Theory of a quasi-phase-matched optical parametric oscillator of a backward wave: threshold and spectrum

We theoretically study the stationary and nonstationary modes of the backward wave generation of an optical parametric oscillator based on quasi phase-matching. We obtain convenient analytical expressions in both modes. We derive, for the stationary lasing mode, the optimal values of the pump intensity and the total length of the structure. We present a numerical estimate of the threshold intensity for PPKTP and LiNbO 3 and a comparison with the experiment. It is shown that the group velocity dispersion leads to a narrowing of the backward wave spectrum. But the forward wave pulse phase modulation contributes to the broadening of the central maximum of the backward wave.