Minimizing transient times in a coupled solid-state laser model

We consider a system of ordinary differential equations modelling the dynamics of two coupled solid-state lasers. Under the dynamics, this system may execute transitions between in-phase and out-of-phase states. For satellite communications and high-speed data transfer the transition times should be reduced to their shortest possible duration. In this paper, we apply optimal control theory to find the values of various laser parameters (e.g. the amplitude of the injected field, detunings, and coupling constants) which minimize the transient times between out-of-phase and in-phase states. The effect of each parameter is shown to be independent of the other two, and the transient time is shown to be a strictly increasing function of detuning and a strictly decreasing function of the coupling constant and amplitude of the injected field. The effect of initial conditions on transient times is also analysed.