Parameterizing wave interactions with aperiodic order: threads in a tapestry

In this paper, a compact overview of a running research program on EM wave interactions with aperiodically-ordered structures is presented. Emphasis has been placed on tools and techniques for analytic parameterization of aperiodic-order induced wave phenomena, originally derived within the framework of solid-state physics. This paper hopes that the outlined research agenda may motivate other researchers to enter the field, and eventually lead to the development of systematic approaches for the exploitation of the additional degrees of freedom featured by aperiodically-ordered geometries in the synthesis of "smart" EM devices and materials