Evidences of evanescent Bloch waves in phononic crystals

Abstract

We show both experimentally and theoretically the evanescent behaviour of modes in the Band Gap (BG) of finite Phononic Crystal (PC). Based on experimental and numerical data we obtain the imaginary part of the wave vector in good agreement with the complex band structures obtained by the Extended Plane Wave Expansion (EPWE). The calculated and measured acoustic field of a localized mode out of the point defect inside the PC presents also evanescent behaviour. The correct understanding of evanescent modes is fundamental for designing narrow filters and wave guides based on Phononic Crystals with defects.

Evanescent waves and deaf bands in sonic crystals

“…This method provides a more complete picture of the physical properties of the system than the classical ω( k) procedures as well as novel interpretation of the existing phenomena. Experimental results are in very good agreement with the prediction of EPWE for the case of both complete 18 and defective 20,21 sonic crystals (SC), which are the periodic system for acoustic waves. In this work we show an example in which the complex band structure predicted by using the EPWE introduces a new interpretation of the physical properties of periodic structures due to consider both propagating and evanescent properties.…”

On the control of propagating acoustic waves in sonic crystals: analytical, numerical and optimization techniques

“…This evanescent behaviour of the modes inside the BG has also been recently measured in [Romero10a]. In Figure 2.7 we have presented novel experimental measurements of the absolute value of the pressure inside SC for propagating and evanescent modes.…”

“…Figure 2.9 shows the acoustic field inside a vacancy created in a square lattice with the same properties as the ones analysed in Figure 2. 3. The incident wave, from the left side of the structure, presents a frequency inside the BG, 1340Hz.…”

“…In these cases when periodicity is broken or when SC have finite size, evanescent modes inside the periodic system may appear. Localized modes or modes inside the BG are characterized by their evanescent behaviour [joannopoulos08,Engelen09,Romero10a,Romero10b]. Then, a more accurate analysis is needed to characterize the properties of the modes inside the periodic system.…”

“…In Equation (3.16) the coefficients S ls are known (see Equation 3.12) and they are determined by the incident wave 1 . However A jq and B ls are unknown and they are related by the boundary conditions of the problem.…”