  A two dimensional flat phononic crystal (PC) lens for focusing off-plane
shear waves is proposed. The lens consists of a triangular lattice hole-array,
embedded in solid matrix. Self-collimation effect is employed to guide the
shear waves propagating through the lens along specific directions.
Dirichlet-to-Neumann Maps (DtN) method is employed to calculate the band
structure of the PC, which can avoid the problems of bad convergence and fake
bands automatically in the void-solid PC structure. When the lens is
illuminated by the off-plane shear waves emanating from a point source, a
subwavelength image appears in the far-field zone. The imaging characteristics
are investigated by calculating the displacement fields explicitly using the
multiple-scattering method, and the results are in good agreement with the
ray-trace predictions. Our results may provide insights for designing new
phononic devices.
