Incorporating Effective Media in the Finite-Difference Time-Domain Method for Spherical Nanoparticle Modeling

A computational formulation is presented for the low frequency single-cell finite-difference time-domain (FDTD) modeling of nanospheres. The methodology is developed based on the observation that the electrostatic field inside a dielectric sphere is similar in nature to that of an FDTD cell, or equivalently by considering the electromagnetic correspondence between the single electric field component across an FDTD cell edge, and the electric dipole moment induced in an electrically small dielectric sphere when the latter is excited by a plane wave. By rigorously applying effective medium theory the physical existence of a subcell dielectric sphere in the FDTD grid is translated into an equivalent material, characterized by an effective permittivity that obeys the Clausius-Mossotti (CM) mixing rule, appropriately defined across the cell edge parallel to the excitation plane wave. A circuit based methodology is devised that allows to easily incorporate the effective medium representation of a subcell dispersive dielectric sphere into FDTD update equations. The theoretically derived results are supported by numerical experiments.