In this work we apply the finite element method to analyze the wave transmission property of solid/fluid composite medium, phononic crystal. The sound attenuation spectrum is obtained to show the forbidden bands of the band gap. First, we construct the finite element model for a two-dimensional phononic crystal, studied by Sánchez-Pérez etc. with PWE and experimentally, constituted of a rectangular array of parallel circular stainless steel cylinders in air. It has demonstrated that our simulation work was feasible; then, we performed the experimental measurements and simulations by using the narrow and wide frequencies. The results show agreement between the experiments and the simulations. We also simulated the crystal samples of filling fraction 5 % and 10 % for square and hexagon lattice, respectively, in both the [100] and [110] direction. The full band gaps are determined from the combination of the results. We have investigated the finite element simulation for the solid/fluid phononic crystal successfully. Both work the results of experiment in the reference and in this work are compared with the FEM simulation. It demonstrates that the finite element method is a good tool for the design of phononic crystal in application to new type sound absorption (isolation) material.

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This thesis presents the synthesis methods and the characterizations of magnetic Fe3O4 nanoparticles, silica spheres with Fe3O4 nanoparticles embedded, and three dimensional magnetic photonic crystals (MPCs) prepared from the spheres. The structure, material composition, magnetic and optical properties, photonic band gaps (PBGs), as well as how these properties depend on the concentration of the magnetic nanoparticles, are investigated by X-ray diffraction (XRD), scanning electron microscopy (SEM), vibrating sample magnetometer (VSM), superconducting quantum interference device (SQUID), Faraday rotation (FR) and optical spectrophotometers. Well-organized, face center cubic (fcc)-structured, super-paramagnetic 3D MPCs have been obtained and their PBGs are investigated through optical spectra. Fe3O4 nanoparticles are synthesized by standard co-precipitation method and a rapid mixing co-precipitation method with particle size varied from 6.6 nm to 15.0 nm at different synthesis temperature (0°C ~ 100°C). The obtained Fe3O4 nanoparticles, which show crystalline structure with superparamagnetic property, are embedded into silica spheres prepared at room temperature through a sol-gel method using the hydrolysis of tetraethyl orthosilicate (TEOS) in a base solution with different concentrations. By controlling the synthesis conditions (e.g., chemicals, the ratio of chemicals and stirring time), different size of MPC spheres in range of 75 nm to 680 nm has been obtained in a narrow distribution. The sphere suspensions in ethanol are dropped on glass substrate in the permanent magnetic field to achieve well organized 3D MPCs with (111) triangular close packed crystal plane of fcc structure parallel to the surface of substrate. From the transmission & forward scattering spectra (TF), five PBGs have been distinguished for these MPCs and they are defined as 1st, 2nd, 3rd, 4th and 5th PBGs according to the order of peaks that appear in mathematic fitting analysis. The positions (peak wavelengths) of PBGs show sphere size dependence: with the increase of the sphere size, they increase linearly. Comparing with pure SiO2 PCs at certain sphere size, the positions of PBGs for MPCs containing moderate Fe3O4 conc. (4.3 wt. %) are at longer wavelengths. On increasing the Fe3O4 conc., however, the PBGs shift back to shorter wavelength. The PBGs shift to longer or shorter wavelength is due to the combined effect of refractive index n increasing, as well as the increase of refractive index difference Δn, which are caused by the embedded Fe3O4 nanoparticles. The transmission spectra (T) with varied incidence angle of p- and s- polarized light are studied, obtaining angular dependent and polarization sensitive PBGs. It is found that with the increase of the incidence angle, the 1st PBGs shift to shorter wavelength while the 3rd ones shift to longer wavelength. High Fe3O4 conc. MPCs (6.4 wt. %) show enhancement of this angular dependence. It is also found that the PBGs show dependence on the polarize direction of incident light. Normally, at a certain incidence angle the PBGs sift more for p- polarized incident light than for s-polarized light with respect to normal incidence. This polarized dependence can also be enhanced for high Fe3O4 conc. MPCs. With a high concentration of Fe3O4 nanoparticles, the polarization sensitivity of p- and s- increased. These PBG properties indicate applications of 3D MPCs as functional optical materials, coatings, wavelength and polarization fibers for fiber optical communications devices and dielectric sensors of magnetic field, etc.. / QC 20110224

