A point electric dipole: From basic optical properties to the fluctuation–dissipation theorem

We comprehensively review the deceptively simple concept of dipole scattering in order to uncover and resolve all ambiguities and controversies existing in the literature. First, we consider a point electric dipole in a non-magnetic environment as a singular point in space whose sole ability is to be polarized due to the external electric field. We show that the postulation of the Green’s dyadic of the specific form provides the unified description of the contribution of the dipole into the electromagnetic properties of the whole space. This is the most complete, concise, and unambiguous definition of a point dipole and its polarizability. All optical properties, including the fluctuation–dissipation theorem for a fluctuating dipole, are derived from this definition. Second, we obtain the same results for a small homogeneous sphere by taking a small-size limit of the Lorenz–Mie theory. Third, and most interestingly, we generalize this microscopic description to small particles of arbitrary shape. Both bare (static) and dressed (dynamic) polarizabilities are defined as the double integrals of the corresponding dyadic transition operator over the particle’s volume. While many derivations and some results are novel, all of them follow from or are connected with the existing literature, which we review throughout the paper.