Edge effects in finite gratings of cylindrical scatterers

Edge effects in finite arrays are studied via the analysis and interpretation of one canonical geometry—a linear grating of thin circular cylinders. The partial field scattered by each element in a finite array is decomposed into three components: (1) the contribution of the infinite or periodic array, (2) a component due to the presence of the left edge of the array, and (3) a component due to the right edge of the array. The scattered field due to either array edge is derived from a separate analysis of the appropriate semi-infinite array and is interpreted in terms of a decaying wave that is launched from the array end. This solution to the well-posed boundary value problem is numerically verified via boundary condition satisfaction, where the accuracy of the edge-wave decomposition persists for all tested values of element spacing and plane wave incidence angles. [Work supported by NSF.]