Approximations to the Mie scattering coefficients for plasmonic and negative-index Rayleigh scatterers

We investigate theoretical expansions for the Mie scattering coefficients (MSCs) concerning their use in the development of scattering theory and applications for lossless plasmonic and negative index Rayleigh scatterers. In general, the simplistic dipole approximation drastically fails to predict the scattered fields and associated physical phenomena at resonance points, thus providing incomplete physical predictions and models. The usual resonance at ε = -2ε0 is reviewed in terms of some of the most common expansions for the Mie scattering coefficients available, based on spherical Bessel functions. Our analysis emphasize how our choice for an adequate mathematical background can radically and erroneously modify the understanding of the physics behind scattering of wave fields by very small plasmonic and negative index particles.