Page 162 - Academic Press Encyclopedia of Physical Science and Technology 3rd Chemical Engineering

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Encyclopedia of Physical Science and Technology EN003H-565 June 13, 2001 20:37

224 Coherent Control of Chemical Reactions

FIGURE 19 Illustration of pulse shaping using a liquid crystal spatial modulator. [Uberna, R., Amitay, Z., Loomis,
R. A., and Leone, S. R. (1999). Disc. Faraday Society 113, 385. Reproduced by permission of the Royal Society of
Chemistry.]

phases and/or amplitudes of the light in each frequency in- ample, only the initial and final states of the control system
terval. To control both amplitudes and phases, two modu- are specified; the multidimensional potential energy sur-
lators are used back-to-back. The two types of devices that faces and the reaction coordinates connecting the initial
have been used for this purpose are a liquid crystal spatial and final states cannot be determined either theoretically
light modulator and an acousto-optic modulator. The mod- or experimentally. In addition, there exist experimentally
ified pulse is finally recompressed by lens L 2 and grating unavoidable uncertainties associated with the controlling
G 2 . fields. The optimal control methods described in previous
The phase and amplitude spectrum of the laser pulse are sections are not well suited for such systems. In such cases,
tailored to create a wave packet with selected properties. a genetic algorithm (GA), which is a global optimization
The various eigenstates that comprise the wave packet are method, may be employed.
populated by different frequency components of the laser A GA has three fundamental operations: reproduction,
pulse, each with its specified amplitude and phase. For crossover, and mutation. By means of these three oper-
1
example, rovibrational wave packets of Li 2 in the E + ations, an ensemble of individuals (i.e., a population) is
g
state were created, consisting of vibrational levels v = 12– adapted to fit its environment. In the first operation, groups
16 and rotational levels J = 17, 19. The phases and am- of individuals that have a higher probability of reproduc-
plitudes of the pump pulse shown in Fig. 20 were gener- ing as a consequence of their better adaptation to their
ated with a 128-pixel liquid crystal SLM. The pulse was environment pass their genetic information onto succeed-
tailored to optimize the ionization signal at a delay time ing generations. In the crossover operation, splicing of the
of 7 ps. The phases used to maximize or minimize the parents’ genes transfers a mixture of their genetic material
ionization signal are shown by solid and dashed lines, re- to their offspring. Genetic diversity of the offspring cannot
spectively, and the intensities at the eigenfrequencies of be created by crossover. By mutation, however, the genetic
the wave packet are indicated by circles. material is altered to avoid premature convergence to an
undesirable trait.
The GA procedure has an interactive feedback (closed)
C. Genetic Algorithms
loop structure without any intervention by the experimen-
There are many cases in which the molecular Hamil- talist. An initial guess of multiple sets of control fields is
tonian and the interactions with the photon fields are evaluated for its success in achieving the target. The most
not completely known. For many isolated polyatomic successful members of this population are transformed by
molecules or for molecules in condensed phases, for ex- the three GA operators, and their offspring are evaluated.