Realizing spatiotemporal effective media for acoustic metamaterials

TL;DR

This paper introduces a method to create acoustic metamaterials with dynamic spatiotemporal properties by switching configurations over time, enabling advanced control of wave phenomena like non-reciprocity and slow-light.

Contribution

It develops an effective medium theory for temporally modulated acoustic metamaterials, incorporating frequency dispersion and Willis coupling, and demonstrates a practical implementation of such dynamic media.

Findings

Effective medium formula for temporally averaged properties.

Negligible impact of phase disorder in modulation.

Enables design of metamaterials for non-reciprocity and slow-light applications.

Abstract

The effective medium representation is fundamental in providing a performance-to-design approach for many devices based on metamaterials. While there are recent works in extending the effective medium concept into the temporal domain, a direct implementation is still missing. Here, we construct an acoustic metamaterial dynamically switching between two different configurations with a time-varying convolution kernel, which can now incorporate both frequency dispersion of metamaterials and temporal modulation. We establish the effective medium formula in temporally averaging the compressibilities, densities and even Willis coupling parameters of the two configurations. A phase disorder between the modulation of different atoms is found negligible on the effective medium. Our realization enables a high-level description of metamaterials in the spatiotemporal domain, making many recent proposals, such as magnet-free non-reciprocity, broadband slow-light and Fresnel drag using spatiotemporal metamaterials possible for implementations in future.