A Technique for Nanoscale Modeling of Uniaxial Spheroids

In this work we develop a technique for nanoscale modeling of uniaxially anisotropic prolate spheroidal nanoantennas. To this end, we develop a formal series solution, valid for any aspect ratio of the spheroidal nanoantenna. To solve the problem, we follow a two-step procedure: first, spherical vector wave functions with discrete wavenumbers are used for the expansion of the fields in the domain of the anisotropic scatterer. Second, these spherical expansions are transformed to spheroidal ones, using suitable expansions relating the spherical vector wave functions with the spheroidal ones. Then, satisfying the boundary conditions at the spheroidal surface, we obtain infinite sets of nonhomogeneous equations from which, upon truncation, we may calculate the bistatic and the total scattering cross section. We sufficiently compare the cross sections obtained by the developed method, for different values of aspect ratio and anisotropy, with the discrete dipole approximation method. The magnetic and electric dipolar resonances are then investigated in the context of nanoantenna design.