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International audience; The advances in topological condensed matter physics enable the manipulation of classic waves in different ways, such as unidirectional propagation featuring the suppression of backscattering and the robustness against impurities and disorder, making it possible to endow classical phenomena with topological properties. Fano resonance, a widely spread and basic kind of resonance, features an asymmetric line shape with an ultrahigh quality factor Q that usually requires delicate designs and precise fabrication. In this work, we achieve a robust Fano mechanical resonance with topological protection by engineering band inversion of two different vibrating symmetries of a pillared beam that gives rise to dark and bright edge modes. The Fano resonance results from the constructive and destructive interferences between topological dark and bright modes. It is further demonstrated that the Fano asymmetric shape of the transmission peak and its frequency are robust against random perturbations in the pillars’ position as long as the symmetry is conserved. If random perturbations break the symmetry and only band inversion is involved, the asymmetric line shape of the Fano resonance weakens until disappearing before the closure of the bulk band gap, since the excitation will couple all fundamental modes of the beam. The analysis of the robustness of Fano resonance originating from band inversion and symmetry protection reveals the nature of topological protection which can be applied to design topological high-Q resonance in sensing application.

We investigate self-organized synchronization in a blue-detuned optomechanical cavity that is mechanically coupled to an undriven mechanical resonator. By controlling the strength of the driving field, we engineer a mechanical gain that balances the losses of the undriven resonator. This gain-loss balance corresponds to the threshold where both coupled mechanical resonators enter simultaneously into self-sustained limit cycle oscillations regime. This leads to rich sets of collective dynamics such as in-phase and out-of-phase synchronizations, depending on the mechanical coupling rate, the frequency mismatch between the resonators, and the external driving strength through the mechanical gain and the optical spring effect. Moreover, we show that the introduction of a quadratic coupling, which results from a quadratically coupling of the optical cavity mode to the mechanical displacement, enhances the in-phase synchronization. This work shows how phonon transfer can optomechanically induce synchronization in a coupled mechanical resonator array and opens up new avenues for phonon processing and novel memories concepts., This work was supported by the European Commission FET OPEN H2020 project PHENOMEN-Grant Agreement No. 713450. P.D. acknowledges the funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754510, and the support from Severo Ochoa Program (MINECO, Grant No. SEV-2017-0706) and funding from the CERCA Programme/Generalitat de Catalunya.

The interaction of phononic cavities modes in one-dimensional nanobeam-based structures is investigated theoretically. The overlapping of two closely spaced phononic cavity modes leads to the formation of symmetric and antisymmetric modes, which can be used for the modulation of the frequency and the quality factors of the propagating cavity modes. In addition, the efficient coupling of cavity modes with the modes of a phononic waveguide connecting the two phononic cavities has been demonstrated. We show that such coupling can be used for routing, controlling, and modulating the phononic cavity modes over large distances between cavities. This demonstration paves the way to engineering complex on-chip phonon networks utilizing mechanical waves to connect quantum systems as phononic or optomechanical cavities.

International audience; We study theoretically subwavelength physical phenomena, such as resonant transmission and broadband sound shielding for Lamb waves propagating in an acoustic metamaterial made of a thin plate drilled with one or two row(s) of rectangular holes. The resonances and antiresonances of periodically arranged rectangular junctions separated by holes are investigated as a function of the geometrical parameters of the junctions. With one and two row(s) of holes, high frequency specific features in the transmission coefficient are explained in terms of a coupling of incident waves with both Fabry-Perot oscillations inside the junctions and induced surface acoustic waves between the homogeneous part of the plate and the row of holes. With two rows of holes, low frequency peaks and dips appear in the transmission spectrum. The choice of the distance between the two rows of holes allows the realization of a broadband low frequency acoustic shielding with attenuation over 99% for symmetric waves in a wide low frequency range and over 90% for antisymmetric ones. The origin of the transmission gap is discussed in terms of localized modes of the ``H'' element made by the junctions, connecting the two homogeneous parts of the plate.

Electronic level structure and density of states (DOS) of a biperiodic superlattice (SL), whose period consists in general of two arbitrary wells coupled via two different barriers (the so-called double-well basis), is investigated with emphasis placed on surface effects due to SL termination by a substrate or a cladding layer. Special attention is paid to the possibility for surface states, i.e., the states confined to the SL/substrate interface, to exist within SL minigaps. Dependence of their properties (i.e., the energy position and the degree of localization) on the choice of substrate is studied for various terminating configurations (depending on the sequence of SL layers approaching the surface) of an AlGaAs-based double-well SL. Surface-induced modifications of extended states forming SL minibands are also discussed, indicating a possibility to arrange\char22{}in a controlled manner\char22{}different local DOS (LDOS) distributions at the SL end. This might have important consequences for particular applications of biperiodic SL's.

