Fig. 6: Spatial and temporal applications.

a Gradient index metamaterials composed of quarter wavelength detuned resonators augmented by an actively controlled loudspeaker under feedback amplification, reproducing the tonotopic frequency mapping of the cochlea with hypersensitivity to low amplitude sounds adapted with permission from ref. ²²⁹. b Metasurface of shunted parallel loudspeakers with time-varying impedance leading to mode transition and non-reciprocal propagation at different Floquet harmonics adapted with permission from ref. ²³³. c Linear array of 113 piezoelectric elements under time-varying grounding conditions that allows the measurement of the complete band diagram of the space-time metamaterial adapted with permission from ref. ²³⁶. d Airborne acoustic circulator based on spatiotemporal modulation of the synthesized moving mass of three loudspeakers terminating a three-port network adapted with permission from ref. ²³⁹.