Minimizing the transition time in lasers by optimal control methods: Single-mode semiconductor laser with homogeneous transverse profile

The introduction of patterned current fronts that steer the transition between directly modulated optical bits allows for a strong modification in the shape of the trajectory evolving from the initial to the final state in semiconductor lasers. The problem of minimal transition time between two stationary points of the system will be formulated in the framework of optimal control theory. In this approach, the patterned current fronts serve as time-dependent control functions for which upper and lower bounds are imposed. We first calculate the optimal control on a Lotka–Volterra model, which qualitatively well describes the dynamic response of several types of lasers. The optimal control is of “bang-bang” type and switches from the upper to the lower value of the control bounds. Then, we consider a more specific semiconductor laser model and show again that the optimal control is bang-bang, and calculate specific trajectories for the transition between the below-threshold state and one where the laser is emitting. The sensitivity of the trajectory to external perturbations is also studied.