Reflection of the individual multipoles fields from a flat substrate in the angular spectrum approach

In this report, we give the derivation of the electromagnetic field of multipoles over a substrate, using the angular spectrum representation. The multipole series up to the electric quadrupole is considered. If necessary, this approach can easily be extended to multipoles of any order. As a result, analytical expressions for the scattered and reflected multipole fields as an infinite sum of plane waves of different polarizations are obtained.