An iteration technique is used for a theoretical study of the field distributions and diffraction losses at the reflectors of an asymmetric confocal cylindrical resonator having an output hole in one mirror for the low-loss TEM00and TEM10modes with Fresnel numbers ofN = 0.8and 1.2. A digital computer is used to numerically iterate an initially launched uniform distribution as it reflects back and forth between the mirrors until a steady-state field distribution occurs. The edge and coupling hole diffraction losses and the power coupled from an output hole in one mirror are also computed. The presence of the coupling hole produces a perturbation of the field distribution with distortion of the field increasing for increasing Fresnel number and for low-order modes. The relationship between hole radius and power output is presented. An optimum-size coupling hole may be selected from this data, which will yield maximum power output in the mode of operation desired. It has been found that, with the use of a coupling hole, mode selection of the lowest order TEM00mode is possible for resonators having large Fresnel numbers (N > 1.0).