Discrimination mechanism

We analyze now the shape of the UV pulse resulting from the previous optimization. Figure 6.16 shows the normalized depletion curves of both molecules, obtained from the shaped pulse (Fig. 6.16 (a)) and from the reference pulse (Fig. 6.16 (b)), with the corresponding experimental UV-IR cross-correlations integrated (as described by Eq. 6.12) superimposed.

In the case of the optimized pulse, we notice that, contrary to the case

Figure 6.16: Left panel: Normalized depletion curves measured with (a) the optimized UV pulse (b) the unshaped UV pulse. Blue: Trp. Red: Tyr.

Open shapes represent the data. Solid lines represent moving averages over 5 points. The integrated experimental cross-correlations (black curves) have been superimposed to the depletion curves for comparison. Right panel:

Experimental cross-correlations for (a) the optimized UV pulse (b) the un-shaped UV pulse. The depletion traces of Trp (blue) and Tyr (red) have been derived and superimposed (the derivative data has been smoothed).

presented in Sect. 6.3.3, the slopes of the depletion curves are not lim-ited by the cross-correlation overall duration. Indeed, while the second

130 CHAPTER 6. ODD OF AMINO-ACIDS

part of the rise (0 ps < τ < 1 ps) of both curves is well superimposed to the integrated cross-correlation, the first part of the rise of both deple-tion curves (−1 ps < τ < 0 ps) grows clearly slower than the integrated cross-correlation trace. As a further verification, we also superimposed to the cross-correlations (Fig. 6.16 (right panel)) the derivatives of the deple-tion curves of Trp and Tyr. If the rise of the depledeple-tion traces was limited by the instrumental response function, their derivatives would have the same duration as the cross-correlation, which is clearly not the case here, neither for the optimized pulse, nor for the reference one.

Figure6.17depicts the X-FROG measurement of the optimized UV pulse.

One can see that the pulse is asymmetric: it presents an important positive chirp, and it shows an elongated tail formed by the blue components of the spectrum. The spectral phase of the optimized pulse could be retrieved by inversion of the X-FROG (Fig. 6.17 (right panel)) and one can see that the dominant trend is a positive chirp, of approximately5100 fs².

Figure 6.17: Left: XFROG of the optimized UV pulse. Right: Retrieved spectral phase of the optimized UV pulse plotted as a function of the wave-length.

We have seen from Fig. 6.14that the optimized pulse has mainly acted on the dynamics of Trp, suppressing the dip on the depletion curve. As we will see in more detail in Chap. 7, the process leading to fluorescence depletion can mainly be attributed to ionization [194, 195]. The IR pulse promotes the molecule to higher ionizing states, namely¹B states corresponding to the deep UV absorption band of Trp centered at 220 nm [196, 197]. The fluo-rescent S₁ state is therefore efficiently depopulated. In addition, numerical simulations have shown that crossings between S1 and other repulsive excited

6.4. DISCUSSION 131 state surfaces exist [172]. This leads to other ionization and non-radiative deexcitation pathways, also contributing to fluorescence depletion. Within this scenario, and in presence of an unshaped laser pulse, we attribute the dip of fluorescence depletion at early times to the opening of a Franck-Condon window toward these higher ionizing and dissociative states. This window, corresponding to a high S₁ −S_N dipole moment, becomes less favorable at longer delays and therefore the absolute value of the depletion tends to an asymptotic constant value after approximately 2 ps.

On the contrary, the optimally shaped UV pulse could lead to the cre-ation of a wavepacket evolving differently, leading to a less efficient coupling between theS₁ vibrational states with the vibrational states of ¹B_a and ¹B_b. This would be an explanation for the absence of dip of the depletion trace of Trp measured for the optimized pulse. Note that the timescale of this process is quite long (∼1 ps), therefore, we expect a loss of coherence by the end of the interaction, preventing the revival of wavepacket oscillations.

6.4 Discussion

The apparent greater success of single-objective optimizations over multi-objective optimizations in this experiment should not be seen as a contra-diction to what has been presented in Chap. 3. The outcome of many optimizations has been biased by several limitations related to the set-up.

The first issue encountered was the noise of the depletion signals, in par-ticular the low S/N ratio of Tyr, that prevented several single-objective, as well as two-objective optimizations to succeed. As already mentioned, in both cases, any definition of the objectives that would give too much weight to δ_{T yr}, was bound to yield poor, or no convergence of the optimiza-tion. We should recall that this experiment is extremely sensitive to the laser phase and intensity fluctuations, even more considering that we employ DUV pulses. Moreover, the laser used was an amplified laser system, contrary to the experiment presented in Chap. 3, which made use of an oscillator, in-herently subjected to much less fluctuations than an amplified chain. It is obvious from these results that in future discrimination experiments, great care should be taken to minimize noise, in order for optimizations to con-verge to reliable solutions. The issue of signal fluctuations due to the control field or to the environment has been addressed both theoretically and ex-perimentally [88, 119, 198, 199, 200, 201, 202] and the importance of both shot-to-shot and long-term stability (typically on the timescale of a GA gen-eration) have been highlighted [119]. Filtering out the bad laser shots, and accounting for slow laser drifts is time consuming. Therefore, setting more

132 CHAPTER 6. ODD OF AMINO-ACIDS constraining conditions in the signal treatment discussed above is of course possible, but should be done with care not to increase in an exaggerated way the optimization time.

Second, unwanted amplitude modulations of the probe by the IR Dazzler also biased optimizations where one of the objectives was explicitly defined as one of the depletion signals (see Eqs. 6.4 and6.5) (Sect. 6.3.3). Although undoubtedly presenting great advantages in terms of ease of alignment and size, making them particularly suitable for our pump-probe set-up, Dazzlers has proven to be difficult to implement in a closed-loop configuration (see also Sect. 2.3.2). To the best of our knowledge, Dazzlers have been used in a limited number of closed-loop control experiments [72, 84, 203, 204, 205], and the bias induced by phase-amplitude coupling in optimizations has been mentioned and addressed in at least two publications [203, 206]. In partic-ular, Form et al. calculated the minimum and maximum values allowed for the linear chirp, in order to ensure a constant diffracted intensity [206]. Al-though severely limiting the range of allowed values of the phase, the authors concluded to the feasibility of optimal control within those limits. However, they did not extend their calculations to the third and fourth order deriva-tives of the spectral phase. From our experience, adding these parameters further limits the "safe" operation range of the Dazzler. This is unfortunate, as for closed-loop control to succeed, there should be as few restrictions on the control field as possible. Also, the complexity of the shapes that Dazzlers can generate is limited. In Sect. 5.4.1 it was shown that the complexity of the pulse shape dramatically limited the intensity of the diffracted beam.

In the same way, generating complex pulse trains, like those responsible for discrimination in Rothet al. [36], would be particularly difficult, specially in the context of a closed-loop optimization.

Finally, the results presented here confirm that it is essential in optimal control to put the process to optimize in competition with another process to avoid convergence to trivial solutions: SHG in the case of FMN two-photon excited fluorescence enhancement (Chap. 3), TPA of water in the case of adenine fluorescence enhancement (Chap. 5), or Tyr depletion against Trp depletion here. Changing the shape of the depletion curve of Trp here would have been impossible if this signal had not been in competition with Tyr depletion. Indeed, maximization or minimization of Trp depletion alone would only yield the algorithmically correct, but trivial solution consisting in a mere temporal shift of the optimized pulse. Care should be taken however not to further increase the complexity of the definition of the objectives, as this leads to a complex and difficult to understand behavior of the objectives.