equal frequency contour (EFC), and the image points can be predicted according to Snell’s law. The results are in good agreement with the calculations of field distributions. It is known that in calculating the band structure of the fluid-solid or void-solid PC, the traditional plane wave expansion (PWE) method encounters the problems of bad conver- gence and fake flat bands [27, 28]. These problems can be resolved by replacing the void part with a “pseudosolid” or “low impedance material” [29, 30], which is an imagined solid material having a very low density and appropriately chosen wave speed (usually very large). When these material parameters are properly chosen, the flat band will appear only in the uninterested high frequency range, and thus we can safely obtain the desired band structure in the moderate frequency range. Although this modified PWE method can indeed avoid the flat band problem, there is no definite way of choosing the material parameters of the pseudosolid, and usually some experiences are needed. In order to reduce the uncertainty, we adopt instead the DtN method to calculate the band structure of the PC. Since this method can be applied to the void-solid case directly, the flat band problem disappears automatically. Up to now DtN method has only been used in calculating the band struc- tures or guided modes of two-dimensional photonic crystal (PhC) systems, however, there is no essential difference mathematically between the two-dimensional (2D) electromagnetic (EM) and acoustic (AC) systems if the polarizations of the waves are properly chosen. For example, the transverse-magnetic (TM) wave propagating in a 2D PhC and the pure shear wave propagating in a 2D solid PC are governed by the same kind of scalar wave equation. Thus an EM wave problem can be easily translated to an AC wave problem and a one-to- one correspondence can be established between these two systems [31]. This consideration implies that DtN method can be used in the present case of pure shear wave. A detailed description of DtN method will be given later. Since in our chosen structure the off-plane shear wave cannot penetrate into the holes, the band structure of the PC is determined only by the geometrical factors (the hole size, lattice constant, and lattice type) and the material parameters (the mass density and the Lam´ e constant for shear wave) of the host medium. In fact, if the lattice type, hole shape and the filling fraction of the hole in a unit cell are all given, the band structure of the PC becomes universal [33, 34] if the dimensionless frequency ωa/ 2 πc$_{t}$ is used as the frequency variable. Here c$_{t}$ represents the propagation speed of the shear wave in the host medium and a is the lattice constant. If we replace the original host medium by another material, 3