Scattering of a scalar field at dielectric surfaces by Born series expansion

A method for the calculation of the transmitted and reflected scalar fields at arbitrary dielectric surfaces is presented. The method is based on an evaluation of the Born series expansion and is of high accuracy as multiple reflections and refractions are taken into account. We show by comparison with Fresnel formulas that with the algorithm the ratio of transmitted and reflected field amplitudes can be calculated exactly. Results obtained by our algorithm are compared with results from rigorous diffraction calculations for a dielectric cylinder. We also demonstrate the application of the method to a more complicated surface geometry. Furthermore, advantages and restrictions of this algorithm are identified. (C) 1998 Optical Society of America.