point source at the far field zone, although the image width (about 0 . 6 λ ) is a little larger than that employing evanescent wave coupling mechanism [22, 35]. The position of focal point can be predicted by considering the refraction of acoustic rays. Although the PC in the chosen frequency cannot be represented by an isotropic effective medium, a formal usage of Snell’s law (the consequence of the continuity of the tangential component of wave vector across the host-PC interface) can still help us to find the position of the focal point approximately. The effective refractive index n = − 0 . 8305 of the PC at reduced frequency k$_{t}$a/ 2 π = 0 . 6 can be derived from the relation n = − c$_{t}$ | k | /ω = −| k | /k$_{t}$ , here k$_{t}$ is the radius of the host EFC, and | k | is the shortest radius (the line segment ΓP in Fig.1(b)) of the PC EFC. We sketch the ray-trace diagram in Fig. 5. The refraction angle are fixed at ± π/ 6, as mentioned above. According to Snell’s law, we have sin θ = n sin( − π/ 6), which gives θ = 0 . 4282 or 24 . 53 ◦ The distances x$_{1}$ and x$_{2}$ are related to d$_{1}$ and d$_{2}$ through the relation x$_{1}$/d$_{1}$ = x$_{2}$/d$_{2}$ = tan θ/ tan( π/ 6) = 0 . 7906. We thus have a constant source- image distant d$_{1}$ + d$_{2}$ + D = 2 . 265 D , consistent with the results obtained in the wave field simulations. This analysis seems to imply only one incident angle is allowable, which is not the case for waves emitted from a point source. The ray trace calculated in this way represents the route having an extremum phase aggregation, that is, waves interfere constructively along this specific route. If a route slightly deviated from this specific one were used, the phase propagation direction (the direction of k ) and beam propagation direction (the direction of 〈 S 〉 ) inside the PC would not be parallel to each other. This leads to partially destructive interference and reduce the strength of the ray. A simple glance of Fig. 3 makes these statements more concrete. The predicted positions for the two images (one inside and one outside of the lens) based on the ray formula and those obtained by wave simulations were compared in Fig. 6. A good agreement between these two methods is found, as can be easily checked. In conclusion, we have proposed a 2D phononic crystal flat lens embedded in solid matrix to achieve far-field subwavelength imaging of off-plane shear waves. The field patterns were computed by using the multiple scattering method, whereas the band structure of the phononic crystal were obtained by using the Dirichlet-to-Neumann map method. Image positions were derived by using ray-trace method, and the results are in good agreement with those from direct wave simulations. Our study has the following novelties. First, our PC lens focuses transverse shear wave, while most of previously proposed PC lenses 7