Consequences of the generalization of Hermite and Laguerre analytic solutions for resonators with limited transverse gain

In this work, we present new consequences of a theory that provides analytical solutions in the paraxial approximation for optical resonators with Gaussian spatial profile gain. This theory is a generalization of the Standard theory of free propagation of Gaussian beams, which consists of introducing spatially confined gain within the optical resonator. We show how the sizes of the transverse modes change as a function of the resonator parameter and also of the size of the excited area. We find the energy efficiency of the resonator modes once the gain is included, which is very important for threshold considerations. Furthermore, the theory reveals the peculiar behavior of what we might call near-planar resonators. These results can be of interest for the design of optical resonators and their pumping systems.