Numerical Models of Broad Bandwidth Nanosecond Optical Parametric Oscillators

We present three new methods for modeling broad-bandwidth, nanosecond optical parametric oscillators in the plane-wave approximation. Each accounts for 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 propagation are calculated separately on alternate steps. One method relies on Fourier transforming the fields between t and ω to handle propagation, with mixing integrated over a Δz step; the other transforms between z and kz in the propagation step, with mixing integrated over Δt. The third method is based on expansion of the three optical fields in terms of their respective longitudinal empty cavity modes, taking into account the cavity boundary conditions. Equations describing the time development of the mode amplitudes are solved to yield the time dependence of the three output fields. These models exclude diffraction and group-velocity dispersion but can be readily extended to include them.