Experimental Evidence of the Existence of Bound States in the Continuum and Fano Resonances in Solid-Liquid Layered Media

Abstract

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.

Friedrich-Wintgen bound states in the continuum and induced resonances in a loop laterally coupled to a waveguide

“…It is worth noting that Eqs. (10) and (11) correspond, respectively, to the eigenmodes of the loop of length d 2 + d 3 in contact with the stub of length d 4 with Dirichlet and Neumann boundary conditions at the bottom side of the loop where d 2 and d 3 are attached. After straightforward algebraic calculations, one can get four types of solutions from Eqs.…”

“…After straightforward algebraic calculations, one can get four types of solutions from Eqs. (10) and (11) where the first three solutions depend on d 4 whereas the fourth one is independent of d 4 :…”

“…The first proposal of BICs was due to Von Neumann and Wigner in 1929 for quantum systems [2]. To date, BICs represent an ubiquitous phenomenon applying to all domains of wave physics, such as acoustics [3][4][5][6][7][8][9][10], mesoscopics [11,12], photonics [13][14][15], and plasmonics [16][17][18]. There are numerous realizations of BICs in classical systems, leading to a wide variety of different applications such as lasers [19], filters [20,21], demultiplexers [22], and sensors [23,24].…”

“…In accordance with the classification presented in * Corresponding author: elboudouti@yahoo.fr review [25], BICs can be categorized into several types based on their physical origin. Among them, one can cite symmetryprotected (SP) BICs [26][27][28], Fabry-Perot (FP) BICs [29], and Friedrich-Wintgen (FW) BICs [30] which have been actively investigated recently [10,29,[31][32][33][34][35][36][37][38][39][40]. SP BICs occur when a system presents modes with symmetry incompatibility, then it is possible to find a bound state of one symmetry class which falls in the continuous spectrum of another symmetry class without any coupling between them [26][27][28].…”

“…FP BICs arise when the resonance frequencies or the spacing between two resonant structures are tuned to make the roundtrip phase shift add up to an integer multiple of 2π . This structure is equivalent to a FP cavity created between two resonant reflectors [10,29,[31][32][33][34]. FW BICs are formed when two resonances, belonging to the same cavity, fall near to each other as a function of a continuous parameter, then interference induces an avoided crossing of the resonances and at one specific set of the parameters, one resonance entirely vanishes and therefore becomes a FW BIC.…”