Abstract

Most theoretical treatments of laser dynamics have been based on the plane wave approximation for the cavity field. They have also led, for the most part, to seemingly incorrect predictions for 'the instability thresholds. In an attempt to characterize the role played by the transverse intensity and phase variations of the cavity field, we have generalized the usual Maxwell-Bloch equations to include several common features that are present in experimental laser systems. We consider a unidirectional ring laser with a resonator containing spherical mirrors of arbitrary reflectivity and radius of curvature. We assume the active medium to behave as a collection of homogeneously broadened two-level systems with a transverse variation of inversion, as is normally found in typical discharge-excited systems, and we simulate the presence of a confining plasma tube with a fictitious transverse linear absorption profile, which is essentially zero everywhere except in the vicinity of the container walls. Our numerical search for the steady-state field distribution inside the cavity shows that well-behaved steady-state solutions may develop an unstable character for gain values that are not significantly higher than the ordinary laser threshold. These low threshold instabilities seem to arise as a result of a large enough mismatch between the transverse profile of the empty resonator field and of the population inversion. Bistability at threshold also seems to be part of the observed phenomenology.

© 1986 Optical Society of America