Realizing Spatiotemporal Effective Media For Acoustic Metamaterials

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, experimental implementation remains an open challenge. Here, we construct an acoustic metamaterial dynamically switching between two different resonance strengths 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 delay between the modulation of different atoms is found to have a negligible effect 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 nonreciprocity, inverse prism, and parametric amplification using space-time metamaterials, possible for implementation in the future.