All-angle negative refraction for surface acoustic waves in pillar-based two-dimensional phononic structures

We describe an all-angle negative refraction effect for surface acoustic waves in two-dimensional phononic crystals made of cylindrical pillars assembled in a square lattice and deposited on the surface of a semi-infinite substrate. The convexity of the iso-frequency contours of some branches leads to a negative refraction effect despite the fact that the effective index is not negative. It occurs for the frequency range where the group velocity is never in opposite direction to the phase velocity. In addition, the use of cylindrical pillars acting as acoustic resonant elements on the surface permits us to achieve this phenomenon with a sub-wavelength feature size structure; therefore, the effect of all-angle negative refraction can be shifted down to low frequencies, which is highly desirable for high-resolution superlensing applications. A flat lens for surface acoustic waves has also been designed. It demonstrates the focusing of an acoustic source into an image on the other side of the finite-size structure with an image resolution of (λ/4), which overcomes the Rayleigh diffraction limit. The numerical simulations are based on the efficient finite element method and analyze pillars and the substrate of lithium niobate.