Defect state of the locally resonant phononic crystal

By taking a two-dimensional solid local resonant phononic crystal as an example, we investigated the mechanism of the defect state on a subwavelength scale. It is well known that, when the working wavelength is much greater than the distance between resonators, the dispersion of the phononic crystal is insensitive to the lattice structure, and the whole structure can be described in terms of the effective medium theory. As a result, it is hard to introduce a defect state in the system by a local real-space disorder. It is shown in this paper that the dispersion of the local resonant phononic crystal can be understood from the long- range feature of the interaction between resonators, so the creation of a defect state in the system is in fact to break such a long- range interaction. Based on this understanding, the mechanisms of the recently reported methods, that are used to create defect states, are discussed. In addition, a waveguide structure that can guide the longitude or transverse waves separately is realized by introducing an anisotropic defect resonator.