Designing multidirectional energy splitters and topological valley supernetworks

Using group theoretic and topological concepts, together with tunneling phenomena, we geometrically design interfacial wave networks that contain splitters which partition energy in two, three, four, or five directions. This enriches the valleytronics literature that has, so far, been limited to two-directional splitters. Additionally, we describe a design paradigm that gives greater detail about the relative transmission along outgoing leads, away from a junction; previously, only the negligible transmission leads were predictable. We utilize semianalytic numerical simulations, as opposed to finite element methods, to clearly illustrate all of these features with highly resolved edge states. As a consequence of this theory, networks, with directionality tunable by geometry, ideal for applications such as beam-splitters, switches, and filters are created. Coupling these networks that contain multidirectional energy-splitters culminates in the realization of a topological supernetwork.