Semilocal density functionals up to the generalized gradient approximation (GGA) level cannot accurately describe band gaps of bulk solids. Meta-GGA density functionals with a dependence on the kinetic energy density ingredient (τ) can potentially give wider band gaps compared with GGAs. The recently developed TASK meta-GGA functional yields excellent band gaps of bulk solids. The accuracy of the TASK functional for band gaps of bulk solids cannot be straightforwardly transferred to low-dimensional materials due to reduced screening in low-dimensional materials. We have developed mTASK from TASK by changing (a) the tight upper-bound for one or two-electron systems (h0X) from 1.174 to 1.29 and (b) the limit of the interpolation function fX(α → ∞) of the TASK functional that interpolates the exchange enhancement factor FX(s,α) from α = 0 to 1, so that mTASK has the screening appropriate for low-dimensional materials. These two conditions guarantee the increased nonlocality within the generalized Kohn-Sham scheme in the mTASK functional and yield a better description of band gaps of low-dimensional materials. We computed the band gaps of bulk solids from mTASK having a wide range of gaps such as Ge, CdO, ZnS, MgO, NiF, Ar. The improvement in the band gaps from mTASK is more consistent than TASK for the large-gaps crystals. We have studied the band structures in two forms of transition metal dichalcogenide (TMD) monolayers, i.e., monolayer hexagonal (1H) and monolayer trigonal (1T) and their nanoribbons. The mTASK functional systematically improves the band gaps and is in close agreement with the experiments or the hybrid level HSE06 density functional for 2D single-layer and nanoribbon systems. In the second part of this assessment, we explore the large tunability of band gaps and optical absorption of phosphorene nanoribbons under mechanical bending from first-principles. Bending can induce an unoccupied edge state in armchair phosphorene nanoribbons. The electronic and optical properties of nanoribbons drastically change because of this edge state. GW-Bethe–Salpeter equation calculations for armchair phosphorene nanoribbons at different bending curvatures show that the absorption peaks generally shift toward the high energy direction with increasing curvature. Our study suggests that bright excitons can also be formed from the transition from the valence bands to the edge state when the edge state completely separates out from the continuum conduction bands. We systematically study the role of the edge state to form bound excitons at large curvatures. Our analysis suggests that the optical absorption peaks of zigzag phosphorene nanoribbons shift toward the low-energy region, and the height of the absorption peaks increases while increasingthe bending curvature. In the third part of this assessment, we extend our study of phosphorene nanoribbons to MoS2 nanoribbons under bending from GW and Bethe-Salpeter equation approaches. We find three critical bending curvatures for armchair MoS2 nanoribbons, and the edge and non-edge band gaps show a non-monotonic trend with bending. The edge band gap shows an oscillating feature with ribbon width n, with a period of ∆n=3. The binding energy and the lowest exciton energy decrease with the curvature. The large tunability of optical properties of bent MoS2 nanoribbon is applicable in tunable optoelectronic nanodevices. / Physics

The vibration of and wave propagation in periodic cellular structures are analyzed. Cellular structures exhibit a number of desirable multifunctional properties, which make them attractive in a variety of engineering applications. These include ultra-light structures, thermal and acoustic insulators, and impact amelioration systems, among others. Cellular structures with deterministic architecture can be considered as example of periodic structures. Periodic structures feature unique wave propagation characteristics, whereby elastic waves propagate only in specific frequency bands, known as "pass band", while they are attenuated in all other frequency bands, known as "stop bands". Such dynamic properties are here exploited to provide cellular structures with the capability of behaving as directional, pass-band mechanical filters, thus complementing their well documented multifunctional characteristics. This work presents a methodology for the analysis of the dynamic behavior of periodic cellular structures, which allows the evaluation of location and spectral width of propagation and attenuation regions. The filtering characteristics are tested and demonstrated for structures of various geometry and topology, including cylindrical grid-like structures, Kagom and eacute; and tetrhedral truss core lattices. Experimental investigations is done on a 2-D lattice manufactured out of aluminum. The complete wave field of the specimen at various frequencies is measured using a Scanning Laser Doppler Vibrometer (SLDV). Experimental results show good agreement with the methodology and computational tools developed in this work. The results demonstrate how wave propagation characteristics are defined by cell geometry and configuration. Numerical and experimental results show the potential of periodic cellular structures as mechanical filters and/or isolators of vibrations.

