title: Generalized Jinc functions and their application to focusing and diffraction of circular apertures.
abstract: A family of generalized Jinc functions is defined and analyzed. The zero-order one is just the traditional Jinc function. In terms of these functions, series-form expressions are presented for the Fresnel diffraction of a circular aperture illuminated by converging spherical waves or plane waves. The leading term is nothing but the Airy formula for the Fraunhofer diffraction of circular apertures, and those high-order terms are directly related to those high-order Jinc functions. The truncation error of the retained terms is also analytically investigated. We show that, for the illumination of a converging spherical wave, the first 19 terms are sufficient for describing the three-dimensional field distribution in the whole focal region.
authors.affiliation: Optische Nachrichtentechnik, FernUniversität Hagen, Universitätsstrasse 27/PRG, 58084 Hagen, Germany. qing.cao@fernuni-hagen.de
authors.forename: Qing
authors.initials: Q
authors.lastname: Cao