Characterizing output beams for lasers that use high-magnification unstable resonators

Laser beams generated from high-magnification on-axis unstable resonators by use of hard-edged optics typically have a doughnut-shaped distribution in the near field (i.e., a flat-top profile with a hole in the middle for an axially coupled beam). We derive analytical expressions describing this distribution by using the flattened Gaussian beams concept. The superposition of two flattened Gaussian beams whose flatness and steepness of edges are controlled by defined parameters (i.e., the beam width and the order) is used to analyze the output beam intensity along the propagation axis. Finally, experimental measurements of beam propagation from a copper-vapor laser fitted with a high-magnification unstable resonator show excellent agreement with theoretical predictions.