Solution box: SOLBOX 21: Near-zero-index shells constructed by using dielectric rods

In the previous issue of SOLBOX (SOLBOX-20), we discussed periodic arrangements of dielectric rods with interesting electromagnetic properties [1]. As computational simulations demonstrate, when material and geometric properties — such as the shapes, sizes, and periodicities of the rods — are properly selected, these arrangements can behave like homogeneous objects with near-zero refractive indices. In SOLBOX-20, this phenomenon was shown by constructing triangular prisms and investigating the refraction of electromagnetic beams through them. Using cylindrical rods with 3.75 mm radius, 17 mm center-to-center periodicity, and 8.8 relative permittivity (corresponding to alumina), near-zero refractive index values could effectively be obtained at 10.3 GHz. As also shown in the same numerical set, modifying the material of the rods, i.e., using 4.0 relative permittivity, dramatically changed the behaviors of the structures, which seemed to possess ordinary refractive index values just above unity. Specifically, without using an appropriate material, such an arrangement of rods did not provide near-zero-index (NZI) characteristics, while the effective relative permittivity induced in the environment simply corresponded to that of a diluted material in vacuum.