FANO resonances in solid-fluid one and two dimensional systems

The gaol of this paper is to demonstrate that the propagation of acoustic waves in a single slab made of a homogeneous one dimensional (1D) solid embedded in a fluid at oblique incidence on a slab made of two dimensional (2D) rectangular rods immersed in a fluid, can exhibit transmission zeros near resonances the so-called Fano resonances

Multifractal analysis of the electronic states in the Fibonacci superlattice under weak electric fields

Influence of the weak electric field on the electronic structure of the Fibonacci superlattice is considered. The electric field produces a nonlinear dynamics of the energy spectrum of the aperiodic superlattice. Mechanism of the nonlinearity is explained in terms of energy levels anticrossings. The multifractal formalism is applied to investigate the effect of weak electric field on the statistical properties of electronic eigenfunctions. It is shown that the applied electric field does not remove the multifractal character of the electronic eigenfunctions, and that the singularity spectrum remains non-parabolic, however with a modified shape. Changes of the distances between energy levels of neighbouring eigenstates lead to the changes of the inverse participation ratio of the corresponding eigenfunctions in the weak electric field. It is demonstrated, that the local minima of the inverse participation ratio in the vicinity of the anticrossings correspond to discontinuity of the first derivative of the difference between marginal values of the singularity strength. Analysis of the generalized dimension as a function of the electric field shows that the electric field correlates spatial fluctuations of the neighbouring electronic eigenfunction amplitudes in the vicinity of anticrossings, and the nonlinear character of the scaling exponent confirms multifractality of the corresponding electronic eigenfunctions.Comment: 10 pages, 9 figure

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

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

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

Bulk and surface acoustic waves in solid–fluid Fibonacci layered materials

We study theoretically the propagation and localization of acoustic waves in quasi-periodic structures made of solid and fluid layers arranged according to a Fibonacci sequence. We consider two types of structures: either a given Fibonacci sequence or a periodic repetition of a given sequence called Fibonacci superlattice. Various properties of these systems such as: the scaling law and the self-similarity of the transmission spectra or the power law behavior of the measure of the energy spectrum have been highlighted for waves of sagittal polarization in normal and oblique incidence. In addition to the allowed modes which propagate along the system, we study surface modes induced by the surface of the Fibonacci superlattice. In comparison with solid–solid layered structures, the solid–fluid systems exhibit transmission zeros which can break the self-similarity behavior in the transmission spectra for a given sequence or induce additional gaps other than Bragg gaps in a periodic structure

Band gaps in phoXonic silicon crystal slab

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