Because of their outstanding characteristics, micro/nano-mechanical (MM) structures have found a plethora of applications in wireless communications and sensing. Many of these MM structures utilize mechanical vibrations (or phonons) at megahertz or gigahertz frequencies for their operation. On the other hand, the periodic atomic structure of crystals is the fundamental phenomenon behind the new era of electronics technology. Such atomic arrangements lead to a periodic electric potential that modifies the propagation of electrons in the crystals. In some crystals, e.g. silicon (Si), this modification leads to an electronic band gap (EBG), which is a range of energies electrons can not propagate with. Discovering EBGs has made a revolution in the electronics and through that, other fields of technology and the society. Inspired by these trends of science and technology, I have designed and developed integrated MM periodic structures that support large phononic band gaps (PnBGs), which are ranges of frequencies that phonons (and elastic waves) are not allowed to propagate. Although PnBGs may be found in natural crystals due to their periodic atomic structures, such PnBGs occur at extra high frequencies (i.e., terahertz range) and cannot be easily engineered with the current state of technology. Contrarily, the structures I have developed in this research are made on planar substrates using lithography and plasma etching, and can be deliberately engineered for the required applications. Although the results and concepts developed in this research can be applied to other substrates, I have chosen silicon (Si) as the substrate of choice for implementing the PnBG structure due to its unique properties. I have also designed and implemented the fundamental building blocks of MM systems (e.g., resonators and waveguides) based on the developed PnBG structures and have shown that low loss and efficient MM devices can be made using the PnBG structures. As an example of the possible applications of these PnBG structures, I have shown that an important source of loss, the support loss, can be suppressed in MM resonators using PnBG structures. I have also made improvements in the characteristics of the developed MM PnBG resonators by developing and employing PnBG waveguides. I have further shown theoretically, that photonic band gaps (PtBGs) can also be simultaneously obtained in the developed PnBGs structures. This can lead to improved photon-phonon interactions due to the effective confinement of optical and mechanical vibrations in such structures. For the design, fabrication, and characterization of the structures, I have developed and utilized complex and efficient simulation tools, including a finite difference time domain (FDTD), a plane wave expansion (PWE), and a finite elements (FE) tool, each of which I have developed either completely from scratch, or by modification of an existing tool to suit my applications. I have also developed and used advanced micro-fabrication recipes, and characterization methods for realizing and characterizing these PnBG structures and devices. It is agued that by using the same ideas these structures can be fabricated at nanometer scales to operate at ultra high frequency ranges. I believe my contributions has opened a broad venue for new MM structures based on PnBG structures with superior characteristics compared to the conventional devices.

Ce travail de thèse porte sur l’étude de la propagation d’ondes de volume et d’ondes de surface dans des cristauxphononiques granulaires en régime linéaire. Différents aspects sont développés dans ce manuscrit. L’effet de la prise encompte des degrés de liberté en rotation des particules sur la structure de bande de différents cristaux phononiquesgranulaires est étudié. En effet, l’introduction de ces degrés de liberté additionnels rend possible l’existence de modes derotation qui interagissent fortement avec les modes transverses. Ce travail s’intéresse aussi à l’existence d’ondeslocalisées et d’ondes de surface dans des cristaux phononiques granulaires et en particulier à la comparaison des théoriesdéveloppées avec les prédictions de la théorie de Cosserat. Dans un premier temps, l’étude d’une chaîne phononique granulaire monoatomique est présentée. En considérant lachaîne semi-infinie avec une condition aux limites appliquée à son extrémité, le modèle analytique démontre l’existence demodes localisés, chaque mode étant composé de deux modes évanescents. Ensuite, une description théorique des modes se propageant dans un cristal phononique granulaire en deux dimensions est présentée. Les particules possèdent trois degrés de liberté, deux en translation et un en rotation. L’analyse des interactions entre ondes de translation et ondes de rotation permet de mettre en évidence une grande richesse de structure de bandes ainsi que des phénomènes particuliers (bandes interdites complètes, cône de Dirac, modes non-monotones, phénomène de double réfraction). Dans un dernier temps, une analyse de l’existence d’ondes de Rayleigh et de cisaillement horizontal dans un cristal phononique granulaire en trois dimensions est effectuée. Les limites de la théorie de Cosserat dans la description d’ondes acoustiques de surface dans les milieux micro- et nano-inhomogènes sont établies. / This work is devoted to the analysis of propagating and surface acoustic waves in granular phononic crystals in thelinear regime. First, the propagation and localization of transversal-rotational waves in a two-dimensional granularchain of equal masses are analyzed. By considering the semi-infinite chain with a boundary condition applied at itsbeginning, the analytical study demonstrates the existence of localized modes, each mode composed of two evanescentmodes. Secondly, the phononic properties of a two-dimensional discrete phononic crystal, made of circular cross-section, infinitely long contacting elastic cylinders arranged on a simple cubic lattice, are described analytically. The theoretical analysis provides a clear physical explanation for the existence of a zero-group velocity point of the lowest-energy acoustic mode in particular directions of the phononic crystal and demonstrates the birefraction phenomenon. Finally, the existence of surfaces elastic waves at mechanically free surface of granular phononic crystals is presented. Depending on the degrees of freedom of the particles, different types of surface waves exist in the structure. First, Rayleigh type surface waves aredemonstrated in a granular phononic crystal with particles possessing two translational and one rotational degrees offreedom; and secondly, shear-horizontal surface waves are studied in a granular phononic crystal with particlespossessing two rotational and one translational degrees of freedom. A comparison with surface waves predicted by theCosserat theories is made in order to establish the limitations of the Cosserat theories.

