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 voidsolid 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.

In this paper we study the characteristics of subwavelength imaging of a photonic crystal (PhC) superlens under the influence of source displacement. For square-and triangular-lattice photonic crystal lenses, we investigate the influence of changing the lateral position of a single point source on the imaging uniformity and stability. We also study the effect of changing the geometrical center of a pair of sources on the resolution of the double-image. Both properties are found to be sensitive to the displacement, which implies that a PhC slab cannot be treated seriously as a flat lens. We also show that by introducing material absorption into the dielectric cylinders of the PhC slab and widening the lateral width of the slab, the imaging uniformity and stability can be substantially improved. This study helps us to clarify the underlying mechanisms of some recently found phenomena concerning imaging instability.