Abstract

We report new and detailed studies of a CO₂ laser system with modulated losses. It has been shown previously both experimentally and theoretically that such a homogeneously broadened laser [1] (and other similar systems [2]) can display instabilities and eventually chaotic behaviour when a parameter is modulated. We have improved the stability of our previous system and using a fast transient recorder we were able to characterize the period-doubling transition to chaos, including a stable f/8 subharmonic. We find periodic windows inside the chaotic region which do not follow the predicted sequence of the well-known logistic map. We present the time behavior, Poincare sections, phase-space portraits and power spectra that permit unequivocal Identification of a transition to chaos. We present other measures of the dynamical behaviour such as bifurcation diagrams showing generalized multistability and phase diagrams in the parameter space which localize the unstable regions. Dimensionality tests on digitized time series show the formation and evolution of a strange attractor as parameters are varied. It was possible to measure the dimension before and at the accumulation point of a Feigenbaum cascade and then into the chaotic region. The results are in good agreement with general theory on nonlinear dynamics [3]. For the first time return maps have been obtained from an experimental system and they reveal the breakdown of an analogy with the Feigenbaum model for a map with a quadratic maximum when we enter into the chaotic region.

© 1985 Optical Society of America