A theoretical approach, based on the discrete dipole approximation, for multipole analysis of light scattering by arbitrary-shaped nanoparticles located near or on a plane surface is presented. The obtained equations include the first multipoles up to the magnetic quadrupole and electric octupole moments. It is discussed how the suggested approach can be applied to the problem of multipole scattering of surface plasmon polaritons. As an example, the theoretical framework is used for investigation of light scattering by cylindrical Si nanoparticles located on different dielectric substrates, manifesting resonant interaction of these particles with light.
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