General reflection rule for electromagnetic multipole fields on a plane interface

The general rule for reflection of a vector 2'-pole field on a plane interface between two media of different dielectric properties is established starting from the expansion of the spherical multipole field as a linear combination of inhomogeneous vector plane waves, In fact, by considering vector multipole fields that satisfy the radiation condition at infinity we are able to define a matrix that effects their reflection on the plane interface, Such a matrix can also be used to reflect a superposition of many 2'-pole fields and so can be useful to describe the effect of a plane surface near to a specified source or to a scattering particle.