# Experimental Demonstration of a Multichannel Elastic Wave Filter in a Phononic Crystal Slab
## 1 Introduction  
The advent of phononic crystals (PnCs) three decades ago has changed the research paradigm of composite materials and unfolded many potential innovations in acoustic and elastic devices. Basically, PnCs consist of periodic inclusion of different materials with a strong contrast of elastic properties in two (2D) or three-dimensional (3D) arrangement embedded in a matrix background [1]. The introduction of a linear defect in perfect PnCs structures enables the manipulation of waves similarly to photonic crystals such as wave resonators [2], waveguiding phenomena [3], filters [4] and demultiplexing of acoustic/elastic waves [5; 6] targeting several applications, among them biophononic devices [7; 8; 9]. The number, position and frequency of transmitted pass band waves are tunable either by altering the waveguide aperture [3] or by using heteroradii pillars to create frequency filters [10; 11]. The wave propagation can also be directed towards predefined trajectories either via defect lines with the aim of splitting the acoustic beam [12; 13] or bending the wave in sharp corners [14; 15; 16; 17; 18]. Due to the benefits of finite thickness in confining elastic waves, slab structures have been studied extensively either by using periodic inclusions such as penetrating a hole in the slab or by mountingperiodic pillars on top of the slab [18; 19; 20; 21]. These latter are of more interest as they have demonstrated two types of band gaps namely, Bragg and hybridization-induced band gaps. The first type results from wave interferences scattered by inclusions while the second is caused by the hybridization between the discrete frequencies of elastic resonances of pillars and the propagating modes of the slab. For both types, a considerable research effort has been devoted to study the theoretical [22; 23; 24; 25], and experimental [26; 27] aspects of band gaps and waveguiding phenomena. In principe, the waveguide can be achieved through the defect paths mechanism, which can be based on either breaking the lattice periodicity by altering the material or changing the geometrical properties of the unit cell [19]. For instance, removing inclusions from perfect crystals is a practical way to break symmetry and to create a line defect inside the band gap region that guides the elastic or acoustic energy [20]. Following the afore-described approach, [PERSON] et al. [21] tuned defect distance to manipulate the number of localized modes inside the band-gap. The study has shown that the number of waveguide modes changes monotonically with the width of the defect. In a closely related study, [PERSON] et al. succeeded in creating one confined mode within the band gap by using different defect sizes [22]. Alternatively, elastic or acoustic waves can be confined through coupled-resonators inserted into a perfect crystal. In particular, the physical and geometrical parameters of a resonator are first tuned to place its discrete frequencies within the band gap range. A number of similar resonators are then placed and coupled through evanescent waves providing a strong confined waveguide. [PERSON] et al. [28] have experimentally demonstrated this approach of waveguiding based on collective resonances of a chain defect in phononic crystal slab at ultrasonic frequencies. One of the main applications of these waveguiding functions is demultiplexing, i.e., the process of separating two or more frequencies by introducing perfectly confined defect modes within the band gap. [PERSON] et al. [29] have reported some theoretical results of a tunable filtering and wave rooting, a type of demultiplexing, using 2D phononic crystals with hollow cylinders. The study was based on waveguiding at selected frequencies inside the band gap by tuning the inner radius of hollow cylinders. The same technique of inner radius tuning was applied more recently by [PERSON] et al. [30] to control whispering-gallery modes in hollow pillars placed on the top of phononic crystal plate.