Effect of sphere radius variation on the guided waves of a metafilm

A metafilm consisting of a planar periodic array of electrically small dielectric spheres that are electrically small in spacing is known to support guided waves in certain frequency ranges. In this paper, we examine the effect of slight radius variations between spheres in the array. Such variations may be due to process effects during fabrication, or may be introduced intentionally in order to obtain certain behavior (guidance or radiation) in prescribed frequency ranges. For a checkerboard-type alternation of sphere radii, we observe Fano resonances in the surface susceptibilities of the metafilm, which carry over to analogous resonant behavior of the guided-wave propagation constants that is not observed for a uniform array.