Sonic metamaterials: reflection on the role of topology on dispersion surface morphology

TL;DR

This paper explores how the topology of two-dimensional sonic metamaterials influences their dispersion surface morphology, revealing how local microstructures and anisotropy can create specific frequency surfaces and band gaps.

Contribution

It introduces a novel approach to controlling dispersion surfaces in sonic metamaterials using local microstructures and topology, highlighting the role of internal anisotropy.

Findings

Six optical frequency-surfaces with negative group velocity can be formed.

Splitting of frequency-surfaces enables the creation of different frequency band gaps.

Internal anisotropy is key to achieving energy-level repulsion analogs.

Abstract

Investigating dispersion surface morphology of sonic metamaterials is crucial in providing information on related phenomena as inertial coupling, acoustic transparency, polarisation, and absorption. In the present study, we look into frequency surface morphology of two-dimensional metamaterials of K3,3 and K6 topologies. The elastic structures under consideration consist of the same substratum lattice points and form a pair of sublattices with hexagonal symmetry. We show that, through introducing universal localised mass-in-mass phononic microstructures at lattice points, six single optical frequency-surfaces can be formed with required properties including negative group velocity. Splitting the frequency-surfaces is based on the classical analog of the quantum phenomenon of "energy-level repulsion", which can be achieved only through internal anisotropy of the nodes and allows us to obtain different frequency band gaps.