Explicit asymptotic modelling of transient Love waves propagated along a thin coating

The official published version can be obtained from the link below.An explicit asymptotic model for transient Love waves is derived from the exact equations of anti-plane elasticity. The perturbation procedure relies upon the slow decay of low-frequency Love waves to approximate the displacement field in the substrate by a power series in the depth coordinate. When appropriate decay conditions are imposed on the series, one obtains a model equation governing the displacement at the interface between the coating and the substrate. Unusually, the model equation contains a term with a pseudo-differential operator. This result is confirmed and interpreted by analysing the exact solution obtained by integral transforms. The performance of the derived model is illustrated by numerical examples.This work is sponsored by the grant from Higher Education of Pakistan and by the Brunel University’s “BRIEF” research award

Transverse Acoustic Waves In Finite Piezoelectric-Metal Superlattices

In this communication, we study the propagation of transverse acoustic waves in a finite superlattice (SL) constituted of alternating piezoelectric and metal layers. Our objective is to determine: i) the transmission and reflection coefficients through a finite SL, ii) the confined modes related to the finite size of the SL and iii) the possibility of existence of the acoustic Brewster angle in these systems.In this communication, we study the propagation of transverse acoustic waves in a finite superlattice (SL) constituted of alternating piezoelectric and metal layers. Our objective is to determine: i) the transmission and reflection coefficients through a finite SL, ii) the confined modes related to the finite size of the SL and iii) the possibility of existence of the acoustic Brewster angle in these systems

Two types of modes in finite size one-dimensional coaxial photonic crystals : general rules and experimental evidence

We demonstrate analytically and experimentally the existence and behavior of two types of modes in finite size one-dimensional coaxial photonic crystals made of N cells with vanishing magnetic field on both sides. We highlight the existence of N−1 confined modes in each band and one mode by gap associated to either one or the other of the two surfaces surrounding the structure. The latter modes are independent of N. These results generalize our previous findings on the existence of surface modes in two semi-infinite superlattices obtained from the cleavage of an infinite superlattice between two cells. The analytical results are obtained by means of the Green’s function method, whereas the experiments are carried out using coaxial cables in the radio-frequency regime

Sagittal acoustic waves in finite solid-fluid superlattices: band-gap structure, surface and confined modes, and omnidirectional reflection and selective transmission

Using a Green’s function method, we present a comprehensive theoretical analysis of the propagation of sagittal acoustic waves in superlattices (SLs) made of alternating elastic solid and ideal fluid layers. This structure may exhibit very narrow pass bands separated by large stop bands. In comparison with solid-solid SLs, we show that the band gaps originate both from the periodicity of the system (Bragg-type gaps) and the transmission zeros induced by the presence of the solid layers immersed in the fluid. The width of the band gaps strongly depends on the thickness and the contrast between the elastic parameters of the two constituting layers. In addition to the usual crossing of subsequent bands, solid-fluid SLs may present a closing of the bands, giving rise to large gaps separated by flat bands for which the group velocity vanishes. Also, we give an analytical expression that relates the density of states and the transmission and reflection group delay times in finite-size systems embedded between two fluids. In particular, we show that the transmission zeros may give rise to a phase drop of π in the transmission phase, and therefore, a negative delta peak in the delay time when the absorption is taken into account in the system. A rule on the confined and surface modes in a finite SL made of N cells with free surfaces is demonstrated, namely, there are always N−1 modes in the allowed bands, whereas there is one and only one mode corresponding to each band gap. Finally, we present a theoretical analysis of the occurrence of omnidirectional reflection in a layered media made of alternating solid and fluid layers. We discuss the conditions for such a structure to exhibit total reflection of acoustic incident waves in a given frequency range for all incident angles. Also, we show how this structure can be used as an acoustic filter that may transmit selectively certain frequencies within the omnidirectional gaps. In particular, we show the possibility of filtering assisted either by cavity modes (in particular sharp Fano resonances) or by interface resonances

Surface and interface acoustic waves in solid-fluid superlattices: Green's function approach

We study the propagation of acoustic waves associated with the surface of a semi-infinite superlattice (SL) consisting of alternating elastic solid and ideal fluid layers or its interface with a semi-infinite fluid. We present closed-form expressions for localized surface and interface waves depending on whether the SL is terminated with a fluid layer or a solid layer. We also calculate the corresponding Green’s function and densities of states. These general results are illustrated by a few applications to periodic Plexiglas-water and Al-water SLs. In the case of a fluid layer termination, we generalize a rule obtained previously about the existence and behavior of surface waves in the case of pure transverse or longitudinal waves in solid-solid SLs, namely (i) the creation from the infinite SL of a free surface gives rise to δ peaks of weight (−1∕4) in the density of states, at the edges of the SL bulk bands, (ii) by considering together the two complementary semi-infinite SLs obtained by the cleavage of an infinite SL along a plane lying within the fluid layer and parallel to the interfaces, one always has as many localized surface modes as minigaps, for any value of the wave vector k∥ (parallel to the interfaces). However, this rule is not fulfilled when the cleavage is carried out inside the solid layer. Indeed, in this case, the dispersion curves may present zero, one, or two modes inside each gap of the two complementary SLs depending on the position of the plane where the cleavage is produced. Finally, we investigate the localized and resonant modes associated with the presence of a fluid cap layer made of mercury, with finite or semi-infinite extent, on top of the above-mentioned SLs. Different guided modes induced by the adsorbed fluid layer are obtained and their properties are investigated

