A Generalization of the Mie Theory for a Sphere with Spatially Dispersive Permittivity

The Mi theory is applicable for the modeling of optical processes involving metals, does not require to simplify the dependence of the permittivity on the light frequency and wavenumber, and does not apply the electrostatic approximation. A relative error of this approximation in calculating the extinction cross-section of a 10 nm-radius silver sphere is shown to exceed 50% in a wide frequency interval.