Multi-branch subwavelength focusing of the lowest-order antisymmetric Lamb mode in a gradient-index phononic crystal

We demonstrate a metasurface design of a multi-branch dispersion that can converge plane wave into a focal region at sub-wavelength scale. The design is based on overlapping the periodic array of steel pillars, whose role is to obtain non trivial multi-branch dispersion for the lowest-order antisymmetric Lamb (A₀) mode, upon the periodic array of air holes in an aluminum plate. The radii of air holes are gradually modulated along the transverse direction to impose the hyperbolic secant profile for the refractive index. The air-coupled method and laser ultrasonic technique are applied to excite the flexural wave and to map the out-of-plane displacement within the gradient-index (GRIN) lens. The multi-branch focusing is observed within two different frequency ranges and its experimental character shows excellent agreement with the numerical results.