Super-resolution within a one-dimensional phononic crystal of resonators using time reversal in an equivalent circuit model

Adam D Kingsley; Brian E Anderson; T J Ulrich

doi:10.1121/10.0013832

Super-resolution within a one-dimensional phononic crystal of resonators using time reversal in an equivalent circuit model

J Acoust Soc Am. 2022 Sep;152(3):1263. doi: 10.1121/10.0013832.

Authors

Adam D Kingsley¹, Brian E Anderson¹, T J Ulrich²

Affiliations

¹ Acoustics Research Group, Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602, USA.
² Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.

PMID: 36182294
DOI: 10.1121/10.0013832

Abstract

An equivalent circuit model has been developed to model a one-dimensional waveguide with many side-branch Helmholtz resonators. This waveguide constitutes a phononic crystal that has been shown to have decreased phase speed below the resonance frequency of an individual resonator. This decreased phase speed can be exploited to achieve super-resolution using broadband time reversal focusing techniques. It is shown that the equivalent circuit model is capable of quantifying this change in phase speed of the crystal and also the small-scale wave-resonator interactions within the crystal. The equivalent circuit model enables the parameterization of the physical variables and the optimization of the focusing bandwidth by balancing the combination of increasing resolution and decreasing amplitude near the resonance frequency. It is shown that the quality factor-in this case, the quality factor determined by the geometric shape of each resonator-controls the range of frequencies that are strongly affected by the Helmholtz resonators.