We investigate theoretically and numerically the possibility of existence of Fano and acoustic-induced transparency (AIT) resonances in a simple though realistic one-dimensional acoustic structure made of solid-fluid layers inserted between two fluids. These resonances are obtained by combining appropriately the zeros of transmission (antiresonance) induced by the solid layers and the local resonances induced by the solid or combined solid-fluid layers with surface free boundary conditions. In particular, we show the possibility of trapped modes, also called bound states in continuum, which have recently found a high renewal interest. These modes appear as resonances with zero width in the transmission spectra as well as in the density of states (DOS). We consider three different structures: (i) a single solid layer inserted between two fluids. This simple structure shows the possibility of existence of trapped modes, which are discrete modes of the solid layer that lie in the continuum modes of the surrounding fluids. We give explicit analytical expressions of the dispersion relation of these eigenmodes of the solid layer which are found independent of the nature of the surrounding fluids. By slightly detuning the angle of incidence from that associated to the trapped mode, we get a well-defined Fano resonance characterized by an asymmetric Fano profile in the transmission spectra. (ii) The second structure consists of a solid-fluid-solid triple layer embedded between two fluids. This structure is found more appropriate to show both Fano and acoustic-induced transparency resonances. We provide detailed analytical expressions for the transmission and reflection coefficients that enable us to deduce a closed-form expression of the dispersion relation giving the trapped modes. Two situations can be distinguished in the triple-layer system: in the case of a symmetric structure (i.e., the same solid layers) we show, by detuning the incidence angle θ, the possibility of existence of Fano resonances that can be fitted following a Fano-type expression. The variation of the Fano parameter that describes the asymmetry of such resonances as well as their width versus θ is studied in detail. In the case of an asymmetric structure (i.e., different solid layers), we show the existence of an incidence angle that enables to squeeze a resonance between two transmission zeros induced by the two solid layers. This resonance behaves like an AIT resonance, its position and width depend on the nature of the fluid and solid layers as well as on the difference between the thicknesses of the solid layers. (iii) In the case of a periodic structure (phononic crystal), we show that trapped modes and Fano resonances give rise, respectively, to dispersionless flat bands with zero group velocity and nearly flat bands with negative or positive group velocities. The analytical results presented here are obtained by means of the Green's function method which enables to deduce in closed form: dispersion curves, transmission and reflection coeffic...

Bound states in continuum (BICs) are resonances with zero width (infinite lifetime) without any leakage into the surrounding media. Their fascinating properties and potential applications have attracted a great deal of interest. In this paper, we give an analytical, numerical, and experimental demonstration of BICs in simple acoustic structures based on either a single solid layer or a triple solid-liquid-solid layer inserted between two liquids. These modes are an intrinsic property of the inserted structure (solid layer or solidliquid-solid triple layer) with free surfaces and are independent of the surrounding media. Two kinds of BICs are discussed: (i) Fabry-Perot (FP) BICs exist as the consequence of the intersection of the local resonances induced by inserted structure intersect the transmission zeros induced by the solid layers. (ii) Symmetry-protected (SP) BICs occur when appear at normal incidence due to the decoupling of the transverse modes in the solid layer from the longitudinal modes that propagate in the solid and solidliquid multilayer media. When the incidence angle departs slightly from the BIC conditions, the latter transform into Fano resonances characterized by an asymmetric line shape in the transmission spectra. In addition, we show that the transmission zeros give rise to negative delay times and therefore acoustic superluminal effect. The theoretical results are obtained by means of the Green's function method, whereas the experimental measurements are carried out in ultrasonic domain using plexiglass plates in water. These results may have important applications to realize subsonic and acoustic superluminal phenomena as well as acoustic filters and sensors.

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We propose a simple solid–liquid–solid triple layer biosensor platform based on bound states in the continuum (BICs) and Fano resonances to detect the acoustic properties of liquids and apply the method to a mixture of water and albumin with various concentrations. The solid–liquid–solid triple layer is composed of an epoxy as a solid layer and an albumin–water mixture as a liquid layer, and the entire system is immersed in water. In this work, we show that the structure exhibits a high sensitivity (S), quality factor (Q), and figure of merit (FOM) with a better detection limit (DL) in the vicinity of the BICs where the transmission spectra exhibit Fano resonances. The Fano resonances shift towards high frequencies as the concentration increases. The detection limit can reach very small values for a small albumin concentration (4.7%). In addition, for a given concentration and layer thickness of the sensing material, we show the effect of the incidence angle on the efficiency of the sensor in terms of the sensitivity and quality factor. The proposed structure can be designed from low-cost material and can be used as a sensor to detect different types of liquids and gases as well.

In this paper, we provide a theoretical and numerical study of the acoustic properties of infinite and semi-infinite superlattices made out of graphene-semiconductor bilayers. In addition to the band structure, we emphasize the existence and behavior of localized and resonant acoustic modes associated with the free surface of such structures. These modes are polarized in the sagittal plane, defined by the incident wavevector and the normal to the layers. The surface modes are obtained from the peaks of the density of states, either inside the bulk bands or inside the minigaps of the superlattice. In these structures, the two directions of vibrations (longitudinal and transverse) are coupled giving rise to two bulk bands associated with the two polarizations of the waves. The creation of the free surface of the superlattice induces true surface localized modes inside the terahertz acoustic forbidden gaps, but also pseudo-surface modes which appear as well-defined resonances inside the allowed bands of the superlattice. Despite the low thickness of the graphene layer, and though graphene is a gapless material, when it is inserted periodically in a semiconductor, it allows the opening of wide gaps for all values of the wave vector k// (parallel to the interfaces). Numerical illustrations of the band structures and surface modes are given for graphene-Si superlattices, and the surface layer can be either Si or graphene. These surface acoustic modes can be used to realize liquid or bio-sensors graphene-based phononic crystal operating in the THz frequency domain.

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