Eigenmodes of an Asymmetric Cylindrical Confocal Laser Resonator with a Single Output-Coupling Aperture

In a previous paper 1 we described the diffraction losses and the field distributions at the reflectors of the low-loss modes of a symmetric cylindrical confocal resonator for Fresnel numbers 0.6 ^ N m ^ 2. We considered the effect of output-coupling apertures in the reflectors but we assumed that both reflectors were identical, each with the same output aperture and the same maximum radius. In this paper we again consider the cylindrical confocal geometry, but we do not require identical reflectors and, in particular, we assume that only one reflector is pierced by an output-coupling aperture, as in the coupling scheme proposed by Patel and others. 2 Figure 1 shows an axial section of the confocal resonator in question. The cavity is bounded at its two ends by confocal spherical mirrors (more exactly, confocal paraboloids 3 ). The first mirror is perfectly reflecting over the annular region 0 % al0 ^ p ^ a l m , the second over the circular section 0 ^ p ^ a2m . The maximum radii (a,m , a2m) are both much less than the mirror separation b. Expressions for the eigenvalues and eigenfunctions of asymmetric rectangular confocal resonators with output coupling slits have been 1919