Acoustic Tamm states in slender tubes

International audienceWe present an analytical and numerical study of the possibility of existence of surface localized modes, the so-called Tamm states, in a one-dimensional (1D) comb-like phononic crystal (PnC). The structure is made out of periodic array of stubs of lengths d2grafted along a waveguide and separated from each other by a tube of length d1. We show the existence of surface modes for the semi-infinite structure. In particular, when one considers two complementary semi-infinite systems obtained by cutting the infinite one into two parts, we obtain one surface mode per gap induced by the surface of the two complementary systems. Furthermore, we demonstrate that these surface modes can be detected from the maxima and minima of the transmission spectrum, when the finite structure is grafted vertically along a homogeneous acoustic waveguide. That means that one can observe experimentally this type of modes for acoustic waves in slender tubes. These results may find many practical applications in noise control and highly sensitive PnC sensors. © 2021 Elsevier Ltd. All rights reserved

Surface modes in plasmonic stubbed structures

International audienceWe present an analytical and numerical study about the existence of surface localized modes, known as Tamm states, in a one-dimensional (1D) comb-like plasmonic band gap structure. Surface plasmon polaritons (SPPs) waveguides with coupled resonators have been widely studied in recent years, because of their potential applications in highly integrated optical circuits. The system studied here is composed of an infinite 1D waveguide, along which stubs of length d1are grafted periodically with spacing period d2. The analytical study has been performed by means of the Green's function method which allows the calculation of the dispersion relations of the bulk, surface states of the plasmonic structure and the transmission coefficient. The band structure, as well as the transmission spectrum exhibit passbands separated by stopbands. The surface modes inside the gaps of the semi-infinite structure can be introduced by a defect at its surface. The analytical results are confirmed by numerical simulation using finite element method via Comsol Multiphysics software. These structures can be used to realize highly sensitive plasmonic sensors

Electromagnetic wave propagation in quasiperiodic photonic circuits

International audienceWe study theoretically and experimentally the properties of quasiperiodicone-dimensional serial loop structures made of segments and loops arrangedaccording to a Fibonacci sequence (FS). Two systems are considered. (i) Byinserting the FS horizontally between two waveguides, we give experimentalevidence of the scaling behaviour of the amplitude and the phase of thetransmission coefficient. (ii) By grafting the FS vertically along a guide, weobtain from the maxima of the transmission coefficient the eigenmodes of thefinite structure (assuming the vanishing of the magnetic field at the boundariesof the FS). We show that these two systems (i) and (ii) exhibit the property ofself-similarity of order three at certain frequencies where the quasiperiodicityis most effective. In addition, because of the different boundary conditionsimposed on the ends of the FS, we show that horizontal and vertical structuresgive different information on the localization of the different modes inside theFS. Finally, we show that the eigenmodes of the finite FS coincide exactly withthe surface modes of two semi-infinite superlattices obtained by the cleavage ofan infinite superlattice formed by a periodic repetition of a given FS

Surface electromagnetic waves in Fibonacci superlattices: theoretical and experimental results

International audienceWe study theoretically and experimentally the existence and behavior of the localized surface modes in one-dimensional (1D) quasiperiodic photonic band gap structures. These structures are made of segments and loops arranged according to a Fibonacci sequence. The experiments are carried out by using coaxial cables in the frequency region of a few tens of MHz. We consider 1D periodic structures (superlattice) where each cell is a well-defined Fibonacci generation. In these structures, we generalize a theoretical rule on the surface modes, namely when one considers two semi-infinite superlattices obtained by the cleavage of an infinite superlattice, it exists exactly one surface mode in each gap. This mode is localized on the surface either of one or the other semi-infinite superlattice. We discuss the existence of various types of surface modes and their spatial localization. The experimental observation of these modes is carried out by measuring the transmission through a guide along which a finite superlattice (i.e., constituted of a finite number of quasiperiodic cells) is grafted vertically. The surface modes appear as maxima of the transmission spectrum. These experiments are in good agreement with the theoretical model based on the formalism of the Green function

Transmission gaps and sharp resonant states in the electronic transport through a simple mesoscopic device

A simple electronic circuit consisting of a single symmetric or asymmetric loop with dangling resonators is designed to obtain possibly large stop bands (where the propagation of electrons is forbidden). Contrary to all known systems of this kind, a spectral transmission gap of nonzero width occurs here even with a single loop. This is obtained by combining appropriately the zeros of transmission of the loop and of the dangling resonators. Sharp resonant electronic states inside the gaps can be achieved without introducing any defects in the structure. This results from an internal resonance of the structure when such a resonance is situated in the vicinity of a zero of transmission or squeezed between two zeros of transmission, the so-called Fano resonances. A general expression for the transmission coefficient is given for various systems of this kind within the framework of the interface response theory. The amplitude and the phase of the transmission are discussed as a function of the wave vector or energy and it is shown that the width of the stop bands is very sensitive to the number of grafted resonators, while the magnitude of the resonant states in the transmission coefficient is very sensitive to the lengths of the different arms constituting the loop and the dangling resonators. These structures may have potential applications in microelectronic devices