Mode losses in unstable resonators with rounded edges

The waveguide approach to unstable resonators is employed for determining the eigenmode losses in unstable 2-D and 3-D resonators with perfectly reflecting round-edged mirrors. It is found that edge rounding in cylindrical mirror configurations leads to mode detachment at lower Fresnel numbers than for the sharp-edged case and that the loss behavior approaches more closely the geometric optical limit for infinite mirrors. Similar effects are observed in resonators with circular mirrors, where mode detachment does not occur at all when the mirror edges are sharp. It is also shown that edge rounding improves the separation between the low-loss detached mode and the next higher order modes.