Temporal Effective Medium for Programmable Acoustic Metamaterials with Multiple Resonances

TL;DR

This paper extends effective medium theory to time-modulated, frequency-dispersive acoustic metamaterials with multiple resonances, enabling advanced control and design of acoustic devices through programmable, time-dependent parameters.

Contribution

It develops a generalized temporal effective medium theory for complex acoustic metamaterials with multiple resonances and modulation, providing explicit averaging rules for design.

Findings

Resonant frequency modulation yields the average monopolar susceptibility.

Modulating resonant strength results in the average of 1/hi.

High-frequency resonances can be renormalized as a non-dispersive background.

Abstract

We extend effective medium theory (EMT) to time-modulated, frequency-dispersive acoustic metamaterials with multiple resonances. While previous studies focused on non-dispersive or single-resonance systems, advances in programmable materials now enable precise control of time-varying responses. We derive explicit averaging rules that account for the interplay between resonant and modulation frequencies. When resonant frequencies are much lower than the modulation frequency, modulating the resonant strength yields the temporal average of monopolar susceptibility \c{hi}, while modulating the resonant frequency results in the average of 1/\c{hi}, applied per resonance mode. In hybrid cases, high-frequency resonances (relative to modulation) can be renormalized as a non-dispersive background before averaging the rest. This generalized temporal EMT offers a unified framework for designing compact, topologically robust, and non-Hermitian acoustic devices, leveraging the possible programmability of time-dependent material parameters in future.