Abstract

We study the dynamical evolution of a laser system under inhomogeneous pumpings which are slowly varying in space. We have considered the case of pumpings which are homogeneous in one direction and have a slow dependence on the other one[1]. This situation corresponds for instance to narrow-gap slab waveguide CO₂ lasers for which a similar approximation is currently made[2]. The basic equations governing the dynamical behaviour of the laser are Maxwell-Bloch equations under the slowly varying envelope and paraxial approximations[3]. We determine the threshold and frequency for global transverse unstable modes, by means of spatio-temporal stability. These modes are nothing but Hermite modes, which appear in a consequence of the spatial inhomogeneity. In the weakly nonlinear study the evolution of localized non linear modes is gonemed by Ginzburg-Landau equation with spatially varying coefficients. An extension to 2D transverse inhomogeneities confirms these results and shows the appearance of localized transverse structures.

© 1996 IEEE