The relationship between reflectivity minima and eigenmodes in multi-layer structures

The tight connection between the various eigenmodes of an arbitrary multi-layer structure and the reflectivity function for TM-polarized (TM standing for transverse magnetic) plane waves incident on this structure is examined. For distinctive multi-layer configurations, we developed a calculation procedure based on a pole-zero representation for determining, for each eigenmode compatible with the field distribution of the incident plane wave, its contribution to the amplitude and phase of the reflectivity. The dissimilarities between the regime of attenuated total reflection and that of transmission are discussed. For the first time we show that an eigenmode associated with a zero of the reflectivity function is always present within the reflectivity minima, but this is a pole only under certain conditions. The accuracy of an approximate pole-zero representation for the reflectivity function is analysed for a wide angular spectrum for different structures. Finally, the dependence of the lateral displacement of Gaussian beams on the eigenmodes of the multi-structure is examined.