Natural modes for the analysis of optical bistability and laser instability

A self-consistent description is given for the propagation of a weak optical probe beam through a homogeneously broadened two-level medium in the presence of a strong, collinear, near-resonant pump beam. The propagation of the probe beam is given in terms of bichromatic natural modes, which contain frequency components symmetrically displaced from that of the pump beam. The two frequency components have a definite relative amplitude and phase, which are determined solely by the frequency detunings of the optical fields from the atomic resonance and by the intensity of the pump field. A simple method for calculating these natural modes is derived, and their importance in describing nearly degenerate four-wave mixing, optical bistability, and the stability of homogeneously broadened ring lasers is discussed.