Effects of dispersion on the performance of a refractive beam shaper

Effects of material dispersion are considered for the case of an aspheric lens pair which transforms a collimated laser beam to a collimated beam with a different transverse irradiance profile. When the lenses are used at a wavelength other than the design wavelength, wavefront aberration is the primary consequence, with distortion of the output profile being a minor effect. Using geometric optics, we derive simple expressions for the effects of dispersion on the output wavefront, which depend only on dispersion and the beam shaping transformation under consideration, but which do not require the solution of the full lens design equations. As an example, detailed results are shown for a practical beam shaping design.