Simplified analytical method for an anamorphic refractive shaping system of laser beams with a large aspect ratio

For reshaping aperture size and correcting low-order aberration of laser beams with large aspect ratios, a simplified analytical method is proposed to design an anamorphic refractive shaping system, which is composed of double-plane symmetric lenses. The simplified method enables performing a global study of aberrations via calculating the analytical primary wave aberration function under paraxial approximation. The aberration balance is analyzed with a three-lens laser collimating system and a compact four-lens laser expanding system. Lens bending and conic surfaces are introduced to decrease ray errors. Through the simplified analytical method, anamorphic refractive shaping systems for laser beams with large aspect ratios can be adequately analyzed and conveniently designed.