Spherical wave expansions for shaped beam synthesis

A technique is proposed that evaluates efficiently the coefficient of a spherical wave expansion and is applicable to the optical synthesis of shaped beams. The method, which extends previously published work, avoids the need to directly evaluate numerically a double integral to compute each coefficient. Examples are given of the technique when applied to Westcott´s (1983) far-field optical synthesis procedure. The use of a tapered optical field distribution to improve the radiation characteristics of a shaped beam antenna is demonstrated.