# Experimental Demonstration of a Multichannel Elastic Wave Filter in a Phononic Crystal Slab
## 2 Theory and Experimental Methods  
The proposed structure is schematically presented in Figure 1a where a 2D square unit cell is zoomed. The geometrical parameters of the unit cell are as follows: Slab thickness \(h=1\,\mathrm{mm}\), Square lattice parameter \(a=4\,\mathrm{mm}\), height of the pillars \(h_{p}=4.4\,\mathrm{mm}\), radius of the pillars \(r_{p}=1.6\,\mathrm{mm}\). The manufactured device is fabricated on the same planar structure using 3D-Printer _ProX_300 via Direct Metal Laser Sintering (DMLS) technology with a resolution of \(0.02\,\mathrm{mm}\), as depicted in Figure 1b. The printed metal is an aluminium alloy _AlSi7 Mg_06 having Poisson ratio \(\
u=0.33\), Young modulus \(E=76.12\,\mathrm{GPa}\) and mass density \(\rho=2670\,\mathrm{kg}\,\mathrm{m}^{-3}\). To demonstrate the demultiplexing application, a compact three linear waveguides channels: \(W_{1}=1.52\,\mathrm{mm}\), \(W_{2}=1.2\,\mathrm{mm}\) and \(W_{3}=0.88\,\mathrm{mm}\) were made inside the pillar based phononic crystal, as shown in Figure 1b. Each of these linear waveguides are distanced from one another by 8 rows of pillars inclusion to avoid any cross-talk between the waveguide lines inside the frequency range of the band gap. The total dimension of the structure is 100 \(\times\) 172 \(\times\) 1 mm\({}^{3}\). The elastic excitation is generated by a piezoelectric ceramic transducer patch made of lead zirconate titanate (Ferroperm PZ27 num. 27303). This PZT patch has a dimension of 15 \(\times\) 8 \(\times\) 1 mm\({}^{3}\) and acts as a vibration source providing an out-of-plane displacement with a frequency up to 2 MHz. In the frequency range of our interest, the electromechanical coupling factor for thickness mode is equal to 0.47. The patch is bonded on the surface of the device under test by using silver glue, granting a good contact with the plate. Figure 1c illustrates the experimental equipment including a Micro System Analyzer (MSA-500 by _Polytec_) supplied by analog displacement vibration decoder model DD-300 with sensitivity of 50 nm V\({}^{-1}\). The latter allows both out and in plane displacement measurements as well as the waveform mapping up to a maximum frequency of 1.5 MHz. The transmission coefficient spectra is estimated by measuring the displacement along both sides of the pillar array. A chirped signal of maximum voltage amplitude of 7 V is supplied between the electrodes of PZT producing mechanical vibration with broadband frequency range extending from 250 kHz to 400 kHz. In order to avoid any surface interaction between the tested device and the \(MSA\) table, an underneath support that consists of foam prism is used as it is shown in Figure 1d. In order to analyze the band diagram and transmission spectrum, we applied Finite Element Method (FEM) to study the band gap effect of equidistant pillar structures in a perfect phononic region. The classical approach based on Bloch-Floquet theorem to represent the boundary conditions of infinite periodicity in \(x\) and \(y\)-directions are applied to the unitary cell as shown in Figure 1a. Particularly, the periodicity has been applied between the two orthogonal faces in \(x\)-direction and also  
Figure 1: (**a**) unit cell configuration with height of pillar, \(h_{p}=4.4\) mm, slab thickness, \(h=1\) mm, radius, \(r_{p}=1.6\) mm, and crystal Lattice, \(a_{x}=a_{y}=4\) mm (**b**) demultiplexer device consists of 3 waveguides channels \(W_{1}=1.52\) mm, \(W_{2}=1.22\) mm and \(W_{3}=0.88\) mm. Soft piezo ceramic (PZ27 by Ferroperm) is glued as source of excitation (**c**) MSA–500 setup to measure transmission spectrum (**d**) foam prism to avoid the device from surface contact with MSA-500 table. the two orthogonal faces in \(y\)-direction. Whereas, the top and bottom surface in the \(z\)-direction have free boundary conditions.