussian shape with a full width at half maximum (FWHM) of 52 nm allowing for bandwidth-limited pulses of about 20 fs. The output power of the oscillator was 305 mW and the repetition rate around 90 MHz. The laser pulses were fully characterized with a second harmonic frequency resolved optical gating (FROG) setup [22, 23]. For feedback controlled optimization purposes the intensity of the pulses was recorded with a SiC diode [24].

3. Results and discussion

The achievable maximum phase shift and horizontal spatial resolution of the TO-SLM were characterized with an interferometer (ZYGO Mark II) at 632 nm. The illumination beam was chopped with a bright/dark ratio of 5:1 and the interference images were recorded during the dark periods. The dark periods were shorter than the response time of the modulator (about 1 s) to avoid fluctuations in the index profile. Figure 2(a) shows the phase modulation extracted from the interferogram for a stripe-like illumination with a grey scale value of 255. The stripe was 5 modulator pixels wide, which corresponded to 2.2 mm in the liquid layer. The measured phase modulation was roughly Gaussian with a FWHM of 3.9 mm and a maximum phase shift of about 6 rad. A deconvolution with the known illumination pattern yielded a spatial response function with a FWHM of about 3.5 mm. The moderate spatial resolution is partly due to the low heat conductivity of the front and back glass windows. A separate calibration measurement with a uniform illumination over the entire active area as a function of the gray scale value revealed a maximum phase shift of 50 rad [Fig. 2(b)]. The nonlinear dependence observed is due to the nonlinearity of the total emitted radiation power as a function of the grey scale value. When the phase shift is plotted versus the measured radiation power at the liquid layer, a linear dependence is found. However, the calibration graph shown in Fig. 2(b) is of greater practical importance. The observed maximum phase shift of about 50 rad is much higher than the maximum of 6 rad when only 5 modulator pixels were on. A similar behavior is observed with deformable membrane mirrors [4]. While in the latter case it is related to the elastic properties of the membrane, here it is affected by the heat transport within and out of the liquid. Knowing the phase response function allows calculating either the resulting phase modulation for a given illumination pattern or, vice versa, the necessary illumination pattern for obtaining a desired phase modulation.

 figure: 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.

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In a first experiment the shaper’s ability to compress phase modulated pulses was tested. All phase calibration data obtained with the interferometer remain approximately valid at 808 nm, because the dispersive properties of water change by less than 1% [19]. In addition to the already present dispersive material a 47 mm thick BK7 glass block, having a second order phase of about 1030 fs2, was inserted into the beam path (see Fig. 1). The SiC diode signal was used as a feedback for a Simplex-Downhill algorithm [25, 26] with the aim to maximize the diode signal and therefore to minimize the pulse duration. Ideally, the shortest pulse duration should correspond to a transform limited pulse. In order to keep the number of fit parameters small, the expected illumination pattern was approximated by a suitable analytic expression. A reasonable choice was y=Aexp[(xx0)2Δx2]+D(xx0)3, where the first term approximates the convolution of a mainly quadratic phase with the spatial response function and the second term allows for some asymmetry if necessary. The index of the modulator pixels is x, x 0 allows for a horizontal offset, A and ∆x control the amplitude and the width of the Gaussian, and D quantifies the asymmetry. The four parameters [A, x 0, ∆x, D] were optimized by the closed loop system and after a few hundred iterations the feedback signal converged. The best parameters found were: A = -231, x 0 = 50.0, ∆x = 4.1, and D= 4.9∙10-5.

The oscillator spectrum and the illumination pattern deduced from the fit parameters are shown in Figs. 3(a) and (b). The phase shift was independently measured with the interferometer and is represented by the dots in Fig. 3(b). In the region where the spectrum is non-zero the phase is of almost perfect quadratic shape, compensating for the large second order phase introduced by the BK7 glass. A polynomial fit [solid line in Fig. 3(b)] to the phase values yields a second order phase of (1300±500) fs2, which is in reasonable good agreement with the expected value.

 figure: 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.

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 figure: 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.

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To independently verify the success of the optimization a sequence of three FROG traces was recorded. The FROG trace of the oscillator pulse [Fig. 4(a)] indicates that there was some residual phase modulation present, which manifests itself in small wings and side lobes. After 47 mm of BK7, the pulse was broadened to several hundred femtoseconds and the corresponding FROG trace in Fig. 4(b) exhibited a relatively complex structure. Despite the simplicity of the analytical illumination function, the FROG trace of the optimized pulse in Fig. 4(c) shows very little structure, implying that most of the phase modulation has been compensated for by the pulse shaper. The result was also better than the original oscillator pulse, as some of the lobes and wings have been removed.

