Level repulsion states and cavity modes excited by evanescent waves in sonic crystals waveguides

Abstract

The relevance of the evanescent modes in sonic crystals is theoretically and experimentally reported in this work. The complex bands structure, kω, calculated using the extended plane wave expansion reveals the presence of evanescent modes in these systems, never predicted by the traditional usual numerical ω(k⃗) methods. The interpretation of the evanescent modes introduces novel explanations of the deaf bands as well as of the level repulsion states in antisymmetric periodic systems. In this work we observe that in the ranges of frequencies, where a deaf band is traditionally predicted, an evanescent mode with the excitable symmetry appears changing drastically the transmission properties. On the other hand, the simplicity of the sonic crystals in which only the longitudinal polarization can be excited is used here to interpret, without loss of generality, the level repulsion between symmetric and antisymmetric bands in sonic crystals as the presence of an evanescent mode connecting both repelled bands. These evanescent modes explain both the attenuation produced in this range of frequencies and the transfer of symmetry from one band to the other. The experimental evidence of the level repulsion and the evanescent coupling are in very good agreement with the theoretical predictions.