Simultaneous negative reflection and refraction and reverse-incident right-angle collimation of sound in a...

The square lattice phononic crystal (PnC) has been used extensively to demonstrate metamaterial effects. Here, positive and negative refraction and reflection are observed simultaneously due to the presence of Umklapp scattering of sound at the surface of PnC and square-like equifrequency contours (EFCs). It is found that a shift in the EFC of the third transmission band away from the center of the Brillouin zone results in an effectively inverted EFC. The overlap of the EFC of the second and third band produce quasimomentum-matching conditions that lead to multi-refringence phenomena from a single incident beam without the introduction of defects into the lattice. Additionally, the coupling of a near-normal incident wave to a propagating almost perpendicular Bloch mode is shown to lead to strong right-angle redirection and collimation of the incident acoustic beam. Each effect is demonstrated both numerically and experimentally for scattering of ultrasound at a 10-period PnC slab in water environment.