The pseudoguided acoustic modes associated with an adlayer deposited on a substrate may become very weak resonances, difficult to detect experimentally, due to their interaction with the substrate modes. In this paper, we show that the observation of these modes can be made possible, or at least facilitated, when the substrate is a superlattice instead of being a homogeneous medium. This is essentially due to the existence of minigaps, and also of two types of polarizations for the minibands, which may prohibit the propagation of the guided modes of the adsorbed layer into the superlattice and therefore increase the degree of localization of these guided modes. These features are especially relevant at high acoustic velocities (in particular around and above the longitudinal velocity of sound in the adlayer) or in the case of a hard layer where the resonances may become very weak if the substrate is made of a homogeneous material. The purpose of this paper is to demonstrate theoretically this new phenomenon with a few illustrations. The localized and resonant modes associated with the adlayer are obtained from a calculation of the total and local density-of-states by means of a Green's function method. The existence and behavior of the guided modes are discussed as a function of the nature and thickness of the adsorbate, the nature of the layer in the superlattice that is in contact with the adlayer, and the wave vector ${k}_{\ensuremath{\parallel}}$ (parallel to the layers).

International audience

We consider the tunneling between two monomode continua through a monomode structure with the symmetry of two orthogonal mirror planes. We derive in closed form the conditions for selective transfer of a single propagating state from one continuum to the other, leaving all other neighbor states unaffected. We illustrate the results of this analysis by analytical solutions for a simple structure made out of one-dimensional photonic waveguides. These theoretical results are confirmed by experiments using coaxial cables. @S0163-1829~99!16735-3#

We investigate the existence and behavior of localized and resonant acoustic modes of sagittal polarization associated with the interface between an isotropic medium and a superlattice, consisting of alternating isotropic layers of two materials. These modes appear as well-defined peaks in the density of states. The local and total densities of states are obtained from an analytical determination of the Green function for the superlattice/substrate system. The reflection coefficients in the substrate are also derived and compared to the density of states. We show that the existence and dispersion of interface modes are dependent upon the relative parameters of the substrate and the superlattice, but also upon the nature of the film in the superlattice, which is in contact with the substrate.

The influence of buffer layers on acoustic waves of shear horizontal polarization in finite superlattices is investigated here theoretically. Using a Green's-function method, we have obtained closed-form expressions of local and total densities of states as a function of the frequency \ensuremath{\omega} and the wave vector ${\mathbf{k}}_{\ensuremath{\parallel}}$ parallel to the layers. The expressions of the phonon trapping times are also derived and compared to the density of states. Due to the substrate/buffer layer/superlattice interaction, different kinds of localized and resonant discrete modes are found and their properties are investigated. In particular, we show the possibility of finding well-defined guided modes in the buffer layer or in the superlattice depending on whether the velocity of the transverse acoustic waves in the buffer is lower or higher than those in the superlattice and the substrate, respectively. These modes appear as well-defined peaks of the density of states and trapping times. Specific applications of our analytical results are given in this paper for a GaAs (Si) buffer layer embedded between a Si (GaAs) substrate and a finite GaAs-AlAs superlattice.

International audience

We report on a combination of experiments to determine the elastic moduli of a soft poly (dimethylsiloxane) rubber that was utilized in a smart experiment on resonant phononic modes [Liu et al., Science 289, 1734 (2000)] and whose reported moduli became widely used as a model system in theoretical calculations of phononic materials. We found that the most peculiar hallmark of these values, an extremely low longitudinal sound velocity, is not supported by our experiments. Anyhow, performing theoretical band structure calculations, we can reproduce the surprising experimental findings of Liu et al. even utilizing the correct mechanical parameters. Thus, the physical conclusions derived in the theoretical works do not require the use of an extremely low longitudinal velocity, but can be reproduced assuming only a low value of the shear modulus, in agreement with our experiments.

Acoustic waves of shear horizontal polarization are studied in a finite superlattice (SL) deposited on a substrate with or without a surface cap layer, or sandwiched between two materials. Using a Green's function method, we have obtained closed-form expressions of local and total densities of states as a function of the frequency \ensuremath{\omega} and the wave vector ${\mathit{k}}_{\mathrm{\ensuremath{\parallel}}}$ parallel to the layers. Due to the substrate-SL-capping layer interaction, different kinds of localized and resonant discrete modes are found and their properties are investigated.

