The primary objective of this thesis was to gain a deeper understanding of acoustic wave propagation in phononic crystals, particularly those that include materials whose properties can be varied periodically in time. This research was accomplished in three ways. First, a 2D phononic crystal was designed, created, and characterized. Its properties closely matched those determined through simulation. The crystal demonstrated band gaps, dispersion, and negative refraction. It served as a means of elucidating the practicalities of phononic crystal design and construction and as a physical verification of their more interesting properties. Next, the transmission matrix method for analyzing 1D phononic crystals was extended to include the effects of time-varying material parameters. The method was then used to provide a closed-form solution for the case of periodically time-varying material parameters. Some intriguing results from the use of the extended method include dramatically altered transmission properties and parametric amplification. New insights can be gained from the governing equations and have helped to identify the conditions that lead to parametric amplification in these structures. Finally, 2D multiple scattering theory was modified to analyze scatterers with time-varying material parameters. It is shown to be highly compatible with existing multiple scattering theories. It allows the total scattered field from a 2D time-varying phononic crystal to be determined. It was shown that time-varying material parameters significantly affect the phononic crystal transmission spectrum, and this was used to switch an incident monochromatic wave. Parametric amplification can occur under certain circumstances, and this effect was investigated using the closed-form solutions provided by the new 1D method. The complexity of the extended methods grows logarithmically as opposed linearly with existing methods, resulting in superior computational complexity for large numbers of scatterers. Also, since both extended methods provide analytic solutions, they may give further insights into the factors that govern the behaviour of time-varying phononic crystals. These extended methods may now be used to design an active phononic crystal that could demonstrate new or enhanced properties.

Poursuivant l'essor des méta-matériaux micro-ondes et photoniques, les cristaux phononiques, organisations périodiques de matériaux acoustiquement différents présentant notamment des bandes d'arrêt, c'est-à-dire de plages de fréquences pour lesquelles aucun mode ne se propage dans la structure, laissent entrevoir des applications acoustiques hors de portée des technologies existantes. Dans cette thèse, nous visons des réalisations aux fréquences RF afin de viser des applications complémentaires des résonateurs ou des filtres acoustiques largement employés dans le domaine des transmissions sans fil. Nous avons tout d'abord développé un procédé de fabrication simple permettant de réaliser des cristaux phononiques à deux dimensions à l'échelle micrométrique sur membrane piézoélectrique, afin de rendre ces systèmes compatibles avec les composants à ondes de Lamb développés au CEA-LETI pour des applications de filtrage de canal dans des architectures de transmission sans fil faible consommation. Ce procédé a été utilisé pour réaliser des cristaux phononiques, ainsi que des résonateurs à ondes de Lamb, ou à ondes de volume et des structures plus complexes comme par exemple des filtres passe-bande. Une étude paramétrique des composants à ondes de Lamb nous a permis d'affiner notre maîtrise de ces dispositifs, ce qui nous a été utile pour la mise au point des lignes à retard permettant de caractériser les propriétés de transmission acoustique des cristaux phononiques. Du point de vue théorique, un modèle de simulation par éléments finis a été mis en place, dans un premier temps pour dimensionner les structures réalisées et prendre en compte les modifications apportées par la réalisation technologique. Nous avons ensuite réalisé des cristaux phononiques que nous avons caractérisés électriquement et optiquement, en collaboration avec l'Institut FEMTO-ST. Les mesures confirment la présence de bandes d'arrêt, aux fréquences attendues, mais d'une largeur a priori bien supérieure à celle prévue par la simulation. Une étude détaillée des diagrammes de bandes attribue ce phénomène à la présence de bandes sourdes dans le cristal ne pouvant être excitées par les transducteurs utilisés. Cet aspect est d'une importance critique dans le dimensionnement de cristaux phononiques en vue d'une utilisation dans des applications pratiques. / In the straight line of photonic and microwave meta-materials, phononic crystals are foreseen to enable novel acoustic applications that existing technologies cannot reach. These phononic crystals are periodic organisation of acoustically different materials exhibiting, for example, qtop bands, which means frequency ranges in which no wave can propagate in the structure. In this thesis we target RF frequencies in order to investigate applications complementary to the conventional resonators or filters widely used in mobile telecommunication systems. We developed a simple process flow to realise micrometric two-dimensional phononic crystals on a piezoelectric membrane. These structures are fabricated along with Lamb wave devices studied in CEA-LETI for channel filtering in low consumption wireless transmission architectures, and with bulk wave resonators or more complex structures like band-pass filters. A parametric study of Lamb wave resonators sharpens our knowledge on these devices, which allow us to design and fabricate delay lines to characterise acoustic transmission properties of phononic crystals. From a theoretical point of view we set up a simulation model using finite element method. This model was used to design the phononic crystal we realised, and to take into account the effects of the modifications brought by the technological realisation. We then fabricated phononic crystals, and electrically and optically characterised them, in collaboration with FEMTO-ST institute. Measurements confirmed the presence of band gaps at the targeted frequency, but over a wider frequency range than predicted by calculation. A detailed study of band diagrams is attributing this phenomenon to the presence of deaf bands, which cannot be excited by interdigitated fingers. This shows that the determination of these deaf bands is of critical importance in designing phononic crystals for practical applications.

