STABILITY PROPERTIES OF A RESONANT CASCADE LASER

The emission of a resonant nondegenerate cascade laser in which up to two fields can be simultaneously amplified inside a cavity is theoreti cally investigated. Each field is resonantly coupled with one of the t ransitions of a ladder three-level atomic system, in conditions of-hom ogeneous broadening. General analytical expressions for zero-, one-, a nd two-field solutions are given. Cooperative emission between both fi elds is found. Through the linear stability analysis of these solution s we obtain phase diagrams showing their respective domains of stabili ty. Together with the existence of Hopf bifurcations associated with o ne-photon processes, which coincide with those of a Lorenz-Haken laser , a genuine Hopf bifurcation due to two-photon processes has been foun d. This last bifurcation does not require the ''bad cavity'' nor the ' 'Lorenz threshold'' conditions. The stability of the orbits that bifur cate from these critical points is analytically investigated. For this we have rewritten one of the standard criteria in a useful and straig htforward way. Finally, the dynamic regimes exhibited by the System we ll above the instability thresholds is numerically investigated reveal ing transitions to chaos via quasiperiodicity.