Tuning negative refractive collimation beam by square lattice sonic crystal with concave incident surface

Negative refractive collimation beam at the low frequency region is achieved in a square lattice sonic crystal with the small magnitude of effective refractive index. A simple tuning approach for such acoustic beam is also proposed by attaching an additional concave surface of incidence to the crystal slab. This can increase the propagation distance of collimation beam, enhance or suppress the beam intensity. The proposed approach is rather general and applicable to other acoustic materials as long as their effective index can be retrieved. Moreover, the results can be applied to wavefront manipulation and transmission enhancement.