Orientador: Hugo Luis Fragnito / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin. / Made available in DSpace on 2018-08-12T16:20:28Z (GMT). No. of bitstreams: 1 Wiederhecker_GustavoSilva_D.pdf: 26845631 bytes, checksum: f23a4b48df09da35f76ca70361b0231d (MD5) Previous issue date: 2008 / Resumo: Neste trabalho são investigadas técnicas para controlar o confinamento de fótons e fônons em fibras ópticas de cristal fotônico (PCF). Utilizando métodos numéricos robustos para resolver as equações de Maxwell, um novo tipo de PCF com núcleo tubular é proposto. Simulações e experimentos demonstram que esta estrutura confina a luz em um buraco de ar com diâmetro de apenas 110 nm. A figura de mérito para efeitos não-lineares nesta pequena região é 10 bilhões de vezes maior do que no caso de um feixe gaussiano altamente focalizado e 100 vezes maior que o atual estado-da-arte em fibras de band-gap fotônico. Também é analisada teoricamente uma fibra PCF do tipo kagomé. Modelos que explicam suas complexas características de guiamento são investigados de forma analítica e numérica. No que diz respeito à fônons em PCFs, é investigado o espalhamento Brillouin copropagante e contra-propagante. Em particular, são demonstradas maneiras de reduzir a interação acusto-óptica nos casos de co- e retro-espalhamento. Também é demonstrada a presença de band-gaps fonônicos nestas estruturas. Finalmente, é investigado o controle óptico coerente de modos acústicos nestas fibras, mostra-se que é possível amplificar ou frear modos acústicos com freqüência de oscilação na faixa de GHz. / Abstract: Techniques that may allow control and tight confinement of photons and phonons in photonic crystal fibers (PCFs) are investigated in this thesis. By means of robust numerical methods to solve Maxwell equations, a new kind of PCF with a tubular core is proposed. Simulations and experimental results show that such structure is able to confine light tighly inside the 100 nm bore, the nonlinear figure of merir for such tiny bore is found to be 10 billion fold larger the focused Gaussian beam counterpart, it is also 100 times larger than the state-of-the-art hollow core photonic band-gap fibers. The guidance mechanism of kagomé structure hollow-core PCF is also investigated, simple models are proposed to explain most of the experimentally observed features and compared to full numerical simulations. In what concerns phonons, both forward and backward Brillouin scattering is investi-gated in PCFs. It is demonstrated how one may suppress both using such fibers. It is also shown the existence of complete band-gaps for in-plane propagation in the PCF cladding. Another set of experiments show that one can perform coherent optical control of the acoustic modes of such fibers, 100-fold amplification or almost complete suppression of GHz oscillations is achieved. / Doutorado / Física / Doutor em Ciências

No description available.

