ANTIPHASED STATES IN INTRACAVITY 2ND-HARMONIC GENERATION - STABILITY OF THE PERIODIC-SOLUTIONS

We study the self-pulsing solutions which emerge from the steady state via a Hopf bifurcation in a laser with intracavity second-harmonic generation. Our main result is the construction of periodic solutions and the derivation of explicit amplitude equations which rule the stability of these periodic solutions. In this way, we have been able to substantiate the classification into four classes of periodic solutions with simple phase and amplitude relations. Near the Hopf bifurcation, the periodic solutions are stable and the sum over the individual mode intensities is not periodic but constant, a signature of antiphase dynamics in this system. A fifth class of periodic solutions has been found numerically where the sum over all modal intensities is periodic. Finally, a numerical analysis complements these results and shows that the phase relations which characterize antiphase dynamics are maintained throughout the route to chaos and in the first chaotic domain when the pump parameter is increased.