  The multipole expansion has found limited applicability for optical
dielectric resonators in inhomogeneous environment, such as on the surface of
substrates. Here, we generalize the method of images to multipole analysis for
light scattering by dielectric nanoparticles on conductive substrates. We
present examples illustrating the physical insight provided by our method,
including selection rules governing the excitation of the multipoles. We
propose and experimentally demonstrate a new mechanism to generate high
resolution surface color. The dielectric resonators employed are very thin
(less than 50 nm), i.e. similar in thickness to the plasmonic resonators that
are currently being investigated for structural color. The generalized method
of images opens up new prospects for design and analysis of metasurfaces and
optical dielectric resonators.
