NUMERICAL-SOLUTION OF DIFFRACTION PROBLEMS - A METHOD OF VARIATION OFBOUNDARIES .3. DOUBLY PERIODIC GRATINGS

We present a new numerical method for the solution of the problem of d iffraction of light by a doubly periodic surface. This method is based on a high-order rigorous perturbative technique, whose application to singly periodic gratings was treated in the first two papers of this series [J. Opt. Soc. Am. A 10, 1168, 2307 (1993)]. We briefly discuss the theoretical basis of our algorithm, namely, the property of analyt icity of the diffracted fields with respect to variations of the inter faces. While the algebraic derivation of some basic recursive formulas is somewhat involved, it results in expressions that are easy to impl ement numerically. We present a variety of numerical examples (for bis inusoidal gratings) in order to demonstrate the accuracy exhibited by our method as well as its limited requirements in terms of computing p ower. Generalization of our computer code to crossed gratings other th an bisinusoidal is in principle immediate, but the full domain of appl icability of our algorithm remains to be explored. Comparison with res ults presented previously for actual experimental configurations shows a substantial improvement in the resolution of our numerics over that given by other methods introduced in the past.