Electrodynamics of an oscillating particle without cheating PART I : In vacuo. PART II : Near a dispersive bulk

In this paper, the electromagnetic radiation from an oscillating particle placed in the vicinity of an object of size comparable to the wavelength is studied. Although this problem may seem academic at first sight, the details of the calculations are presented throughout without any detail left under the carpet. A polyharmonic decomposition of the radiation sources allows the diffraction problem to be fully characterised while satisfying energy conservation. Finally, the source expressions obtained are suitable for use in a numerical code. A 3D illustration using finite elements is provided.