The band structure and the EFC of the PC calculated using DtN method are shown in Fig.1 (a) and 1(b). We have also calculated the same band structure using the pseudosolid method, and no visible difference between the results of these two methods can be found. The accuracy of the band structure is thus confirmed. The two inclined straight lines in Fig. 1(a) stand for the “sound lines” of the host medium. To focus the shear waves emanating from a point source, we choose k$_{t}$a/ 2 π = ωa/ 2 πc$_{t}$ = 0 . 6 as the operating (reduced) frequency. The EFC of the PC at this frequency looks like a hexagon, which occupies an area a little smaller than the corresponding circular EFC of the host medium. The frequency surface ω ( k ) of the PC in the 2nd band around the Γ point has a negative curvature (negative effective phonon mass), which leads to k · v$_{g}$ < 0, and thus negative refraction can occur. Here v$_{g}$ = ∇$_{k}$ ω is the group velocity, pointing in the direction of the greatest rate of increase of ω and is perpendicular to EFC. It can also be shown that the direction of v$_{g}$ is the same as the direction of energy flow (averaged Poynting vector) [32]. When a plane wave of wave vector k is incident upon a PC, the refracted wave vector k ′ can be determined by three rules. First, the incident and refracted waves have the same frequency. Thus the tips of k and k ′ are located on the host and PC EFCs, respectively. Second, the wave phase on the two sides of the host-PC interface must be the same, which means the tangential component of k is equal to that of k $^{′}$. Third, the normal component of v$_{g}$ does not change sign in the refraction process, which is a consequence of the energy conservation law ∇ · 〈 S 〉 = 0 for monchromatic wave. An illustration of this refraction process in terms of the k -space description and its corresponding r -space configuration is shown in Fig.1(b). The thick black arrows represent the incident and refracted wave vectors, whereas the pink arrows indicate the v$_{g}$ (energy flow) directions. Hereafter we always assume ΓK be the orientation of the host-PC interface. The EFC plot in Fig. 1(b) also indicates that if the incidence angle is in the interval ( − π/ 3 , π/ 3), wave can penetrate into the PC and the refraction angle of ray (energy flow) are almost fixed at ± π/ 6. This is caused by the self-collimation effect of the hexagonal shaped EFC. On the other hand, if the incident angle is beyond ( − π/ 3 , π/ 3), no refracted wave can be excited, and the incident wave will be totally reflected. These phenomena are illustrated in Fig.2 (a)-(c). Here we use Gaussian beams as incidence waves instead of plane waves. The Gaussian source used in these simulations is formed by giving a Gaussian strength profile along 20 aligned point sources distributed evenly within 4 a . The incidence angles in Fig. 2(a), (b) and (c) are π/ 18 (10 $^{◦}$) and 2 π/ 9 (40 $^{◦}$), and π/ 3 (60 $^{◦}$), 5