Fig. 4: Experimental demonstration in a 1D acoustic lattice.

a Photo of the 3D-printed experimental sample, consisting of six ring resonators and two half rings on the boundaries. The green and yellow boxes indicate the areas with additional loss. b The measured electric signal imposed on the loudspeaker. c The time evolution of sound pressure for the left-moving acoustic wave. The signals are measured at the middle position of the first site ring (blue) and second site ring (yellow), respectively. d The time evolution of sound pressure for the right-moving acoustic wave. The signals are measured at the middle position of the first site ring (blue) and second site ring (green), respectively. e–g Acoustic energy fields measured at (e) 3.5 ms, (f) 8.5 ms, and (g) 9.5 ms for both right and left incidences. h–j Acoustic energy fields measured in an empty waveguide without additional loss under the same complex-frequency excitation at (h) 3.5 ms, (i) 8.5 ms and (j) 9.5 ms for both right and left incidences.