Supplemental Material: Analysis of the Laser Pulse Shapes
A central issue in this paper is whether the classical rate equations can account for the
measured growth curve of the pyrazine ion. To integrate these equations it is necessary to know
the envelope of the pump pulse. The envelopes of simple pulses, such as a TL pulse train, were
measured using an SD-FROG. For the genetically optimized pulses, three simpler methods were
used to determine the pulse envelope. In the first method, the pulse shape was calculated from the
optimized phase function. In the second method, the envelope was obtained from a crosscorrelation (CC) measurement. In the last method, the calculated pulse was convoluted with the
pulse shape of the probe (a Gaussian function with a 60 fs time constant) and truncated at its tails,
using the CC pulse to determine the endpoints. The classical growth curves obtained using all
three pulse shapes are compared in Fig. S1 with the experimental curves for control times, T, of
(a) 1.0, (b) 1.5, and (c) 5.0 ps. In all three cases the classical growth curves differ substantially
from the measured ones. In cases (a) and (b) the predicted and measured growth curves agree
quantitatively in the asymptotic region (t > 5 ps) and differ substantially at earlier times, regardless
of the method used to obtain them. We note that in case (a) the calculated pulse shape gives the
best agreement with the data in the vicinity of the signal maximum (2 < t < 5 ps). In case (c) the
classical curves at t < 0 obtained using the CC and convoluted pulses are in excellent agreement
with measured one, whereas the ones calculated using the optimized phase function contains
spurious structure. The asymptotic behavior demonstrates that for the early GA the final quantum
yield is unchanged by shaping the pulse, whereas for the late GA control occurs by manipulation
of the absorption step rather than by localization of the wave packet.
Figure S1. Comparison of the calculated and measured ion growth curves using three different methods for
determining the envelope of the pump pulse. The pulse envelopes are estimated by calculation using the optimized
phases (Calc), cross correlation measurements (CC), and by convolution of the calculated pulse shape with the
transform limited pulse, with the tails windowed by endpoints of the CC measurement (Conv).
A second concern is the extent of amplitude modulation obtained when only the spectral
phase is manipulated by the pulse shaper. Figure S2 shows the measured spectrum of the (a) TL
pulse, (b) a pulse train obtained with sine phase, and (c) a genetically optimized pulse with T = 1.5
ps. Both the sine phase and GA pulses show substantial amplitude modulation. The spacing of the
oscillations in the sine pulse spectrum matches the period of the spectral phase function (0.31 vs.
0.30 nm), indicating that the amplitude modulation is likely caused by space-time coupling in the
pulse shaper.35-38 This effect results from diffraction of the laser beam by the phase mask (in this
case the quartz AOM crystal), which introduces a lateral time-dependent spatial shift for different
frequency components of the beam. Stephen Clow38 measured the coupling for sine phases similar
to ours with spatial frequencies of 0.29 and 1.63 periods/mm. In the first case the coupling was
weak, while in the second case it was substantial. In our example, the spatial frequency was ≥
0.80 periods/mm, midway between Clow’s measurements.a
Figure S2. Spectra of the laser pulses for (a) transform-limited pulse, (b) a sine phase pulse, and (c) a genetically
optimized pulse.
The effect of space-time coupling can be rather large if the spectral phase varies
significantly over the spot size of individual frequency components in the Fourier plane of the
pulse shaper.36,38 This condition is likely to occur for a genetically optimized pulse unless a
constraint in included in the algorithm to reduce the phase variation. An example of the spectral
phase generated by the early GA is shown in Fig. S3. The phase jumps at features (a) and (b) are
840 and 115 rad/nm, respectively, corresponding to phase variations ≥ 3.4 rad and ≥ 0.5 rad across
the spot size.a Although it is possible that amplitude modulation contributed to the control
mechanism, the fact that the probe volume was only 1% of the focal volume of the pump laser
mitigated such an effect.
Figure S3. Example of the optimized spectral phase for the early GA.
a
The lower bound applies if the 5 nm width of the laser pulse completely fills the 20 mm aperture of the AOM
crystal.