We study an elastic composite described by the position-dependent mass density \ensuremath{\rho}(r), the longitudinal speed of sound ${\mathit{c}}_{\mathit{l}}$(r), and the transverse speed of sound ${\mathit{c}}_{\mathit{t}}$(r). For a spatially periodic composite---a ``phononic crystal''---we derive the eigenvalue equation for the frequencies ${\mathrm{\ensuremath{\omega}}}_{\mathit{n}}$(K), where n is the serial number of the band and K is the Bloch wave vector. This is applied to the special case of a binary composite and, further, to the case of infinite cylinders that form a two-dimensional lattice. For this configuration (and no wave-vector component parallel to the cylinders) there are two independent modes of vibration. The elastic displacement u(r) is parallel to the cylinders for one of them---the transverse polarization mode. The other one is a mixed (longitudinal-transverse) polarization mode with u(r) perpendicular to the cylinders. Specifically we consider circular cylinders that form a square lattice. We compute the band structures for the transverse modes of nickel alloy cylinders in an aluminum alloy host, and vice versa. In both situations we find band gaps which extend throughout the Brillouin zone. Within these gaps the transverse vibrations, sound, and phonons are forbidden. We also investigate the dependence of the band gap on the filling fraction and on the material parameters.

International audience; In the frame of long-wavelength Heisenberg model, a simple magnonic device is designed to obtain possibly transmission stop bands (where the propagation of spin waves is forbidden). This simple device is composed of an infinite one-dimensional mono-mode waveguide (the backbone) along which N(N′) side resonators are grafted at two sites. Contrary to all known systems of this kind, a spectral transmission gap of nonzero width occurs here even with this simple structure. This is obtained by combining appropriately the zeros of transmission of the side resonators. Sharp resonant 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 placed between two zeros of transmission, the so-called Fano resonances. A general analytical expression for the transmission coefficient is given for various systems of this kind within the framework of the Green’s function method. The amplitude, the phase, and the phase time of the transmission are discussed as a function of frequency and it is shown that the width of the stop bands is very sensitive to the number of the side resonators. These results should have important consequences for designing integrated devices such as narrow-frequency optical or microwave filters and high-speed switches.

We study theoretically, by means of layer-multiple-scattering techniques, the propagation of elastic waves through finite slabs of phononic crystals consisting of metallic spheres in a polyester matrix, embedded in air. In particular, we focus on the study of modes localized on the surfaces of the structure. Their origin and behavior, as well as the physical parameters that influence and determine their appearance, are investigated in detail. Our results reveal the existence of absolute phononic frequency gaps in these finite structures, and point out the possibility, under an appropriate choice of the parameters, of tunable regions of frequency free of propagating and/or surface-localized modes. © 2008 The American Physical Society.

We investigate theoretically the band structure of a phononic crystal of finite thickness constituted of a periodical array of cylindrical dots deposited on a thin plate of a homogeneous material. We show that this structure can display a low-frequency gap, as compared to the acoustic wavelengths in the constituent materials, similarly to the case of locally resonant structures. The opening of this gap requires an appropriate choice of the geometrical parameters, and in particular the thickness of the homogeneous plate and the height of the dots. However, the gap persists for various combinations of the materials constituting the plate and the dots. Besides, the band structure can exhibit one or more higher gaps whose number increases with the height of the cylinders. We discuss the condition to realize waveguiding through a linear defect inside the phononic crystal dots. The numerical simulations are performed by using the finite difference time domain and the finite element methods.

The acoustic properties of three- and two-dimensional phononic crystals consisting of hollow spheres or cylinders are studied by means of numerical calculations by the layer-multiple-scattering and the finite-difference--time-domain methods. The frequency band structure of these crystals is analyzed in conjunction with relevant transmission spectra, and the nature and physical origin of the different modes is elucidated. The building units of these crystals exhibit localized resonance states which can lead to almost dispersionless bands within an otherwise absolute gap. A feature that makes such systems potentially useful in the way of practical applications as efficient frequency filters. The influence of different geometric and material parameters on the position of these resonances is systematically examined. Such an optimized system made of a polymer material is proposed and studied in detail.

