Optimum pulse shape

Step 3 To determine the optimum pulse shape the excitation profile should be calculated. The excitation profile can be simulated using either the Excitation Profile option of the Bloch module or as in Check it 5.2.2.1 a ID spectrum. The Bloch module can display both transverse magnetization components on the same graph while ID WIN-NMR can only show either the x- or the y-component (see Check it 5.2.2.1). 

Figure 19.1 Diagram showing the arrangement for closed-loop learning control. Following a femtosecond laser pulse, the products of the photochemical process are detected and compared with the user-defined objectives stored on the computer. A learning algorithm then calculates the modified electric fields required to shape the laser pulse and further optimize the yield of the desired product. Cycling through the loop many times gives the optimum pulse shape and best product yield. Adapted from Brixner et o/, Chem. Phys. Chem., 2003, 4 418, with permission of John Wiley Sons Ltd...

Fourier Transform-limited 100 fs, 800 nm, 1015 W cm 2 laser pulse and (b) the optimum result obtained by means of an 80-parameter unrestricted optimisation (dashed line) and a restricted 3-parameter optimisation (full line). The inset in (b) shows the evolution of the fitness value for the 80 parameter optimisation (full squares maximum fitness, open squares average fitness), (c) Autocorrelation trace of the optimal pulse corresponding to the 80 parameters optimisation. The pulse shapes consists of two pulses of 120 fs of equal amplitude separated by 500 fs. 

Figure 13.9 Aspects of optimum laser pulses in adaptive feedback control of products pi laser excitation of CpFe(CO)2Cl, Autocorrelation G2(t) is shown for three different cases described in text. Pulse shape differences in these three pulses is evident. (Taken from Fig. 4 Ref. [43].)...

Finding the best shaped pulses (optimum field) to identify a compound can be a time consuming task given the almost infinite number of possibihties that a pulse-shaper provides. Using 100 pixels and only 100 phase values with 10 different amplitudes results in 10300 possible laser fields (pulse shapes). Such a staggering number of experiments... 

In the first scheme it is not necessary to use two different lasers if a femtosecond pulse with a broad spectral range is used for excitation. The different spectral components in the pulse give rise to many different excitation paths. In order to achieve optimum population in the excited state, the relative phases of these different spectral components have to be optimized. This can be realized by the pulse-shaping techniques discussed in Sect. 6.1.11 (Fig. 10.11). Here a plate of many liquid crystal pixels are placed in the laser beam, which changes the phases of the lightwave by orientation of the molecules where a feedback loop with a learning algorithm is used to maximize or minimize the wanted decay channel of the excited state [1402,1403]. 

It is important to emphasize that, in the above examples, knowledge of the PES was not required for the optimization process. The adaptive-control learning algorithm explores the available phase space and optimizes the evolution of the wave packet on the excited state PES without any prior knowledge of the surface. Thus, the intrinsic information about the excited-state dynamics of these polyatomic systems remains concealed in the detailed shape and phase of the optimized pulse. Inevitably, however, scientific curiosity, together with a desire to imder-stand how chemical reactions can be controlled, has led to pioneering studies that aim to identify the underlying rules and rationale that lead to a particular pulse shape or phase relationship that produces the optimum yield. 

Further advances in the field of coherent chemistry will require improved time resolution and tunability of the laser sources in the experiments [434]. Shorter laser pulses with a pulse duration of less than 20 fs will be appropriate. The optimum control technique will be achieved by specially tailored femtosecond pulse shapes [435-439], determined by sophisticated calculations using the theories of coherent chemistry [440-444]. Finally, more elaborate polarization and multipulse excitation schemes, including chirped and ultra-short pulses, will be needed. 

The peak rf amplitude required to achieve optimum excitation with a selective excitation pulse is given in comparison to the rf amplitude required to achieve an on-resonance 90° flip-angle with a selective rectangular pulse, the simplest conceivable shape. 

The success of an ultrasonic NDC application depends upon the selection of the best-qualified transducer (i.e., one with optimum frequency response, pulse width and shape). Transducer characteristics can be customized through the use of the best-suited piezoelectric material, such as lead zirconate-lead titanate, lead metaniobates, polymer piezoelectrics, and other advanced ferro-electric materials. 

Load the configuration file ch5236.cfg and perform a set of simulations varying the power level of the shaped pulse spO 61, 62.5 (optimum for a 90° tilt angle), 64 and 68 [Hz]. Process the set of data in ID WIN-NMR in exactly the same way zero filling of Sl(r+i) 32k and apodization EM, LB 7.0 [Hz]. Compare the spectra using the ID WIN-NMR multiple display mode. 

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