Unidirectional zero sonic reflection in passive $\mathcal{PT}$ symmetric Willis media

TL;DR

This paper demonstrates that combining $ ext{PT}$ symmetry with Willis acoustic media enables unidirectional zero reflection, offering new ways to control sound reflection and absorption.

Contribution

It unifies Willis coupling and $ ext{PT}$ symmetry in a theoretical framework, revealing exceptional points that lead to one-way zero reflection in acoustic systems.

Findings

Experimental validation with asymmetrically side-loaded waveguides.

Identification of exceptional points causing unidirectional zero reflection.

Gauge transformations and loss biasing enable tailored unidirectional acoustics.

Abstract

In an effective medium description of acoustic metamaterials, the Willis coupling plays the same role as the bianisotropy in electromagnetism. Willis media can be described by a constitutive matrix composed of the classical effective bulk modulus and density and additional cross-coupling terms defining the acoustic bianisotropy. Based on an unifying theoretical model, we unite the properties of acoustic Willis coupling with $\mathcal{PT}$ symmetric systems under the same umbrella and show in either case that an exceptional point hosts a remarkably pronounced scattering asymmetry that is accompanied by one-way zero reflection for sound waves. The analytical treatment is backed up by experimental input in asymmetrically side-loaded wavesguides showing how gauge transformations and loss biasing can embrace both Willis materials and non-Hermitian physics to tailor unidirectional reflectionless acoustics, which is appealing for purposeful sound insulation and steering.