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.
The steady-state bistability and the evolution of the field envelope of a ring-cavity optical-bistable system including the effect of the transverse radiation field and the effect of an inhomogeneously broadened atomic medium are studied by means of the mean-field approximation and dressed-mode theory in this paper. Our study shows that the bistable region enlarges with an increase of the ratio
r0/
w0 (
r0 is the radius of the cylindrical atomic sample and
w0 the beam waist of the Gaussian beam), and decreases with increasing width of the inhomogeneously broadened line. The transverse-field effect has more impact on the magnitude of the bistable region than the inhomogeneous broadening under certain conditions. In the case of two unstable modes, the evolution of the field envelope before reaching the stable oscillation regime differs remarkably from that in the case of the plane-wave approximation with a homogeneously broadened atomic medium.