Subwavelength resonant acoustic scattering in fast time-modulated media

This article provides a rigorous mathematical analysis of acoustic wave scattering induced by a high-contrast subwavelength resonator whose material density is periodically modulated in time, and with a modulation frequency that is much larger than the one of the incident wave. We find that in general, the effect of the fast modulation is averaged over time and that the system behaves as an unmodulated resonator with an apparent effective density. However, under a suitable tuning of the modulation, which achieves a matching between temporal Sturm-Liouville and spatial Neumann eigenvalues, the low frequency incident wave becomes suddenly able to excite high frequency modes in the resonator. This phenomenon leads to the generation of scattered waves carrying high frequency components in the far field, and to the existence of exponentially growing outgoing modes. From these findings, it is expected that such time-modulated system could serve as a spontaneously radiating device, or as a high harmonic generator.