Theory of output beam divergence in pulsed unstable resonators

The evolution of the far-field pattern of pulsed large-Fresnel-number unstable resonators is analyzed. Both geometrical optic and physical optic descriptions are given as a function of the number of trips around the unstable resonator. The analysis determines apparent size and distance to the image of the spontaneous emission source, as seen from the output aperture by looking back through multiple passes of the resonator. It is shown that this image is not obstructed by intervening apertures. The output far-field pattern is predicted to be the pattern generated by the output aperture when illuminated by incoherent light from the image of the spontaneous emission source. Far-field intensity patterns are analyzed for square and circular apertures, and the beam quality of the output is determined.>