Multi-periodicity induces prominent optical phenomena in plasmonic multilayers

We introduce multi-periodicity in plasmonic multilayers and develop a general theory for the description of their eigenwaves. We define the order of multi-periodicity as the number of different kinds of plasmonic interfaces present in the multilayer, and investigate the optical effects that arise as this order increases from one (simple periodic multilayers) to two (bi-periodic multilayers) and beyond. For example, we show the formation of additional photonic bands, multi-refringence of p-polarized light, Dirac and mixed states.