Evanescent waves and deaf bands in sonic crystals

The properties of sonic crystals (SC) are theoretically investigated in this work by solving the inverse problem k(¿) using the extended plane wave expansion (EPWE). The solution of the resulting eigenvalue problem gives the complex band structure which takes into account both the propagating and the evanescent modes. In this work we show the complete mathematical formulation of the EPWE for SC and the supercell approximation for its use in both a complete SC and a SC with defects. As an example we show a novel interpretation of the deaf bands in a complete SC in good agreement with multiple scattering simulations. © 2011 Copyright 2011 Author(s).This work was supported by MCI-Secretaria de Estado de Investigacion (Spanish government) and the FEDER funds, under grant MAT2009-09438. LMGR would like to thank the UPV for the grant PAID-00-11. VRG is grateful for the support of "Programa de Contratos Post-Doctorales con Movilidad UPV (CEI-01-11)."Romero García, V.; García Raffi, LM.; Sánchez Pérez, JV. (2011). Evanescent waves and deaf bands in sonic crystals. AIP Advances. 1(4):416011-416019. https://doi.org/10.1063/1.3675801S4160114160191