Power emitted by a multipole near an interface

The power emitted by an electric or a magnetic multipole of arbitrary order located near an interface with a layer on a substrate is studied. The power in the far field can be expressed in terms of Fresnel reflection and transmission coefficients for plane waves. When eliminating the transmission coefficients in favor of the reflection coefficients and combining the various contributions, it appears that the power has three distinct parts: (i) the first term is the power emitted by an unbounded multipole, and the process of reflection and transmission redistributes the angular dependence of this power; (ii) the second term represents the interference between the multipole waves which travel directly towards a detector and the waves which are reflected by the interface, a mechanism which modifies the emission rate, primarily depending on the distance between the multipole and the interface; (iii) the third term accounts for evanescent multipole waves which are converted into traveling waves upon transmission through the layer. When the distance between the multipole and the interface is about or less than a fraction of a wavelength, this third term can be extremely large compared to the emission rate by an unbounded multipole (for which all power comes from traveling multipole waves).