Optical absorption by a small sphere above a substrate with inclusion of nonlocal effects

A method for the calculation of the optical absorption by a small sphere, which has a nonlocal dielectric function and is located above a substrate, is developed. Numerical calculations of absorption spectra are performed for a metallic and a dielectric sphere above a dielectric or metallic substrate. From comparisons with the corresponding spectra of free spheres, it is found that the presence of the substrate causes a redshift of the main absorption resonance and the appearance of subsidiary absorption peaks.