Transverse effects and mode couplings in OPOS

We investigate the triply resonant optical parametric oscillator using a spherical mirror cavity with a pump of arbitrary width. We show that, depending on the size of the pump and the cavity geometry, a cross-coupling between different pairs of oscillating cavity modes occurs. These coupling integrals for the various mode amplitudes are derived from the classical nonlinear field equations in the paraxial approximation and analytically evaluated for a TEM(00) pump field. The corresponding differential equations for the time evolution of the self-consistent mode amplitudes are derived for typical cavity geometries including the propagation integrals within the crystal. We discuss the new physical effects introduced by these couplings in some typical cases. This includes a change of the OPO threshold and stable simultaneous oscillation of several mode pairs with fixed relative phases as well as oscillating self-pulsing type solutions.