Optical cavities as iterative maps in the complex plane

In a periodic optical system, the evolution of a gaussian beam of light, as well as of a short pulse, has a direct interpretation as an iterative map in the complex plane. Trajectories for arbitrary initial conditions and the general condition for the existence of fixed points of high periodicity we re obtained. The cases of confined and unconfined beams and cavities with a nd without apertures are discussed. Among other applications, this approach promises to be fruitful for the description of Kerr lens mode locking lase rs. As an illustration of this possibility, the rise of a collective behavi or in a large number of maps coupled through a Kerr nonlinearity is shown. (C) 1999 Published by Elsevier Science B.V. All rights reserved.