Progress in modeling nanosecond optical parametric oscillators

The main challenge in developing a comprehensive numerical model of nanosecond optical parametric oscillators (OPO) is adequately accounting for both dispersion inside the nonlinear crystal and diffraction inside and outside the crystal. In separate accounts we have described how diffraction and dispersion can be handled individually in approximate OPO models. It is relatively straightforward to combine the diffractive and dispersive models, and we have recently done so. Briefly, we use a split-step algorithm in which dispersive/diffractive beam propagation is handled using fast Fourier transform (FFT) methods, while nonlinear mixing is computed using Runge-Kutta integration. Simulations of typical nanosecond OPO with linewidths of a few cm^-1 and pump pulse durations of a few nanoseconds run on a 400 MHz personal computer in a few hours with memory demands of order 100 Mbytes. Dispersion in nanosecond OPO is usually important only if the signal and idler have broad bandwidth due to initiation from quantum noise fields, so a complete OPO model must provide a realistic simulation of the noise fields. We do this by defining as an initial condition input signal and idler noise fields that will impinge on the OPO mirrors over the time interval of the pump pulse. Each signal and idler input field mode is filled with light of random phase with a random amplitude exponentially weighted to average one photon per mode. A sufficient number of spectral modes are filled to span the acceptance bandwidth of the nonlinear crystal, and a sufficient number of spatial modes are included to span the angular acceptance of the crystal and cavity. Any input signal and idler coherent light, such as cw seed light, is added to this noise field. This makes it possible to simulate both the angular and frequency spectra of the OPO output and its pulse-to-pulse variation