Optimal pump pulse shapes for optical parametric oscillators

In this paper we theoretically investigate the most efficient pump temporal shape for pulsed operation of optical parametric oscillators (OPOs). The theoretical analysis consists of solving the optimal control problem using the rate equation formalism. The OPO optimal buildup behavior is derived for any OPO configuration, and we show that the optimal pump pulse shape is a double rectangle. The first rectangle is optimized for the buildup process, while the second one is optimized for the steady state, and both depend differently on the OPO mirror reflectivities as well as the available pump energy and maximum peak power. This double rectangle is quantitatively described and is consistent with previous results reported in the literature. Also, numerical simulations are used to validate our analytical model on a doubly resonant OPO and show consistent results. The numerical simulations also show that an optimal top-hat temporal profile could provide performances very close to the ones achieved with the optimal double rectangle. (C) 2016 Optical Society of America