Dynamic maps in phase-conjugated optical resonators

In this article the dynamical behavior of a beam within a ring-phase-conjugated resonator is modeled using two-dimensional iterative maps. In particular and as an example it is explicitly shown how the difference equations of the Duffing map can be used to describe the dynamic behavior of what we call Duffing beams i.e. beams that behave according to the Duffing map. The matrix of a Duffing map generating device is found in terms of the Duffing parameters, the state variables and the resonator parameters. To our knowledge this is the first time that the mathematical characteristics of an optical device in an optical cavity are stated so that a Duffing map is obtained as the dynamics for the ray beams.