Analytical solution for a lossy singly resonant optical parametric oscillator

We present a simple analytical solution for a singly resonant optical parametric oscillator (OPO). The analysis permits calculating the depletion efficiency of the OPO even when the resonated signal (or idler) suffers from strong intracavity losses. The main results are (1) that the maximum efficiency as a function of the pump power is highly dependent on the mirror reflectivity and on the intracavity losses; (2) that the threshold intensity and the pump intensity at which maximum efficiency is reached depend on the reflectivity, and the ratio between the two intensities maintains the relation 1 ≤ I^max₃/I^th ≤ π²/4; and (3) that the maximum efficiency for a Gaussian beam is 70%.