Polarizability analysis of cubical and square-shaped dielectric scatterers

The polarizability characteristics of nonspherical scatterers, especially cubes and squares, are studied. A surface integral equation for the electrostatic potential has been numerically solved for a cube and a square-shaped object. Nonuniform gridding of the dielectric object has been used to get a good accuracy in the solution. The results obtained for the polarizability of cubes using the surface integral equation are compared with those obtained from the volume integral equation and show a good agreement. We give simple approximation formulas for the polarizabilities as functions of the permittivity of the inclusions. The results give an improvement compared to earlier literature and also present a way to predict the effective properties of mixtures where cube-shaped inclusions are embedded in dielectric environment, which type of mixtures strongly generalize the effective-medium theories of the present literature