Theoretical and experimental evidence of level repulsion states and evanescent modes in sonic crystal stubbed waveguides

TL;DR

This paper combines theoretical and experimental approaches to reveal evanescent modes and level repulsion in sonic crystal waveguides, challenging classical predictions and enhancing understanding for future acoustic device design.

Contribution

It demonstrates the presence of evanescent modes in sonic crystals using EPWE, providing new insights into wave behavior and transmission properties not captured by traditional methods.

Findings

Evanescent modes appear in frequency ranges with deaf bands.

Level repulsion is explained by connecting evanescent modes.

Experimental results confirm the theoretical predictions.

Abstract

The complex band structures calculated using the Extended Plane Wave Expansion (EPWE) reveal the presence of evanescent modes in periodic systems, never predicted by the classical \omega(\vec{k}) methods, providing novel interpretations of several phenomena as well as a complete picture of the system. In this work we theoretically and experimentally 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 interpretation of the transmission properties. On the other hand, the simplicity of the sonic crystals in which only the longitudinal polarization can be excited, is used 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, obtained using EPWE, explain both the attenuation produced in this range of frequencies and the transfer of symmetry from one band to the other in good agreement with both experimental results and multiple scattering predictions. Thus, the evanescent properties of the periodic system have been revealed necessary for the design of new acoustic and electromagnetic applications based on periodicity.