Depolarization field of spheroidal particles

A compact analytical formula up to the order of k3, where k is a wave vector, is derived for the depolarization field Ed of a spheroidal particle by performing explicitly the steps of the recipe outlined by Meier and Wokaun [Opt. Lett.8, 581 (1983)]. For the static component of Ed a general electrostatic formula valid for a particle of a general shape is rederived within the Meier and Wokaun framework. The dynamic k2-dependent depolarization component of Ed is shown to depend on dynamic geometrical factors, which can be expressed in terms of the standard geometrical factors of electrostatics. The Meier and Wokaun recipe itself is shown to be equivalent to a long-wavelength limit of the Green's function technique. The resulting Meier and Wokaun long-wavelength approximation is found to exhibit a redshift compared against exact T-matrix results. At least for a sphere, it is possible to get rid of the redshift by assuming a weak nonuniformity of the field Eint inside a particle, which can be fully accounted for by a renormalization of the dynamic geometrical factors. My results may be relevant for various plasmonic, or nanoantenna, applications of spheroidal particles with a dominant electric dipole scattering, whenever it is necessary to go beyond the Rayleigh approximation and to capture the essential size-dependent features of scattering, local fields, SERS, hyper-Raman and second-harmonic-generation enhancements, decay rates, and photophysics of dipolar arrays.