Confocal Multimode Resonator for Millimeter Through Optical Wavelength Masers

Multimode resonators of high quality factor will very likely play a significant role in the development of devices, such as the maser, which operate in the millimeter through optical wavelength range. It has been suggested that a plane-parallel Fabry-Perot interferometer could act as a suitable resonator. In this paper a resonator consisting of two identical concave spherical reflectors, separated by any distance up to twice their common radius of curvature, is considered. Mode patterns and diffraction losses for the low-loss modes of such a resonator are obtained analytically, using an approximate method which was suggested by W. D. Lewis. The results show that the diffraction losses are generally considerably lower for the curved surfaces than for the plane surfaces. Diffraction losses and mode volume are a minimum when the reflector spacing equals the common radius of curvature of the reflectors. For this case the resonator may be termed confocal. A further property of the concave spherical resonator is that the optical alignment is not extremely critical.