The Effective Permeability of an Array of Thin Conducting Disks

Abstract

A three-dimensional array of thin conducting disks has found special application as an artificial refracting medium at microwave frequencies. Treatment of these refractive properties at oblique incidence requires specification of the dielectric and permeability coefficients of the medium. When an alternating magnetic field is parallel to the disk faces, the field is undisturbed and the relative permeability coefficient is unity. When the alternating magnetic field is normal to the disk faces, circulating currents are induced on them. The boundary value problem of determining the current distribution on a single perfectly conducting disk is carried out in detail for the case where the disk diameter is small compared to the wave-length. This current distribution is found to be representable by a magnetic dipole. If the disks in an array are far enough apart to neglect interaction, a simple summation of the dipole moments shows the array to have a diamagnetic susceptibility in the direction normal to the disk faces. Combining this result with an expression for the dielectric coefficient, which was developed earlier by Kock, the constants of the anisotropic array are completely specified.