Oscillation characteristics of continuous-wave optical parametric oscillators: beyond the mean-field approximation

We reconsider the equations describing the continuous-wave behavior of optical parametric oscillators (OPOs) by exactly taking into account the parametric interaction between the three waves in the nonlinear crystal, in contrast to the most recent approaches that used a linearized expansion of this interaction (mean-field approximation). Universal expressions using normalized forms are derived that fully include pump depletion and reconstruction effects, as well as the detunings of the signal and idler waves with the cavity resonances. These expressions allow us to discuss the threshold, saturation, output power, and oscillation frequencies of singly resonant OPOs, balanced or unbalanced doubly resonant OPOs, and pump-enhanced OPOs. These expressions also allow us to find the validity range in which the usual linearized regime is retrieved as a limit case of the general expressions. We show in particular that the linear theory is hardly applicable in the SROPO case but has a broader range of relevance for most doubly resonant OPOs. These results will be very useful for the development of cw OPOs that use efficient nonlinear materials and high-power pump lasers. (C) 2002 Optical Society of America.