Fractal diffraction and focusing properties of binary phase gratings

Abstract

We observed, that a simple binary phase grating under certain circumstances exhibits pronounced focusing properties. In the paraxial approximation, the on-axis intensity as a function of the grating duty cycle shows a perfect fractal behavior. We discuss the properties of lens scaling and phase binarization in the paraxial, the non-paraxial and the rigorous case. Furthermore, we investigate the optimal focusing conditions for binary phase gratings. Also, possible applications in light concentration, image scanning and wave-front sensing are discussed