Applicability conditions for the dipole approximation in the problems of scattering of surface plasmon polaritons

Using the method of the tensor Green's function of the wave equation, the conditions have been determined under which the dipole approximation is sufficient in the problem of the scattering of surface optical electromagnetic waves (surface plasmon polaritons) on a small spherical particle. The independence of the electric field inside the scatterer of the spatial coordinates is used as the main requirement of the dipole approximation. Conditions are obtained in the form of inequalities involving the wavenumber, the material parameters of the system, and the size of the scatterer and its position with respect to the surface on which plasmon polaritons are excited.