Low frequency finite-difference time-domain modeling of a PEC sphere based on a quasi-analytical coupled dipole approximation

A computational formulation is presented for the low frequency single-cell finite-difference time-domain (FDTD) modeling of a perfectly electric conducting (PEC) sphere. The approach is based on the fact that the scattered field from electrically small objects can be expressed in terms of an electric and magnetic dipole. These dipoles can be decomposed with respect to the dipole moments that can be defined along the discrete field components that comprise the cell wherein the PEC sphere is inscribed. The dipole moment components couple to each other, and this mechanism is quantified by a quasi analytical coupled dipole approximation (CDA). The quasi-analyticity requires to substitute the involved dyadic Green's function (DGF) terms, in the CDA formula, by their numerically computed, FDTD compatible, equivalents. The material properties of the equivalent electric and magnetic spheres are derived using the quasi-analytical CDA that leads to expressions that resemble the Claussius-Mossotti mixing formula. The theoretically derived results are supported by numerical simulations.