Analysis of mode competition in unstable optical resonators

The dynamic coupled modes (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 modes 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 more realistic temporal evolution of the mode competition and gain saturation within the resonator, which can give further information of spatial coherence properties. The temporal information becomes particularly valuable when the laser transient is a matter of interest or when a continuous wave steady output is never reached, as occurs in pulsed lasers. 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. The new general formulation does not assume that lasing medium fills the optical cavity and is suitable for modeling the dependence of small-signal gain and power gain on the transverse and longitudinal coordinates, thus providing a valuable tool for design of lasers with particular spatial coherence or mode discrimination requirements. Results of the numerical implementation of the DCM method with dynamic gain are in very good agreement with experimental measurements reported previously