A further useful test is to apply a sinusoidal phase pattern, which produces a pulse train that replicates the original pulse; this is important for many coherent control applications [11, 12, 27]. Figure 5 (top row) shows FROG traces for sinusoidal phase modulations with 8 and 13 periods across the modulator area. In both cases the grey scale value was oscillating between 0 and 255. The replica are separated by 137 fs and 213 fs from their nearest neighbors, which is in good agreement with the simulations [28] shown in Fig. 5 (bottom row). To reproduce the relative amplitudes of all replica, the peak-to-peak values of the sinusoidal phases were adjusted to 2.7 and 1.5 rad, respectively. In other words, as the number of periods increases the accessible amplitude range of the sinusoidal phase modulation decreases. Such a behavior is expected from the finite spatial response function of the modulator. The higher the spatial frequency of the sinusoidal illumination pattern, the more the phase pattern is blurred by the response function. Here, the useful number of periods is limited to about 20, restricting the maximum inter-pulse delay to 340 fs.

 figure: 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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4. Conclusion

We have presented a new type of programmable phase modulator for femtosecond pulse shaping, which is based on a thermo-optically induced spatial variation of the refractive index. Initial experiments have proven that the modulator is adequate to achieve some selected tasks

Acknowledgments

We would like to thank A. Friedrich for manufacturing the dielectric coatings. This work was supported in part by the Swiss National Science Foundation under project 200020 109262/1 and the National Center of Competence in Research: Quantum Photonics, subproject 5C.

References and links

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

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

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

8. P. Wnuk, Radzewicz J. S., and J.S. Krasinski, “Bimorph piezo deformable mirror for femtosecond pulse shaping,” Opt. Express 13,4154–4159 (2005). [CrossRef]   [PubMed]  

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. 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]  

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]  

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

15. B. Xu, J. M. Gunn, J. M. Dela Cruz, V. V. Lozovoy, and M. Dantus, “Quantitative investigation of the multiphoton intrapulse interference phase scan method for simultaneous phase measurement and compensation of femtosecond ,” J. Opt. Soc. Am. B 23,750–759 (2006). [CrossRef]  

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

17. 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).

18. 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.

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

20. SCHOTT Technical Information, TIE-29: Refractive Index and Dispersion, April 2005).

21. 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]  

22. 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]  

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

24. 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]  

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.

References

  • View by:

  1. A.M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71,1929–1960 (2000).
    [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]
  6. M. Shapiro and P. Brumer, Principles of the quantum control of molecular processes (Wiley-Interscience, 2003).
  7. S. A. Rice and M. Zhao, Optical Control of Molecular Dynamics, (John Wiley and Sons, 2000).
  8. P. Wnuk, Radzewicz J. S., and J.S. Krasinski, “Bimorph piezo deformable mirror for femtosecond pulse shaping,” Opt. Express 13,4154–4159 (2005).
    [Crossref] [PubMed]
  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. 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]
  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]
  14. N. Dudovich, D. Oron, and Y. Silberberg, “Single-pulse coherently controlled nonlinear Raman spectroscopy and microscopy,” Nature (London) 418,512–514 (2002).
    [Crossref]
  15. B. Xu, J. M. Gunn, J. M. Dela Cruz, V. V. Lozovoy, and M. Dantus, “Quantitative investigation of the multiphoton intrapulse interference phase scan method for simultaneous phase measurement and compensation of femtosecond ,” J. Opt. Soc. Am. B 23,750–759 (2006).
    [Crossref]
  16. F. Reinert and W. Lüthy, “Optically controlled adaptive mirror,” Laser Phys. Lett. 1,551–554 (2004).
    [Crossref]
  17. 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).
  18. 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.
  19. D. R. Lide, CRC Handbook of Chemistry and Physics (Boca Raton CRC Press, 1998) p. 10-218.
  20. SCHOTT Technical Information, TIE-29: Refractive Index and Dispersion, April 2005).
  21. 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]
  22. 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]
  23. K. DeLong, “Frog3 Program,”http://www.femtosoft.biz.
  24. 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]
  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)

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]

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]

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)

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]

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

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

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]

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).
[Crossref]

Appl. Phys. Lett. (1)

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. Chem. Phys. (1)

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]

J. Opt. Soc. Am. B (1)

Laser Phys. Lett. (1)

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

Nature (London) (2)

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]

Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. A (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]

Proc. SPIE (1)

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).

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. 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]

Science (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]

Other (8)

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

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

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

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

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

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.

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

SCHOTT Technical Information, TIE-29: Refractive Index and Dispersion, April 2005).

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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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