Abstract

Instabilities due to an abrupt change of parameters are considered in terms of general dynamical systems. A definition of the threshold for such instability is proposed by using the language of attractors and their basins. An analytically solvable one­dimensional model is constructed to illustrate this definition. As simple examples in optical systems, the Lorenz-Haken model with a step-type pump and the single-mode optical bistable systems with the input field changed in a form of a jump are considered. In the former example this consideration leads to a much lower pulse threshold than the well-known second threshold for the bad cavity case, whereas in the good cavity case for which there is no instability of the lasing state, pulsing motions can be observed using this method. In the latter example, we show the existence of the anomalous switching for the purely absorptive case as well, in contrast to the earlier assertions. The switchings with and without critical slowing-down are revealed and explained. Application of this study are proposed as a means to experimentally observe various pulsations including chaos in both systems whose observation is otherwise impossible or requires high pump or external field values.

© 1991 Optical Society of America