BIFURCATION DIAGRAMS FOR 2ND HARMONIC-GENERATION IN PASSIVE CAVITIES

We study analytically and numerically second harmonic generation in a passive resonant cavity excited by an external laser beam at the fundamental frequency. We consider the double limit in which (i) the nonlinear doubling crystal acts as an instantaneous converter and (ii) the mirrors of the cavity fully reflect the fundamental mode. We determine domains of stability for the steady solution and for the periodic solutions which are found in the vicinity of the steady solution. We also describe hystereses between periodic solutions and between the stable steady solution and a periodic solution.