We report on a theoretical investigation of plasmon propagation in the coaxial cylindrical geometries using Green-function (or response-function) theory in the presence of an applied axial magnetic field $(\stackrel{P\vec}{B}\ensuremath{\Vert}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{z})$. The magnetoplasmon excitations in such multiple-interface structures are characterized by the electromagnetic (EM) fields that are localized at and decay exponentially away from the interfaces. Green-function theory, when generalized to be applicable to such quasi-one-dimensional systems, enables us to derive explicit expressions for the corresponding response functions (associated with EM fields), which can in turn be used to compute numerous physical properties of the system under consideration. A rigorous analytical diagnosis of the general results in diverse situations leads us to reproduce exactly the previously well-established results on planar systems, both in the presence and absence of $\stackrel{P\vec}{B}$, obtained within the different theoretical frameworks. As an application, we present several illustrative examples on the dispersion characteristics of the confined and extended magnetoplasmons in the single- and double-interface structures. These dispersive modes are also substantiated through the computation of local as well as total density of states. It is found that, unlike as in the zero-field case, the magnetoplasma propagation is nonreciprocal with respect to the sign of the index $m$ of the Bessel functions involved. The effects of an applied magnetic field and the aspect ratio on the dispersion of the confined magnetoplasmons are discussed. We also briefly clarify some delusive traces of the edge magnetoplasmons for a plasma shell embedded between two identical or unidentical dielectrics. The elegance of theory lies in the fact that it does not require matching of the messsy boundary conditions and it also lies in its simplicity and the compact form of the desired results. Our theoretical framework can also serve as a powerful technique for studying the intrasubband plasmons and magnetoplasmons in the emerging mutiple-walled carbon nanotubes.

We consider the effect of surface polaritons on the shift of a beam of light of finite cross section on reflection from a two-layered semi-infinite medium. The beam is incident upon the first layer at an angle greater than the critical angle; the evanescent wave (in the first layer) interacts with the surface polariton at the interface between the first layer and the second layer. The plane-wave components of the incident "finite-cross-section" beam are absorbed and phase shifted by various amounts. The resultant emerging (reflected) beam, therefore, undergoes a shift. It is found that the calculated shift can assume very large values.

International audience; We present a theoretical study of the bulk and surface magnons of a semi-infinite stack of two different ferromagnetic films. Each film is modeled by a simple-cubic lattice of spins coupled via nearest-neighbor exchange (Heisenberg ferromagnet). The superlattice has a larger periodicity in the direction perpendicular to the slabs and therefore many magnon branches in the folded Brillouin zone. In the gaps exisiting between these magnon branches appear the surface-localized magnons. The simplicity of our model allows one to obtain in closed form the bulk and (001) surface Green's functions for this magnetic superlattice. The analytic knowledge of these functions enables us to study easily all the bulk and and surface magnetic properties of a ferromagnetic superlattice. We give here the analytic expression we obtained for the folded bulk magnons and also the expression that gives the surface-localized modes, which may appear within the extra gaps which exist between the folded bulk bands. One figure for a specific case illustrates these results.

The vibrational properties of a coherent interface between two different crystals are studied in this paper on an atomic model. In the long-wavelength approximation, we recover the well-known Stoneley waves of elasticity theory and their existence conditions. We establish also that when these localized Stoneley waves do not exist, one has nevertheless at least one semilocalized acoustic mode (localized in one of the crystals and resonant in the other one). We also report for the first time on a few other interface modes: localized in interface gaps appearing for some values of the propagation vector ${k}_{\ensuremath{\parallel}}$ parallel to the interface; localized, semilocalized, and resonant modes, some of them being in the optically active region. The relations between these different interface modes are discussed. We also derive in this paper for the first time an atomic model's variation in the low-temperature specific heat due to a bicrystal interface and to a planar bulk defect.

International audience

We present a theory of Rayleigh waves on a superlattice when the surface is perpendicular to the alternating layers. The method consists of first Fourier analyzing the equations of motion in the direction perpendicular to the layers so as to include automatically the boundary conditions at the different interfaces. For each value of the wave vector $k$ perpendicular to the layers, this gives a set of wave vectors parallel to the layers, i.e., perpendicular to the surface. Then a surface wave is constructed from a superposition of these solutions. The frequencies of the surface Rayleigh waves are obtained by using the Fourier-analyzed conditions of vanishing stresses at the free surface. Numerical calculations are performed by limiting the number of Fourier components taken into account. For two relatively similar layers in the superlattice there are two different Rayleigh branches near the Brillouin-zone boundary which result from the folding of the dispersion curve for a Rayleigh wave on a homogeneous medium. The higher branch can disappear when the two layers differ significantly in their elastic properties. We present a few examples of the dispersion curves and of the associated displacement fields. We also present examples showing the variation of the gap between the two Rayleigh branches versus the parameters of the layers and their thicknesses.