Coupled dipole method determination of the electromagnetic force on a particle over a flat dielectric substrate

We present a theory to compute the force due to light upon a particle on a dielectric plane by the coupled dipole method. We show that, with this procedure, two equivalent ways of analysis are possible, both based on Maxwell's stress tensor. The interest in using this method is that the nature and size or shape of the object can be arbitrary. Even more, the presence of a substrate can be incorporated. To validate our theory, we present an analytical expression of the force due to the light acting on a particle either in presence, or not, of a surface. The plane wave illuminating the sphere can be either propagating or evanescent. Both two- and three-dimensional calculations are studied.