Numerical models of broad-bandwidth nanosecond optical parametric oscillators

We present three new methods for modeling broad-bandwidth, nanosecond optic al parametric oscillators in the plane-wave approximation. Each accounts fo r the group-velocity differences that determine the operating linewidth of unseeded optical parametric oscillators, and each allows the signal and the idler waves to develop from quantum noise. The first two methods are based on split-step integration methods in which nonlinear mixing and propagatio n are calculated separately on alternate steps. One method relies on Fourie r transforming the fields between t and w to handle propagation, with mixin g integrated over a Delta z step; the other transforms between z and k(z) i n the propagation step, with mixing integrated over Delta t. The third meth od is based on expansion of the three optical fields in terms of their resp ective longitudinal empty cavity modes, taking into account the cavity boun dary conditions. Equations describing the time development of the mode ampl itudes are solved to yield the time dependence of the three output fields. These models exclude diffraction and group-velocity dispersion but can be r eadily extended to include them. (C) 1999 Optical Society of America [S0740 -3224(99)02103-7] OCIS codes: 190.2620, 190.4410, 190.4970, 230.4320, 140.3 430.