Optimal control of the electric susceptibility of a molecular gas by designed nonresonant laser pulses of limited amplitude

We present a theoretical study on optimal control of the electric susceptibility change of a homogeneous molecular gas resulting from orientational anisotropy induced by nonresonant lasers with limited intensity. It is assumed that the molecular gas is initially in thermal equilibrium. Two types of optimal control objectives have been considered: terminal control and temporal profile control (i.e., trajectory control). A step function is introduced into the cost functionals which successfully helps to realize the restriction on the magnitude of the field amplitude in numerical optimization, as demonstrated by the examples. Calculations are carried out for CS₂ which has a small rotational constant (B =0.1091 cm^-1) and a quite large polarizability anisotropy (Δα=9.6 ų); For terminal control of a maximal susceptibility change at a target time T, it is found that the optimal control field is composed of a series of rectangular pulses with identical amplitudes equal to a preassigned bound value. All of the optimal fields for terminal control are functions of (T-t) over the time interval [0,T] with characteristic time 1/8B and period 1/2B. For temporal profile control, the degree of control is strongly dependent on the length of time interval over which a target profile is defined. Usually, if a time interval is shorter than 1/8 B and a target profile is a smooth and non-negative function with a reasonable maximal value, the control can be achieved perfectly. In other cases the detailed assignment of the weight function in the cost functional plays an important role in determining how to make an optimally controlled susceptibility change profile approach the target profile. Furthermore, we have also examined the temperature effects on optimal control in this paper. It can be shown that the general optimal control properties observed by CS₂ will also be valid for other linear molecular gases with small rotational constants.