Gaussian-beam theory of lenses with annular aperture

The light distribution produced by a lens with an annular aperture with approximately Gaussian cross-section is calculated by summing over Laguerre-Gaussian modes. The advantage of this approach is that it gives the intensity at all points in space. This is of particular value when the cross-section of the annulus is narrow compared with its radius, because then the intensity varies slowly along the optic axis. Intensity is plotted for the region near the focus, far from the focus, along the optic axis, and on the geometrical cone of illumination. Contours of equal intensity in the focal region are also plotted. The possibility of constructing low-loss resonators with annular mirrors is also discussed.