Multipolar expansions for scattering and optical force calculations beyond the long wavelength approximation

We review three different approaches for the calculation of electromagnetic multipoles, namely, the Cartesian primitive multipoles, the Cartesian irreducible multipoles, and the spherical multipoles. We identify the latter as the best suited to describe the scattering of electromagnetic radiation, as exemplified for an amorphous silicon sphere. These multipoles are then used to calculate the optical force acting on semiconductor, dielectric or metallic particles in a wide wavelength range, from the dipolar regime down to the Mie regime.