Controlling surface acoustic waves (SAWs) via temporally graded metasurfaces

In this manuscript, the temporal rainbow effect for surface acoustic waves (SAWs) is illustrated through a temporal analog of space metagradings. We show that a time-modulated array of mechanical resonators induces a wavenumber-preserving frequency transformation which, in turn, dictates Rayleigh-to-Shear wave conversion. The process is unfolded through the adiabatic theorem, which allows us to delineate the transition between a solely frequency-converted wave packet and a temporally-driven mode conversion. In other words, our paper explores the role of time modulation in the context of elastic metasurfaces, and we envision our implementation to be suitable for designing a new family of SAW devices with frequency conversion, mode conversion, and unusual transport capabilities.