Depolarization field of spheroidal particles

Abstract

A compact analytical formula up to the order of k 3 , where h is a wave vector, is derived for the depolarization field E d 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 E d a general electrostatic formula valid for a particle of a general shape is rederived within the Meier and Wokaun framework. The dynamic k 2 -dependent depolarization component of E d 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 E int 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-harmonicgeneration enhancements, decay rates, and photophysics of dipolar arrays. © 2009 Optical Society of America.