Laser pulses optimal control theory

Optimal control theory, as discussed in Sections II-IV, involves the algorithmic design of laser pulses to achieve a specified control objective. However, through the application of certain approximations, analytic methods can be formulated and then utilized within the optimal control theory framework to predict and interpret the laser fields required. These analytic approaches will be discussed in Section VI. 

In early work in the optimal control theory design of laser helds to achieve desired transformations, the optimal control equations were solved directly, without constraints other than those imposed implicitly by the inclusion of a penalty term on the laser huence [see Eq. (1)]. This inevitably led to laser helds that suddenly increased from very small to large values near the start of the laser pulse. However, physically realistic laser helds should tum-on and -off smoothly. Therefore, during the optimization the held is not allowed to vary freely but is rather expressed in the form [60] ... 

In Section IVB1, a perturbative treatment for wave packet control in a weak field was presented. In this section, a general theory based on an optimal control theory is presented. The resulting expression for laser pulses is applicable to strong as well as weak fields. 

Encouraged by the confirmation of the control concept, two-parameter control was considered in order to manipulate different processes in dimers and diatomic molecules. In addition to the pump-probe time delay, the second control parameter involved the pump [72, 73] or probe [66, 67] wavelength, the pump-dump delay [69, 74, 75], the laser power [121], the chirp [68, 76], or the temporal width [70] of the laser pulse. Optimal pump-dump control of K2 has been carried out theoretically in order to maximize the population of certain vibrational levels of the ground electronic state using one excited state as an intermediate pathway [71, 292-294]. The maximization of the ionization yield in mixed alkali dimers has been performed first experimentally using closed-loop learning control [77,78, 83] (CLL) and then theoretically in the framework of optimal control theory (OCT) [84]. 

A field like Eq. (4.3) with separate and overlapping pulses is capable of giving an almost 100% population transfer. This above-the-barrier mechanism is also obtained when using the more sophisticated optimal control theory. Here the laser pulse form is obtained from maximizing the functional (see, e.g.. Ref [48])... 

Tailoring Laser Pulses with Spectral and Fluence Constraints Using Optimal Control Theory. 

Very recently, Jakubetz et al. have extended the applications of our variant of Rabitz s theory of optimal control by IR femtosecond/picosecond laser pulses [31 from vibrational transitions to isomerizations, specifically for the HCN = CNH reaction [4],... 

---