Topology optimization of non-dispersive elastic metasurfaces for broadband high-numerical-aperture focusing

Elastic metasurfaces, with the subwavelength thickness, have showed promising potential for elastic wave manipulation. However, the inherent velocity dispersion and accumulated phase dispersion during elastic wave propagation result in narrow bandwidths and strong functionality dispersions. More importantly, for the near-field elastic focusing frequently required in practical applications, the primary challenge lies in effectively enhancing the numerical aperture (NA) of the metasurfaces while achieving broadband non-dispersive focusing. To address this issue, a density-based inverse-design methodology is applied to realize broadband non-dispersive and high-NA focusing of longitudinal waves by elastic metasurfaces. Following the fundamental bandwidth limits, two representative types of metasurfaces, broadband (40%) non-dispersive and broadband (25%) non-dispersive high-NA (0.71), are inversely designed to support broadband near-field focusing of longitudinal waves, which are numerically and experimentally demonstrated to break the conventional Rayleigh-Abbe diffraction limit. Furthermore, it has been discovered that the broadband modulation of linear effective index required the similar vibrational modes across the whole frequency range. Combining with geometric-phase mechanisms, the synergistic interplay between the optimized modulus-tuning slits and density-tuning resonators constitutes the fundamental design principle for high-refractive-index microstructures that are essential to realize broadband non-dispersive high-NA metasurfaces. The present study contributes to the design strategy for the elastic metasurface focusing devices which are promising in the high-precision ultrasound non-destructive testing of complex solids.