Focusing of the lowest-order antisymmetric Lamb mode behind a gradient-index acoustic metalens with local resonators

We have investigated the focusing of the lowest-order antisymmetric Lamb mode (A(0)) behind a positive gradient-index (GRIN) acoustic metalens consisting of air holes drilled in a silicon plate with silicon pillars erected on one face of the lens. We have analyzed the focusing in the near field as the result of the coupling between the flexural resonant mode of the pillars and the vibration mode of the air/silicon phononic crystal. We highlight the role played by the polarization coherence between the resonant mode and the vibration of the plate. We demonstrate both numerically and experimentally the focusing behind the lens over a spot less than half a wavelength, paving a way for performance of acoustic lenses beyond the diffraction limit. Our findings can be easily extended to other types of elastic wave.