Broadband sub-diffraction and ultra-high energy density focusing of elastic waves in planar gradient-index lenses

We demonstrate experimentally and theoretically the broadband sub-diffraction and ultra-high energy density focusing of elastic wave inside planar gradient-index (GRIN) plate lenses based on thickness variation. The full width at half maximum is -0.40 times the minimum wavelength inside the lens ?0 or -1/11 times the incident wavelength in the background plate ?B. We analytically elucidate the underlying physical mechanism as the rapid oscillations in the propagator function at the focal distance. Our design displays several advantages including the broadband sub-diffraction behavior, three-order of magnitudes higher energy intensity at the focal point, and focusing capacity with a narrow transverse width of the lens, over the usual metastructure and/or phononic crystal based GRIN lenses. The broadband sub-diffraction and ultra-high energy density focusing can be used for energy harvesting and signal sensing.