Abstract

We generalize the traditional Maxwell-Bloch theory of a ring laser and analyze the dynamic role of transverse effects. With the help of a suitable extension of the uniform field limit we perform an essentially analytical study of the steady state and linear stability properties of a ring resonator containing a homogeneously broadened active medium. Our calculations include the effects of curved reflecting surfaces, the possible lack of uniformity of the pump, and the detailed structure of the cavity modes. In the uniform field limit we prove that the laser in steady state operates in a single longitudinal and transverse mode and that this configuration can be destabilized even a few percent above the threshold for ordinary laser action. A study of the most interesting geometrical and physical parameters of this model indicates that instabilities are strongly affected by the ratio between the transverse size of the active medium and the beam waist, although the curvature of the mirrors and the geometry of the cavity also play important roles. Our main claim is that transverse effects are very plausible causes of the observed low-threshold instabilities in real laser systems.

© 1987 Optical Society of America