Correcting astigmatism and ellipticity in Gaussian beams using a cylindrical lens pair with tunable focal lengths

Correcting astigmatism and ellipticity in laser beams is critical for improving performance in many applications like microscopy, atomic physics, quantum information processing, and advanced manufacturing. Passive correction methods based on cylindrical lens telescopes require choosing lenses with precise focal lengths, effectively limiting the range of tunability when using standard catalog optics. Active solutions based on diffractive optical elements can achieve superior performance and dynamic response, but they are bulky, expensive, and suffer from finite diffraction efficiency and added complexity. Here, we introduce a simple method to convert astigmatic elliptical beams into circular Gaussian beams without astigmatism. Our method comprises three cylindrical lenses. The first lens focuses the beam along its major axis to create a plane where the intensity profile is radially symmetric. The second and third lenses are placed one behind the other in that plane at a relative angle, acting as a biaxial lens pair with tunable focal lengths. By adjusting the relative angle of the lenses, the two separate beam waists of the astigmatic beam can be overlapped, resulting in a circular Gaussian beam without astigmatism. We theoretically validate our method, numerically quantify its robustness to experimental imperfections, and experimentally demonstrate its ability to circularize the output beam of a commercial laser source. Compared to SLM-based approaches, our design is significantly more compact and cost-effective, with component prices comparable to standard lenses and dimensions suitable for integration into tabletop optical paths. Its performance is ultimately limited by the validity of the paraxial approximation (breaking down for beam sizes comparable to the wavelength), the finite inter-lens distance between the second and third lenses, and the inability of cylindrical lenses to address higher-order aberrations. Its simple and compact design makes it well-suited for both laboratory and industrial optical systems.