Numerical calculation of the use of a concave–convex lens for shaping axisymmetric laser beams

Based on transformation matrices in meridian plane and sagittal plane, a geometrical lens design method is presented with the aim of obtaining an improved spot. A concave–convex convergent lens (CCCL) is employed as a shaping lens to focus a group of oblique laser beams from a CO2 laser with axially symmetrical fold combination (ASFC) resonator. The cases including interference, noninterference, different wavelength, and misalignment have been analyzed. Through theoretical analysis and numerical calculation, a smaller beam radius in a specific reference plane and a smaller far-field divergence angle can be obtained.