A simplified method for predicting unstable resonator mode profiles

The qualitative features of the lowest order mode profile of an unstable resonator can be predicted by a simple technique based on Fresnel zone theory. The number of rings in the pattern and the occurrence of a local minimum or a local maximum on-axis can be predicted by computing the number of Fresnel zones subtended at the observation plane by the cavity aperture uniformly illuminated by a point source at the virtual focus. This technique has been verified by computer calculations of mode profiles both inside and external to the cavity for moderate Fresnel numbers. The results were also confirmed by experimentally measured mode profiles on an unstable cavity He-Xe laser. The predicted cyclic nature of the mode loss with cavity aperture diameter was also confirmed experimentally.