A method to construct refracting profiles
arXiv:math-ph/0404032 · doi:10.1088/0266-5611/20/1/013
Abstract
We propose an original method for determining suitable refracting profiles between two media to solve two related problems: to produce a given wave front from a single point source after refraction at the refracting profile, and to focus a given wave front in a fixed point. These profiles are obtained as envelopes of specific families of Cartesian ovals. We study the singularities of these profiles and give a method to construct them from the data of the associated caustic.
12 pages, 5 figures