Non-dispersive, non-reciprocal amplification of wavepackets in sonic metamaterials

Active metamaterials harbor sound processing capabilities that are impossible in passive structures. However, the desirable response is often restricted to narrow frequency ranges, limiting its utility for signals composed of a mix of frequencies. For instance, parametric amplification--injecting energy into sound waves via periodic modulation of elastic stiffnesses--is typically restricted to specific multiples of the modulation frequency. Inspired by a recent proposal in optics, we describe a mechanism for one-way amplification of sound waves across an entire frequency band using a traveling-wave modulation of local stiffnesses. When the speed of the modulation wave approaches that of the speed of sound in the metamaterial--a regime called the sonic limit--nearly all modes in the forward-propagating acoustic band are amplified, whereas no amplification occurs in the reverse-propagating band. We find wide ranges of parameters for which the strength of the effect is nearly uniform across the band, enabling amplification of wavepackets while preserving their speed, shape, and spectral content. Our mechanism provides a route to designing acoustic metamaterials which can propagate wave pulses without losses or distortion across a wide range of frequencies.