FIG. 1: (a) The band structure of the triangular lattice hole-array PC. (b) The equal frequency contours (EFC) and the refraction diagram. The lattice constant is a , and the radius of the holes is r$_{0}$ = 0 . 4 a . The two straight lines in (a) are the “sound lines” for the shear wave. The hexagonal blue curve marked 0.6 and the red circle in (b) represent the EFCs of the PC and of the host medium respectively, at reduced (dimensionless) frequency k$_{t}$a/ 2 π = ωa/ 2 πc$_{t}$ = 0 . 6. The two thick black arrows indicate the k vectors of the incident and refracted waves. The continuity of the wave phase along the host-PC interface implies that these two k vectors have the same component along the interface. The two pink arrows represent the energy flow (averaged Poynting vector) directions of the incident and refracted waves. The wave vector length | k | = ΓP is chosen for calculating the effective refraction index n . Note that the direction of the refracted ray (energy flow) is approximately fixed at ± π/ 6. Besides, it is not possible to excite a propagating mode of the PC if the incident angle is larger than π/ 3. [35] Pi-Gang Luan, Kao-Der Chang, J. Nanophotonics 1, 013518 (2007). 10