Valley Hall In-Plane Edge States as Building Blocks for Elastodynamic Logic Circuits

In this work, we investigate theoretically and demonstrate experimentally the existence of valley-Hall edge states in the in-plane dynamics of honeycomb lattices with bi-valued strut thickness. We exploit these states to achieve non-trivial waveguiding of optical modes that is immune to backscattering from sharp corners. We also present how different types of interfaces can be combined into multi-branch junctions to form complex waveguide paths and realize a variety of structural logic designs with unconventional wave transport capabilities. We illustrate this potential with two applications. The first is a direction-selective energy-splitting waveguide tree featuring a pronounced asymmetric wave transport behavior. The second is an internal waveguide loop along which the energy can be temporarily trapped and periodically released, effectively working as a signal delayer. The modal complexity of in-plane elasticity has important consequences on the regime of manifestation of the edge states, as the availability of viable total bandgaps is shifted to higher frequencies compared to the out-of-plane counterpart problem. It also poses additional experimental challenges, associated with proper acquisition and deciphering of the in-plane modes, the solution of which requires a systematic use of in-plane laser vibrometry.