(Color online) Steady-state absorption spectra of 1,3-cyclohexadiene (CHD, dot-dashed line) and cis-1,3,5-hexatriene (Z-HT, solid line). The oscillator strength of HT is approximately eight times that of CHD (Ref. 6). A cartoon (not to scale) of the electronic states and molecular conformations playing a role in the photochemistry of CHD is also shown in the figure.
Comparison of the probe pulses used for detection of the photoproduct Z-HT. The anticipated difference spectrum for the production of Z-HT from CHD in cyclohexane (dashed line) is shown for comparison. The discrete probe using the UV lines generated in a high-pressure Raman cell consists of narrow peaks at 266, 276, 287, 299, and . The dot-dashed line illustrates a typical UV continuum probe. The points represent a difference spectrum obtained using the UV continuum probe and a transform-limited pump pulse . This spectrum shows resolution of the full 0-0 peak of Z-HT.
Trajectory illustrating the fitness of the best pulse for each generation (filled) and median fitness of each generation (open circles) of a typical experiment. Fitness is normalized to the plateau rather than absolute best fitness.
(Color online) Sample difference spectra that best met the control goal in GA searches using the Raman probe. The dashed line is the expected difference spectrum for the production of cis-1,3,5-hexatriene from CHD. The pulse optimized under control goal 2 produced strong absorption for two of the probe lines (triangles) compared with the transform-limited pulse (circles).
(Color online) Difference spectra observed following excitation of CHD in hexane with an pulse. The time delay of the probe was . Dashed line: the difference between the steady-state spectra of Z-HT and CHD. Solid line: fit to the difference spectra observed following excitation of solvent-only samples with transform-limited pulses. Filled circles: the difference spectrum produced by excitation of CHD in hexane with randomly generated pulse shapes. Diamonds: the difference spectrum observed following excitation of CHD in hexane with transform-limited pulses. Open circles: the difference spectrum obtained by the GA with the control goal 1. Triangles: the difference spectrum obtained by the GA with control goal 2.
UV-VIS spectra obtained from irradiated samples of the CHD solution (solid) and neat hexane (dashed). The pulse is transform limited. The structure of the hexatriene spectrum is clearly resolved following excitation of CHD. Additional photoproducts are seen in both the CHD solution and pure hexane. However, Z-HT is observed only in the CHD solution.
(Color online) UV-VIS difference spectra were obtained as the difference between a sample irradiated with the optimal pulse and a reference sample irradiated with a nearly transform-limited pulse. Difference spectra for three pairs of pulse shapes are shown (solid, small dashes, and dot-dashed lines). A reference spectrum for Z-HT is also shown (large dashes). The inset shows the phase responsible for the corresponding difference spectra. Negative chirp is a common feature among the pulses with higher Z-HT yield. A phase function with pure linear chirp, , is shown in the inset for reference (large dashes).
Correlation between the pulse fitness and the calculated nonlinear power for a GA experiment with the goal of doubling pulses in a BBO crystal. The nonlinear power spectrum was calculated using calibrated phase and amplitude profiles for every pulse tested in the algorithm. Both the measured and calculated powers have been normalized to the pulse with the highest conversion efficiency. The measured second-harmonic power is highly correlated with the calculated .
Correlation between the pulse fitness and calculated nonlinear power for two different GA experiments using control goal 1. The nonlinear power spectrum was calculated using calibrated phase and amplitude profiles for every pulse tested in the algorithm. The GA experiment in (a) had the probe at a relatively short delay of ca. , while the GA experiment in (b) had the probe at a long time delay of ca. .
Wigner representation plots of optimal pulses from a narrow bandwidth experiment (top left) and a broad bandwidth experiment (top right). Each pulse exhibits a negative quadratic phase with (left) and (right). Negative cubic phase is responsible for the prepulse train evident in the intensity profiles for the two pulses (bottom).
Pulse performance is compared with the second-order (top) and third-order (bottom) terms from a polynomial fit. Pulse fitness converged to a linear chirp parameter, . Convergence was less clear in the cubic chirp parameter.
Chirp parameters for best pulse shapes. Unless otherwise specified the delay time between the pump and probe is at least and the solvent was hexane. Pulse energies increase moving down the table. All pulse energies are within a factor of 2.
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