Features of Rayleigh Scattering by a Particle Near an Interface

Features of Rayleigh scattering by a solid particle at a small distance compared to the wavelength from an impenetrable plane boundary are revealed. The choice of the Green’s function in the integral representation of the Helmholtz equation makes it possible to reduce integration only over the particle surface and eliminate the contribution of the interface surface. When expanding over a small wave parameter, a well-known approach is used, making it possible to represent the solution of a given order as the sum of a potential function and a component expressed in terms of lower-order approximations. The potential component is found, expressed in terms of solid irregular harmonics centered on the particle and its mirror image. The vibrational velocity of the center of a particle and the scattering amplitude are determined. In the lowest order of the wavenumber, the scattering amplitude is expressed in terms of the monopole and dipole components.