Properties of unstable resonators with large equivalent Fresnel numbers

The results are given of numerical calculations of oscillation modes in unstable resonators. It is shown that slight smoothing of the mirror edges leads to a considerable improvement of the selective properties of a resonator. It is shown that, contrary to the predictions of the theory of unstable resonators with sharp-edged mirrors, oscillation in the lowest transverse mode described by the geometrical approximation is possible in real resonators with large equivalent Fresnel numbers.