Analysis of the Dispersion Diagrams of 3D Cubic Periodic Arrangements of Metallic Spheres

This paper investigates the dispersion properties exhibited by three different three-dimensional (3D) periodic arrangements of metallic spheres with the following underlying lattices: simple cubic (sc), body-centered cubic (bcc) and face-centered cubic (fcc) lattice. Their Brillouin zone (BZ) and the corresponding irreducible BZ are introduced. We then examine the dispersion properties along the edges of their respective irreducible BZs. The findings demonstrate that structures with a non-sc arrangement and higher symmetry can improve design versatility while simultaneously reducing the anisotropy of the structure and broadening the operating frequency range. These advantages are beneficial for the development of 3D graded-index (GRIN) lenses.