Propagation of Gaussian beams through active layers

Knowledge of propagation, transmission and reflection properties of space- and time-limited beams is relevant to the classical description of electromagnetic field modes in laser and other optoelectronic devices. For many reasons, Gaussian beams have been the most widely studied; for instance, they correspond to the fundamental mode in cylindrical or rectangular resonators, and they are often desirable at the output of amplifiers. To describe the behavior of beams with a Gaussian amplitude profile, the usual method consists of making an approximation in Maxwell equations, such that the solution of the approximate equations is a Gaussian beam. In this work we propose a different method to study Gaussian beams in active media, describing the beam by a continuous spectrum (spatial or temporal) of plane waves. We consider active media far from saturation, i.e. the gain is independent of the electric field amplitude. As a first step in the study of propagation, transmission and reflection of pulses through thin layers of active media, we analyze the properties of the transmitted beam in the case of a thin slab with gain between two isotropic transparent semi-infinite media, assuming normal incidence of a two-dimensional, space- or time-limited gaussian beam.