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

Abstract

Investigating dispersion surface morphology of sonic meta materials is crucialin 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 (2D) meta materials of K3,3 and K6topologies. Theelastic structures under consideration consist of the same substratum lattice points and form a pair of sublatticeswith 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.