Low-Dimensional Attractors for a Single-Mode He-Xe Ring Laser

Abstract

Calculations of the order-2 information dimension, D2, and the order-2 Kolmogoroff entropy, K2, from digitized intensity versus time sequences from experimental measurements of an unstable, unidirectional, single-mode, inhomogeneously-broadened He-Xe ring laser indicate that the dynamical evolution of the laser can be characterized by an attractor of relatively low dimensionality. Clear states of periodic and period-doubled pulsations give an attractor dimension of one. Pulsations corresponding to broadband Intensity power spectra yield a fractal dimensionality larger than two, confirming that the origin of the irregular pulsations is deterministic chaos. This behavior, which is similar to that found in an earlier analysis of data from a Fabry-Perot laser using the same lasing medium, is deemed rather surprising in view of the fact that inhomogeneously broadened lasers are usually modelled in phase spaces of very high dimensionality.