Optical response of a thin film of spherical particles upon a dielectric substrate: retarded multipolar treatment including multiple reflections

Multipolar expansions were recently used to calculate the optical behavior of a square network of metal spheres sitting upon an infinitely thick dielectric substrate. Here a more realistic substrate of finite thickness is treated, and multiple reflections are taken into account. Retarded field forms are consistently used throughout the treatment for calculating multipole-multipole interactions and scattered fields. Transmission and reflection properties are fully described by 2 × 2 matrices, whose elements provide the optical response as a function of the polarization state. Numerical results are presented in graphic form: They apply to a particular sample consisting of gold particles upon a sapphire substrate.