Abstract

Three-level lasers are interesting nonlinear systems which present a wide variety of dynamical behaviors. Consideration of spatial instabilities in the transverse section of such laser beams may enrich considerably this scenario, as has been shown recently by Yu et al. [1], who have numerically obtained spatial patterns and even turbulent behavior in the emitted field intensity of ā coherently optically pumped laser. In the present work we analyze a physically different kind of three-level system, namely a cascade laser. In this sort of laser two longitudinal modes, corresponding to two stimulated transitions in cascade with a common intermediate level, are amplified and interact with each other through the gain medium [2]. An analysis of the interplay between this interaction and diffraction effects in both longitudinal modes seems very interesting at this point. Following this idea, we have developed the Maxwell-Bloch equations for a cascade laser in the presence of transverse effects. A preliminary numerical study of these equations shows that the transverse behaviors of the two emitted electrical fields affect one another. We have specifically analysed the behavior of the system in the vicinity of the lasing threshold for the symmetric case [2] and small detuning. A coupled pair of complex Swift-Hohenberg equations has been obtained [3], whose solutions are analysed.

© 1996 IEEE