Single-mode instability in optical bistability

This paper gives a detailed description of the plane-wave Gaussian models of optical bistability and of the experimental investigations of the single-mode instability induced on a beam of sodium atoms in a cavity by an external driving field. Our goal is to provide a careful comparison of the theoretical and experimental results. We focus on the shape of the instability domain, the nature and behavior of the spontaneous output oscillations produced by the instability, and their frequency dependence on the control parameters. We carry out this comparison using both the plane-wave and Gaussian models. Our analysis shows that the latter is in good quantitative agreement with the experimental results. We investigate in detail the main assumption of the Gaussian model, namely, that the internal cavity field retains the same radial profile as the input field.