Anisotropic polarizability tensor of a dimer of nanospheres in the vicinity of a plane substrate

We derive analytically the effective dipole polarizability tensor of a dimer of spheres located near a plane substrate. This is used to determine the extinction cross sections and other optical properties of the particles, and we use the results to study the experimentally observed red and blue shifts of the plasmon resonance of the dimer as a function of the distance between the particles or between the particles and the substrate. The results show that bringing the dimer towards the surface always leads to red shifted plasmon excitation. The plasmon resonance of the dimer may be red shifted or blue shifted as the particles are brought toward each other (at fixed distance from the surface) depending on the polarization. The size of the blue shift is smaller when the particles are close to the surface than when they are far away, but the red shifts are essentially unchanged.