Abstract
Recent years have heralded the introduction of metasurfaces that advantageously combine the vision of sub-wavelength wave manipulation, with the design, fabrication and size advantages associated with surface excitation. An important topic within metasurfaces is the tailored rainbow trapping and selective spatial frequency separation of electromagnetic and acoustic waves using graded metasurfaces. This frequency dependent trapping and spatial frequency segregation has implications for energy concentrators and associated energy harvesting, sensing and wave filtering techniques. Different demonstrations of acoustic and electromagnetic rainbow devices have been performed, however not for deep elastic substrates that support both shear and compressional waves, together with surface Rayleigh waves; these allow not only for Rayleigh wave rainbow effects to exist but also for mode conversion from surface into shear waves. Here we demonstrate experimentally not only elastic Rayleigh wave rainbow trapping, by taking advantage of a stop-band for surface waves, but also selective mode conversion of surface Rayleigh waves to shear waves. These experiments performed at ultrasonic frequencies, in the range of 400–600 kHz, are complemented by time domain numerical simulations. The metasurfaces we design are not limited to guided ultrasonic waves and are a general phenomenon in elastic waves that can be translated across scales.
Highlights
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In contrast to acoustic[2,3,4] and electromagnetic[5] situations, where the main advantage of the rainbow effect is the spatial segregation of waves accompanied by the local enhancement of their amplitude, the elastic rainbow for elastic surface waves has an additional remarkable property which is that of broadband mode conversion from Rayleigh surface waves into bulk shear waves
We have conclusively demonstrated via experiments in the ultrasonic regime, complemented by theory and numerical simulations, that mechanical metasurfaces can be designed to create elastic rainbow trapping and to generate surface Rayleigh wave to bulk shear wave conversion
Summary
Rainbow trapping is generated by the nearly flat branch approaching zero group velocity at the edge of the Brillouin zone, while the conversion is due to a hybrid mode, typical of this metasurface, connecting the Rayleigh with the S-wave line Both phenomena are functions of the resonance frequency of the microrods and for the proposed designs in Fig. 1c and d, the trapping and turning points are precisely predicted using Eq (1) (see later discussions). The speed of propagation and the polarization suggest that waves in the elastic substrate are mainly propagating as S and Rayleigh phases with only little disturbances induced by the presence of the lateral boundaries
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