OPTIMAL-CONTROL OF SELECTIVE VIBRATIONAL-EXCITATION OF HARMONIC MOLECULES - ANALYTIC SOLUTION AND RESTRICTED FORMS FOR THE OPTIMAL FIELDS

Analytic solutions of the optimal fields giving selective local excitation in harmonic molecules are presented, and calculated by a numerically stable algorithm. It is shown that the optimal fields can be decomposed into a finite number of monochromatic laser fields, with the following properties: (a) the number of component frequencies is equal to the number of normal modes of the molecule; (b) the component frequencies go to the molecular vibrational normal mode frequencies in the limit of low amplitude; (c) there is an inverse relationship between the amplitude of the fields (as controlled by the weighting factor for the field fluence term) and the time T at which the objective is reached; (d) there exists a limiting form for the optimal fields as the controlling time T → ∞ (which had been observed empirically in previous work and now has a regorous mathematical basis). The intensity of the component laser fields, and thus the optimal field can be reduced to any desired level with a corresponding lengthening of the pulses. Thus by varying the design criteria one may determine a corresponding entire family of optimal fields with each member equivalently leading to the desired final local excitations. The optimization procedure clearly illustrates the trade off between optimal pulse length and amplitude. In order to try and achieve the control objectives with consideration of laboratory constraints on the laser fields a formalism is presented for designing the optimal fields with constrained functional forms. An illustration based on linear chain molecules shows that the objectives may be quite well achieved by using realistically constrained optimized fields. © 1990 American Institute of Physics.