| In this thesis, we derive a periodic Green's function for dipoles radiating inside a layered medium. In order to do so, we proceed as follows: first the spatial Green's function for a dipole inside a layer is derived in terms of Hertz potentials. Next, it is shown that this periodic Green's function can be calculated in the spectral domain provided that the Fourier integrals do not have poles on the real axis. The derived expressions indicate that this spectral sum is rapidly converging for most source-observation pairs. However, they are not so for the source and observation pair lying on either the top or bottom interfaces. To overcome this, a Kummer's transformation is proposed. We validate our Green's function via reduction to a canonical half-space problem. The periodic layered medium Green's function is validated numerically by comparison with analytical data for reflection and transmission from a single layer. |
