Unstable resonators with distributed saturable gain and nonuniform reflectivity outcouplers in the geometrical optics limit

An existing geometrical optics method for calculating the longitudinal and transverse dependence of the mode intensities in unstable resonators with sharp-edged feedbacks mirrors and distributed saturable gain is modified to include the nonuniform reflectivity of the outcoupling feedback mirror. Results show that the mode extends increasingly outward as the gain increases, so the size of a limiting aperture must be chosen with care to prevent unwanted diffraction. An attempt to prescribe an arbitrary spatially limited output function of a loaded cavity and to find the required mode and reflectivity profiles yields spatially unlimited functions.