Subwavelength and directional control of flexural waves in zone-folding induced topological plates

TL;DR

This paper demonstrates a topological plate structure that enables subwavelength, directional control of flexural waves, leveraging zone-folding and topological band gaps to guide spin-dependent waves along complex paths.

Contribution

It introduces a novel plate design with zone-folding induced topological band gaps for controlling flexural waves at subwavelength scales.

Findings

Successfully moves double Dirac cone to lower frequencies

Creates topologically distinct subwavelength band gaps

Guides spin-dependent flexural waves along complex paths

Abstract

Inspired by the quantum spin Hall effect shown by topological insulators, we propose a plate structure that can be used to demonstrate the pseudo-spin Hall effect for flexural waves. The system consists of a thin plate with periodically arranged resonators mounted on its top surface. We extend a technique based on the plane wave expansion method to identify a double Dirac cone emerging due to the zone-folding in frequency band structures. This particular design allows us to move the double Dirac cone to a lower frequency than the resonating frequency of local resonators. We then manipulate the pattern of local resonators to open subwavelength Bragg band gaps that are topologically distinct. Building on this method, we verify numerically that a waveguide at an interface between two topologically distinct resonating plate structures can be used for guiding low-frequency, spin-dependent one-way flexural waves along a desired path with bends.