Point-dipole approximation for surface plasmon polariton scattering: Implications and limitations

We consider in detail the point-dipole approximation of surface plasmon polariton (SPP) scattering and its limitations imposed by the energy conservation. In the framework of the point-dipole approach, we analytically calculate the scattered electric fields of both the waves propagating away from a metal-dielectric interface and SPP waves. This allows us to establish the relation between the scalar and vectorial models of SPP scattering by dipolar particle. The differential and total scattering cross sections related to SPP-to-SPP scattering and scattering of SPP's into waves propagating away from the interface are studied with respect to the configuration and material parameters of the system. Using the Poynting theorem, we show that the condition of constant field inside a dipolelike scatterer is also essential for the energy conservation in the scattering process, resulting in additional requirements on the sphere radius and other system parameters. In addition to the general case, different limiting cases are considered exemplifying the relative importance of these requirements.