Self-locking of laser modes

An analytic investigation is made of the conditions for self-locking of laser modes. It is based on a system of reduced equations in terms of partial derivatives of the field amplitudes and polarizations and in terms of the difference between the populations of the active levels. The shape of the field pulses under modelocked conditions is calculated. The results of these calculations are applicable to ring gas lasers and to solid-state lasers with homogeneously broadened lines.