Wavefront and caustics of a plane wave refracted by an arbitrary surface

A simple expression is given for the k-function associated with the general solution of Stavroudis to the eikonal equation for refraction or reflection of a plane wave from an arbitrary surface. Using this result, we specialize the solution to derive analytic expressions for the wavefront and caustic surfaces after refraction of a plane wave from any rotationally symmetric surface. The method is applied to evaluating and comparing the wavefront and caustic surfaces formed both by a planospherical lens and a planoaspheric lens used for laser beam shaping, which provides understanding of how the irradiance is redistributed over a beam as the wavefront folds back on itself within the focal region.