Angular bandgaps in sonic crystals: evanescent waves and spatial complex dispersion relation

Open Access

Abstract

Phononic crystals are artificial materials made of a periodic distribution of solid scatterers embedded into a solid host medium with different physical properties. An interesting case of phononic crystals, known as sonic crystals (SCs), appears when the solid scatterers are periodically embedded in a fluid medium. In SCs only longitudinal modes are allowed to propagate and both the theoretical and the experimental studies of the properties of the system are simplified without loss of generality. The most celebrated property of these systems is perhaps the existence of spectral band gaps. However, the periodicity of the system can also affect to the spatial dispersion, making possible the control of the diffraction inside these structures. In this work we study the main features of the spatial dispersion in SCs from a novel point of view taking into account the evanescent properties of the system, i.e., studying the complex spatial dispersion relations. The evanescent behavior of the propagation of waves in the angular band gaps are theoretically and experimentally observed in this work. Both the numerical predictions and the experimental results show the presence of angular band gaps in good agreement with the complex spatial dispersion relation. The results shown in this work are independent of the spatial scale of the structure, and in principle the fundamental role of the evanescent waves could be also expected in micro- or nanoscale phononic crystals. ; This work was supported by MCI Secretaria de Estado de Investigacion (Spanish government) and the FEDER funds, under Grant Nos. MAT2009-09438, FIS2011-29734-C02-02, and from Generalitat Valencia through Project No. GV/2011/055. V.R.G. is grateful for the support of "Programa de Contratos Post-Doctorales con Movilidad UPV (CEI-01-11)." We acknowledge the Centro de Tecnologias Fisicas: Acustica, Materiales y Astrofisica and the Sonic Crystal Technologies Research Group of the Universitat Politecnica de Valencia for the use of the anechoic chamber and the ...