Transmisison hysteresis and edge modes in bounded space-time composites

The vibrational frequency response of bounded composites, e.g., metamaterials and sonic crystals, is often understood thanks to band diagrams established in the absence of boundaries. Introducing a pump wave that modulates in time the properties of the composite challenges the correspondence between the vibrations picture and the waves picture. The talk revisits this correspondence in the context of the nonreciprocal acoustics of space-time composites. Specifically, we establish in the weak coupling regime how the hybridization of total bandgaps into pairs of one-way bandgaps triggers nonreciprocal hysteresis transmission loops in the space-frequency domain and alters, qualitatively and quantitatively, the vibrational frequency response in the presence of reflecting boundaries. The theoretical analysis is assessed numerically and exploited to shed new light on previously obtained experimental data. Last, extrapolating our study to the strong coupling regime, transmission hysteresis is shown to explain the emergence of topological vibrational modes with one-way edge-bulk and bulk-edge transitions.