Taming leaky waves in fluid-loaded thin structures via space- and time-modulated metamaterials

We leverage space- and time-periodic resonators to produce tunable acoustic radiation in fluid-loaded metamaterials, where the propagation angle becomes a controllable degree of freedom for spatial focusing. Under such a modulation, the waveguide generates leaky waves that radiate energy across a wide angular span—from shallow emission to broadside— through selective activation of Floquet harmonics that concentrate energy into desired acoustic beams. To characterize this behavior, we develop numerical methods that resolve the complex-valued dispersion relation, which, in turn, captures the radiation properties in spatially and temporally modulated thin elastic waveguides. We demonstrate that the tunable radiation is inherently governed by the modulation parameters and the resulting wavenumber and frequency transformations, with predictions corroborated by time-domain simulations. By exploring the physics of fluid-loaded resonant metamaterials with spatially- and temporally-varying properties, this paper points toward opportunities in areas ranging from underwater communication to transcranial ultrasound for imaging, diagnosis, and therapy.