Optical resonators and dynamic maps

摘要

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