Analysis of steady-state stability for intracavity optical parametric oscillator: method of small-parameter expansion

The aim of the study is to analytically determine the linear stability of a steady-state operation point for an optical parametric oscillator (OPO) intracavity pumped by a semiconductor disk laser (SDL). Methods. In order to build the analytic approximation to the characteristic equation roots, the method of small-parameter expansion is used. The results of analytic and numerical methods are compared with each other. Results. As the primary pump intensity does not exceed the threshold value of parametric generation $\sigma_{OPO}$, the steady-state operation point is shown to be stable, like that of an ordinary SDL does. Small deviations relax to the steady state in the form of a pulse sequence with a period that equals one round-trip time. Relations defining the attenuation decrement and the carrier frequency of the pulse sequence are presented. The relative changes in these deviations during one cavity round-trip are independent of this round-trip time. It is shown that in the above-threshold regime there is such a pump intensity $\sigma_{AH}$ > $\sigma_{OPO}$ at which the steady state loses stability as a result of the Andronov-Hopf bifurcation. Discussion. The results of the study could be applied for making and analysis of new optical devices based on nonlinear-optical interaction.