Bidimensional dynamic maps in optical resonators

Abstract

In this article an introduction to the dynamical behavior of a beam within a ring phase-conjugated optical resonator is presented and modeled using two dimensional iterative maps. Three well known iterative maps are described: Duffing, Tinkerbell and Hénon, and are applied to the description of optical resonators. It is explicitly shown how the difference equations of these maps can be used to describe the dynamic behavior of what we call Tinkerbell, Duffing and Hénon beams i.e. beams that behave according to these maps. The matrix of a map generating device are found in terms of the specific map parameters, the state variables and the resonator parameters for each of the three named maps.