title: Diffracted-ray approach to the fast evaluation of diffractive lenses.
abstract: We employ a combination of asymptotic methods to speed up the computation of fields in the focal region of a diffractive lens (DL). The DL is treated locally as a linear grating with a slowly varying period and groove orientation. We employ rigorous electromagnetic diffraction theory locally to obtain the field just behind the DL. A simple diffracted-ray formula is derived for the field in the focal region of the DL at observation points that are not in the immediate vicinity of the optical axis. A careful study of the range of validity of this formula is made. For observation points that are not in the immediate vicinity of the optical axis the new algorithm is 3 x 10(5) times faster than the application of numerical integration to the double integrals involved and approximately 1000-1200 times faster than a recently published algorithm based on using asymptotic theory to replace the double integral with a single integral.
authors.affiliation: Department of Physics, University of Bergen, Allégaten 55, N-5007 Bergen, Norway. nickolai.sergienko@fi.uib.no
authors.forename: N
authors.initials: N
authors.lastname: Sergienko
authors.forename: J J
authors.initials: JJ
authors.lastname: Stamnes