Absolute instabilities in lasers with host-induced nonlinearities and dispersion

We analyze the occurrence of absolute instabilities in lasers that contain a dispersive host material with third-order nonlinearities. Starting from the Maxwell-Bloch equations, we derive general multimode equations to distinguish between convective and absolute instabilities. We find that both self-phase modulation and intensity-dependent absorption can dramatically affect the absolute stability of such lasers. In particular, the self-pulsing threshold (the so-called second laser threshold) can occur at few times the first laser threshold even in good-cavity lasers for which no self-pulsing occurs in the absence of intensity-dependent absorption