Reflection properties and effective parameters of two-dimensional phononic crystals

Using the eigenmode match theory (EMMT) method, we calculate the reflection coefficient of two-dimensional phononic crystal slabs, which are made up of lead rods in epoxy matrix and mercury rods in water matrix, respectively. In the long wavelength limit, the effective parameters of the phononic crystal slabs have been well calculated. The obtained effective velocities agree well with the results calculated directly from the slope of the corresponding bands near the Γ point of the first Brillouin zone. The numerical results show that the scheme presented in this Letter is an efficient way to determine the effective elastic parameters of 2D periodic structures.