Energy yield of pulsed optical parametric oscillators: a rate-equation analysis

In this paper, for the first time, to our best knowledge, single explicit self-contained rate equations describing the dynamic behavior of pulsed optical parametric oscillators are derived, exactly taking into account the parametric interactions between the three waves in the nonlinear crystal, in contrast to most previous approaches which used a linearized expansion of this interaction. Universal expressions using normalized forms are derived which fully include pump depletion and reconstruction effects. Straightforward numerical integration of these equations allow us to study the input energy-output energy characteristics of these pulsed devices. We thus discuss the subthreshold behavior, threshold power, saturation, and build-up time of optical parametric oscillators and find the validity range in which the usual undepleted regime is retrieved as a limit case of the general expressions. Explicit approximated expressions of build-up times are derived which show in particular that the number of round trips needed to reach a CW behavior may be very large.