Ce travail porte sur l’étude de matériaux micro/nano structurés permettant l’ingénierie des structures de bande dans le domaine des ondes élastiques. Nous nous sommes intéressés en particulier à l’intégration de ces matériaux dans les dispositifs électro-acoustiques et l’étude de l’interaction avec les ondes acoustiques de surface.La démarche consiste à mener des simulations par la méthode des éléments finis, pour calculer les structures de bande et les spectres de transmission. Nous avons étudié l’effet des paramètres géométriques et élastiques des micro-plots sur les branches acoustiques représentant les modes de surface. Nous avons ensuite discuté l’effet de la symétrie de l’arrangement sur la polarisation des modes de surface. Nous avons également étudié l’effet de la symétrie sur la sensibilité des modes de surface à une variation de température.Sur le plan expérimental, Nous avons élaboré des transducteurs inter-digités sur un substrat piézoélectrique de LiNbO3. Nous avons intégré divers cristaux phononiques composés de micro-plots de Ni, obtenues par électrodéposition. Les spectres de transmission ont été mesurés à l’aide d’un analyseur de réseau et comparés aux résultats theoriques.En dehors des cristaux phononiques basés sur des plots du nickel, d’autres structures ont également été présentées dans ce travail, incluant des matériaux bidimensionnels à base de nanoparticules magnétiques auto-assemblées et des nanofils du nickel électrodéposés à travers des membranes nano-poreuses d’alumine. / This work concerns the study of micro/nano structured materials for the engineering of band structures in the field of elastic waves. We were interested in particular to the integration of these materials in electro-acoustic devices and the study of the interaction with the surface acoustic waves.The approach is to carry out the simulation using the finite element method to calculate the band structures and the transmission spectra. We studied the effect of geometrical and elastic parameters of micro-pillars on acoustic branches representing surface modes. Then we discussed the effect of the symmetry of the arrangement on the polarization of the surface modes. We also investigated the effect of the symmetry on the sensitivity of surface modes with the variation of temperature.Experimentally, we have developed interdigital transducers on a piezoelectric substrate of LiNbO3. We have fabricated various phononic crystals composed of nickel micro-pillars, obtained by electrodeposition. The transmission spectra were measured by a network analyzer and compared with the theoretical results.Besides the phononic crystals based on nickel pillars, some other periodic micro/nano structures were also involved in this work, such as two dimensional materials based on self-assembled magnetic nanoparticles and nickel nanowires electroplated through nano-porous alumina membranes.

Le "Trou Noir Acoustique" (TNA) constitue un moyen passif de réduction des vibrations des structures sans pour autant augmenter leur masse. Il s’agit d’un amincissement local de la structure, revêtu d’un matériau viscoélastique. L’effet TNA résulte alors de l’augmentation locale de l’amplitude vibratoire,qui sollicite fortement le revêtement, donnant lieu à un amortissement important. Une analyse détaillée des mécanismes de dissipation du TNA est réalisée :la diffusion des ondes de flexion par un TNA est étudiée lorsque ce dernier est inséré dans une plaque infinie. On montre que le revêtement induit un amortissement local important, permettant d’augmenter significativement l’amortissement global. Le TNA étant surtout efficace en hautes fréquences (HF),il est périodisé sur une plaque pour tirer parti des bandes interdites en basses fréquences (BF). Deux réseaux (carré et triangulaire) sont étudiés numériquement par la méthode PWE et expérimentalement par mesure de mobilités vibratoires. Les résultats montrent que la plaque est à la fois amortie en BH par effet de réseau et en HF par l’effet TNA. / The "Acoustic Black Hole" (ABH) is a passive device of reducing vibrations of structures without increasing their mass. It consists in a local thinning of the structure, coated with a thin layer of viscoelastic material. The ABH effect results from the local increase in vibratory magnitude, which strongly solicits the coating, giving rise to local significant damping. A detailed analysis of the mechanisms of dissipation of the ABH is carried out : the scattering of bending waves by an ABH is studied when the latter is inserted in an infinite thin plate. It is shown that the coating induces a significant local damping, allowing to significantly increase the global damping. The ABH is especially effective at high frequencies(HF), it is periodized on a plate to take advantage of the band gaps effect at low frequencies (LF). Two lattices (square and triangular) are studied numerically by the PWE method and experimentally by measuring vibratory mobilities. The results show that the plate is damped at the same time in LF by the lattice effect and in HF by the ABH effect.