Traveling waves on two- and three-dimensional periodic arrays of lossless magnetodielectric spheres

This paper describes an analytic investigation of traveling waves on two-dimensional (2D) and three-dimensional (3D) infinite periodic arrays of lossless magnetodielectric spheres using a spherical-wave source scattering-matrix formulation. We limit our attention to traveling waves propagating in the direction of the array axis. It is assumed that only the lowest order multipole fields (electric and magnetic dipoles) are significant in analyzing scattering from the array elements. We focus on the kd-ßd equation (diagram) that relates the traveling wave electrical separation distance ßd of the array elements in the direction parallel to the array axis to the corresponding free-space electrical separation distance kd.