Numerical solution of diffraction problems: a method of variation of boundaries II. Dielectric gratings, Pade approximants and singularities

Numerical solution of diffraction problems: a method of variation of boundaries III. Doubly periodic gratings Oscar P. Bruno * Fernando Reitich* We present a new numerical method for the solution of the problem of diffraction of light by a doubly periodic surface. This method is based on a high order rigorous perturbative technique, whose application to singly pe-riodic gratings was treated in the first two papers of this series. We briefly discuss the theoretical basis of our algorithm, namely, the property of an-alyticity of the diffracted fields with respect to variations of the interfaces. While the algebraic derivation of some basic recursive formulae is somewhat involved, it results in expressions which are easy to implement numerically. We present a variety of numerical examples (for bi-sinusoidal gratings), in order to demonstrate the accuracy exhibited by our method as well a