Bloch-wave expansion technique for predicting wave reflection and transmission in two-dimensional phononic crystals

In this paper acoustic wave reflection and transmission are studied at the interface between a phononic crystal (PC) and a homogeneous medium using a Bloch wave expansion technique. A finite element analysis of the PC yields the requisite dispersion relationships and a complete set of Bloch waves, which in turn are employed to expand the transmitted pressure field. A solution for the reflected and transmitted wave fields is then obtained using continuity conditions at the half-space interface. The method introduces a group velocity criterion for Bloch wave selection, which when not enforced, is shown to yield non-physical results. Following development, the approach is applied to example PCs and results are compared to detailed numerical solutions, yielding very good agreement. The approach is also employed to uncover bands of incidence angles whereby perfect acoustic reflection from the PC occurs, even for frequencies outside of stop bands.