Model for mode hopping in optical parametric oscillators

We have developed a model for mode hopping in doubly resonant optical parametric oscillators. The pump produced two pairs of signal-idler modes. We obtain various steady states of interest, namely, when only the first pair oscillates with the other pair that has null amplitudes and vice versa. Stability analysis reveals that there can be an exchange of stability between the oscillating and the zero amplitude pairs. We derive conditions for the exchange of stability in terms of cavity parameters, which can change because of changes in the cavity length or because of fluctuations in the phase of the pump. We demonstrate the exchange of stability from numerical solutions of coupled nonlinear equations for five complex modes (i.e., the pump and the two signal idler pairs). For a specific choice of parameters we also demonstrate the excitation of both the pairs. (C) 1997 Optical Society of America.