Nonconfocal multimode resonators for masers

The case of a resonator composed of two concave spherical reflectors separated by an arbitrary distance is examined. The general problem of the electromagnetic field distribution over the nonconfocal aperture is first formulated by means of the Huygens principle. The solution of the resulting integral equation is obtained analytically in the highly nonconfocal limit. It was found that when the reflector spacing d is much larger than the radius of curvature b of the reflectors, the aperture field distribution is in the form of traveling waves. For arbitrary d/b, the eigenvalues and eigenfunctions of the lowest order mode is obtained by numerical solution using the IBM 7090 computer. The diffraction loss was found to increase rapidly when d→2b and a geometrical interpretation of this behavior is given. Furthermore, it was found that as the spacing departs from the confocal value, the apertures are no longer surfaces of constant phase. The optimum spacing for maximum Q of the resonator is also obtained.