Whispering-gallery laser resonators. II. Analysis of mirrors with nonuniform curvature

For pt.I see ibid., vol.27, p.1069-77 (1991). Although the whispering-gallery mirror shows great promise for use at short wavelengths, undesired beam divergence at the mirror exit can be a significant issue in the design of laser resonators. This problem can be alleviated by appropriate choice of the mirror geometry: elongated mirror shapes can give reduced beam divergence without requiring too large an overall size. It is shown that, for circular geometries, beam propagation along the mirror surface is conventionally described in terms of normal modes. Elliptical mirrors are shown to admit a similar analysis, thereby providing a convenient prototype for the elongated geometries of interest. They are found to offer a substantial, though ultimately limited, reduction of beam divergence