Volume Integral Formulation for the Calculation of Material Independent Modes of Dielectric Scatterers

Previous studies have demonstrated that the representation of the electromagnetic field scattered by a homogeneous object at a given frequency in terms of modes independent of its permittivity can be useful to investigate resonant scattering phenomena, and to design metamaterials. However, these modes have never been calculated for arbitrarily shaped particles in the full-retarded regime. In this paper, we introduce a numerical method based on volume integral equations (VIEs) for their calculation. We show, by studying the electromagnetic scattering from a finite-length cylinder of dimensions comparable to the incident wavelength, that only a moderate number of modes are needed to accurately describe the scattered far-field. Moreover, the presented modal expansion is computationally advantageous compared to the direct solution of the VIE when the scattered field has to be computed for many different values of the dielectric permittivity, given the size, and shape of the dielectric body.