Reciprocal and non-reciprocal wave phenomena in quasi-periodic particle chains

Quasi-Periodic (QP) particle chains exhibit unique properties not observed in periodic ones. Furthermore, they inherently support significant long-range interactions and radiation to the surrounding medium. Hence they are fundamentally different from traditional QP structures governed by the Harper's model or the almost-Mathieu operator. We present a mathematical framework for QP particle chains and study their electrodynamics. They support guided modes that exhibit a complex interaction with the light cone, and possess a two-dimensional fractal-like structure in the frequencywavenumber space thus making the unique definition of modal phase velocity impossible. However, a well-defined group velocity is revealed due to the fractals inner structure. We also show initial study of non-reciprocal QP structures.