We generalize the traditional Maxwell-Bloch theory of a ring laser and analyze the dynamical 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. In this context we incorporate the effects of curved reflecting surfaces, the possible lack of transverse uniformity of the pump, and the detailed structure of the cavity modes. In the uniform-field limit we prove that the laser steady state is of the single-mode variety and that lack of stability can be induced in this field configuration even only a few percent above the threshold for laser action. Thus our main claim is that transverse effects can be responsible for low threshold instabilities. This explanation is more plausible to explain the observed pulsations in many lasers than what is available in terms of the traditional plane-wave theories.

• Received 10 August 1987

DOI:https://doi.org/10.1103/PhysRevA.37.3847