“…The coupling losses determine the extent to which a waveguide mode is coupled back onto itself after being reflected from the resonator mirrors, and play a crucial role in determining the properties of waveguide resonators [3]. Abrams [2], Degnan and Hall [3], Avrillier and Verdonck [5] and Boulnois [6] have studied the single mode losses of resonators in the hollow circular waveguide and rectangular waveguide (including square waveguide), respectively, and report that there exist three special geometries to provide the lowest coupling losses, corresponding to plane-parallel, half-concentric and semiconfocal configurations. In recent years coaxial waveguides have been increasingly used for gas lasers operating with RF transverse excitation and diffusion cooling [7,8].…”