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.
© 2008 Optical Society of America
Original Manuscript: April 28, 2008
Revised Manuscript: July 3, 2008
Manuscript Accepted: July 27, 2008
Published: August 25, 2008
David L. Shealy and John A. Hoffnagle, "Wavefront and caustics of a plane wave refracted by an arbitrary surface," J. Opt. Soc. Am. A 25, 2370-2382 (2008)