Abnormal topological refraction into free medium at sub-wavelength scale in valley phononic crystal plates

TL;DR

This paper introduces a topological valley phononic crystal plate that demonstrates unique sub-wavelength refraction behaviors, including evanescent modes and topological edge states, enabling novel elastic wave control devices.

Contribution

It presents a new topological valley phononic crystal design with detailed analysis of edge states, refraction behaviors, and potential for functional elastic wave devices.

Findings

Distinct refraction behaviors at domain walls and edges.

Evanescent modes occur at deep sub-wavelength scales.

Designs for one-way waveguides and monopole/dipole emitters.

Abstract

In this work we propose a topological valley phononic crystal plate and we extensively investigate the refraction of valley modes into the surrounding homogeneous medium. This phononic crystal includes two sublattices of resonators (A and B) modeled by mass-spring systems. We show that two edge states confined at the AB/BA and BA/AB type domain walls exhibit different symmetries in physical space and energy peaks in the Fourier space. As a result, distinct refraction behaviors, especially through an armchair cut edge, are observed. On the other hand, the decay depth of these localized topological modes, which is found to be solely determined by the relative resonant strength between the scatterers, significantly affects the refraction patterns. More interestingly, the outgoing traveling wave through a zigzag interface becomes evanescent when operating at deep sub-wavelength scale. This is realized by tuning the average resonant strength. We show that the evanescent modes only exist along a particular type of outlet edge, and that they can couple with both topological interface states. We also present two designs of topological functional devices, including an elastic one-way transmission waveguide and a near-ideal monopole/dipole emitter, both based on our phononic structure.