Two-dimensional Phononic Crystals with Acoustic-Band Negative Refraction

TL;DR

This paper demonstrates that two-dimensional phononic crystals can exhibit negative energy refraction in the longitudinal mode at low frequencies, with implications for acoustic cloaking due to their anisotropic properties.

Contribution

It introduces the calculation of effective elastodynamic properties showing negative density components and negative refraction in 2D phononic crystals at low frequencies.

Findings

Negative effective density components at low frequencies.

Negative energy refraction observed in longitudinal mode.

High anisotropy ratio suitable for acoustic cloaking applications.

Abstract

A two-dimensional phononic crystal (PC) can exhibit longitudinal-mode negative energy refraction on its lowest (acoustical) frequency pass band. The effective elastodynamic properties of a typical PC are calculated and it is observed that the components of the effective density tensor can achieve negative values at certain low frequencies on the acoustical branches for the longitudinal-mode pass-band, and that negative refraction may be accompanied by either positive or negative effective density. Furthermore, such a PC has a high anisotropy ratio at certain low frequencies, offering potential for application to acoustic cloaking where effective material anisotropy is essential.