Coupled mode competition in unstable resonators using the exact cavity equations of motion with dynamic gain

The dynamic coupled mode (DCM) method has been applied to study the transverse mode competition in optical resonators. In this work a differential equation for the homogeneously saturating dynamic gain is included in the original dynamic coupled mode method, thus increasing its physical resemblance and allowing the retrieval of gain temporal evolution at every point within the lasing medium. This new model provides a realistic temporal evolution of the mode competition and gain saturation within the resonator, which can give further information on spatial coherence properties. The new general formulation does not assume that lasing medium fills the optical cavity and is suitable for modelling the dependence of small-signal gain and power gain on the transverse and longitudinal coordinates. The application of the method to a typical CO2 unstable confocal resonator is fully described; results and their connection to relevant physical properties of gas lasers, such as spiking and relaxation oscillations, are discussed. Results of the numerical implementation of the DCM method with dynamic gain are in very good agreement with experimental measurements reported previously.