Wide-Stopband Aperiodic Phononic Filters

TL;DR

This paper introduces a method to create wide phononic stopbands using aperiodic structures composed of multiple filter stages, surpassing traditional phononic crystal limitations, with potential applications in thermal conductance reduction.

Contribution

It presents a novel approach to synthesize wide phononic stopbands from aperiodic structures, enabling enhanced control over phonon transmission beyond single-lattice phononic crystals.

Findings

Aperiodic phononic filters can achieve broader stopbands than periodic structures.

Simulations show effective phonon transmission suppression in multi-moded waveguides.

Estimated thermal conductance reduction by an order of magnitude at 75mK.

Abstract

We demonstrate that a phonon stopband can be synthesized from an aperiodic structure comprising a discrete set of phononic filter stages. Each element of the set has a dispersion relation that defines a complete bandgap when calculated under a Bloch boundary condition. Hence, the effective stopband width in an aperiodic phononic filter (PnF) may readily exceed that of a phononic crystal with a single lattice constant or a coherence scale. With simulations of multi-moded phononic waveguides, we discuss the effects of finite geometry and mode-converting junctions on the phonon transmission in PnFs. The principles described may be utilized to form a wide stopband in acoustic and surface wave media. Relative to the quantum of thermal conductance for a uniform mesoscopic beam, a PnF with a stopband covering 1.6-10.4 GHz is estimated to reduce the thermal conductance by an order of magnitude at 75mK.