Optical bistability in a small sample

A general formulation, developed earlier, is applied to the problem of optical bistability in a sample with dimensions that are small compared with the wavelength of light. A self-consistent model of radiative relaxation is introduced in which atom–atom correlations are taken into account. This is based on the screened interaction approximation of the many-body theory. The degree of correlation is internally determined by the dynamics of the system. The validity of the S-conservation approximation is investigated; it is concluded that this approximation may be valid only in the weak-field limit, since the local-field fluctuations become appreciable as the pump-field strength is increased. As a result, the system undergoes a first-order phase transition, in contrast to the second-order transition predicted by the S-conserving model. The method is quite general, and it can be applied to other damping mechanisms. As an illustration, a simple collision model is also considered. In the limit of a zero external field and thermodynamic equilibrium, our results reduce to the results of existing theories; the system exhibits a second-order phase transition.