The evolution of relevant beam parameters of a light beam propagating
through an iterated sequence of spherical lenses and Gaussian aperture
s immersed in an active medium is investigated. This structure is a cl
assical model for an optical resonator. The effective size of the fiel
d distribution, the beam quality factor and the radius of wave front c
urvature are calculated as functions of the number of transits. Steady
-state values of these parameters are also determined and the dependen
ce of the results on the gain of the medium, the aperture width and th
e focal length is illustrated. A comparison with the case without acti
ve medium is also discussed.