Optical and Quantum Electronics 28 (1996) 1021-1027 Parametric characterization of Gaussian beams propagating through active media J. R. MARTIN DE LOS SANTOS, R. MART[NEZ-HERRERO, P. M. MEJiAS Departamento de Optica, Facultad de Ciencias F(sicas, Universidad Complutense, 28040 Madrid, Spain Received 7 August; revised 13 October; accepted 25 October 1995 On the basis of the intensity moment formalism, within the thin-sheet approach, the beam width, the beam quality and the kurtosis parameter of a Gaussian beam propagating through active media are investigated. The analysis considers both the homogeneously and inhomogeneously broadened cases. The dependence of the above three parameters on the small-signal gain, saturation intensity and input beam size is studied. The validity of the thin-sheet approximation for the range of propagation distances and physical parameters of the system is also discussed. 1. Introduction In recent years much work has been done concerning the description of laser beams by means of key parameters. In particular, the beam width and the beam quality were shown to be closely connected with the second-order moments of the intensity and radiant intensity of the field [ 1-6]. More recently, it was pointed out that information about the shape of the beam profile can be inferred from the so-called kurtosis parameter, which is given in terms of higher-order measurable intensity moments [7, 8]. This parameter, which represents the degree of flatness (or sharpness) of the laser intensity distribution, has proved useful in evaluating quantitatively the capabilities of lasers in materials processing, such as welding, cutting or hole drilling [9]. The changes in the above parameters due to beam propagation through first-order optical sys- tems have been investigated in the literature. However, although several important non-ABCD optical systems (such as supergaussian transmittances [ 10-12], hard-edge apertures [ 13] and Kerr-like media [14]) have also been analysed, little attention has been devoted to active media such as those appearing in laser amplifiers. In the present work attention will be concen- trated on the three parameters of beam width, beam quality and kurtosis and their behaviour through gain media. More specifically, in Section 2 the formalism and definitions to be used will be given. We will apply a procedure described earlier [15] which is based on the intensity moment formalism, and we will use the thin-sheet approach introduced by Milonni [16], which establishes some conditions on the magnitude of both diffraction and susceptibility along the active medium. In Section 3 the evolution of the beam width, beam quality and kurtosis of a Gaussian beam propagating through an amplifier is plotted in terms of the small-signal gain and of the saturation intensity. Finally, in Section 4 the main conclusions are summarized. 0306-8919 9 1996Chapman & Hall 1021