Generalized Confocal Resonator Theory

The existence of modes in an open structure such as the confocal Fabry-Perot type resonator has been demonstrated by Boyd and Gordon 1 and by Fox and Li,2 This resonator consists of two spherical reflectors separated by their common radius of curvature, as shown in Fig. 1. The reflectors were assumed to be of equal aperture and square 1 or circular 2 if viewed in the ^-direction. Uniform reflectivity over the reflecting surface was postulated. Goubau and Schwering 3 * 4 have also reported on this problem and have obtained similar results. A mode may lie defined as a field distribution t h a t reproduces itself in spatial distribution and phase, though not in amplitude, as the wave bounces back and forth between the two reflectors. Because of losses 1347 1348 T H E IIKLL S Y.ST KM TECHNICAL J O U R N A L , JULY 1M2 / p'(x; y ' t *.y ' - - -- 4 A2 / / Fig. 1 -- Confocal resonator with spherical reflectors.