Geometric optics-based design of laser beam shapers

When diffraction effects are not important, geometrical optics (ray tracing, conservation of energy within a bundle of rays, and the constant optical path length condition) can be used to design laser beam shapers by solving beam shaping equations or by optimizing a beam shaping merit function for the configurations, including aspheric ele- ments or spherical-surface gradient-index lenses, which are required to change the input irradiance and phase profile into a more useful form. Geometrical optics-based methods are presented for shaping both rota- tionally and rectangular symmetric laser beam profiles. Solutions of the beam shaping equations are presented for a two-plano-aspheric lens system for shaping a circular symmetric Gaussian beam into a top-hat output beam profile and a two-mirror system with no central obscuration for shaping an elliptical Gaussian input beam into a Fermi-Dirac output beam profile.