<p>With the emergence of 5G/mm-Wave communication, there is a growing need for novel front-end electromechanical devices in filtering and carrier generation applications. CMOS-MEMS resonators fabricated using state-of-the-art Integrated Circuit (IC) manufacturing processes provide a significant advantage for power, area and cost savings. In this work, a comprehensive physics-based compact model capable of capturing the non-linear behaviour and other non-idealities has been developed for MEMS resonators seamlessly integrated in CMOS. As the first large signal model for CMOS-embedded resonators, it enables holistic design of MEMS components with advanced CMOS circuits as well as system-level performance evaluation within the framework of modern IC design tools. Global Foundries 14nm FinFET (GF14LPP) Resonant Body Transistors (fRBT) operating at 11.8 GHz are demonstrated and benchmarked against this large-signal electromechanical model. </p> <p><br></p> <p>Additionally, there is a growing interest in CMOS-integrable ferroelectric materials such as Hafnium Dioxide (HfO2) and Aluminum Scandium Nitride (AlScN) for next-generation memory and computation, as well as electromechanical transduction in CMOS-MEMS devices. This work also explores the performance of 700 MHz Ferroelectric Capacitor-based resonators in the Texas Instruments HPE035 process under high-power operating conditions. Identification of previously unreported characteristics, together with the first nonlinear large signal model for integrated ferroelectric resonators, provides insights on the design of frequency references and acoustic filters using ferroelectric transducers. </p> <p><br></p> <p>Extending the range of unreleased CMOS-MEMS resonators to lower frequency using novel design, we also investigate embedded transducers in chip-scale devices for physical sensing. We have simulated and modeled the transducer coupling for low-frequency propagating modes and benchmarked their projected performance against state-of-the-art conventional MEMS sensors. A new approach to phononic crystal (PnC) Interdigitated Transducers (IDTs) is presented emulating the acoustic dispersion in conventional ICs. Unloaded quality factors up to 15,000 have been measured in $\sim$80 MHz resonators, demonstrating their capacity for resonant rotation sensing. We present a unique methodology to amplify and collimate acoustic waves using CMOS-design-rule-compliant Graded Index (GRIN) Phononic IDTs. Ultimately, the CMOS-MEMS techniques presented in this work for both RF applications and physical sensing can facilitate additional functionality in standard CMOS and emerging 3D heterogeneously integrated (3DHI) ICs with minor or no modifications to manufacturing and packaging. This enables new paradigms in next-generation communications, internet of things (IoT), and hardware security.</p>

This work is dedicated to the theoretical and numerical study of nonlinear phononic crystals. The studied nonlinearities are those due to the second (quadratic) and third (cubic) order elastic constants of the materials that constitute the crystals. Nonlinear effects are studied by the means of finite element methods, used to simulate the propagation of an elastic wave through the crystals. A first research project concerns the study of a bone structure, namely the dispersion of elastic waves in a structure composed of collagen and hydroxy apatite alternate constituent layers. Simulations showed that it exists a strong link between bones hydration and their ability to dissipate the energy. The second study relates to an elastic resonator. A structure composed of steel inclusions in a silica matrix shows a switch behavior when the cubic nonlinearities of steel are taken into account. This strong nonlinear effect appears when the amplitude of the incident wave reaches a threshold. A full analytical model is provided. The last study demonstrates the design of composite materials with both strong cubic nonlinearities and weak quadratic nonlinearities. The derivation of the mixing laws of the elastic parameters of a nonlinear material inside a linear one is performed up to order three. Equations show a strong amplification of the nonlinear parameters of the material for some concentrations. Numerical simulations allow to conclude that the above mentioned resonator can be produced. For this thesis, an innovative tool based on the Discontinuous Galerkin (DG) finite element method is developed for the simulation of elastic wave propagation, in linear and nonlinear systems and in finite and semi-infinite media. The implementation of this DG code for 2D and 3D simulations benefits from the efficient exploitation of modern computer infrastructure (GPU units, clusters) using the property of massive parallelization of DG algorithms. This thesis is part of a joint agreement for an international Ph.D. degree between École Centrale de Lille and the Materials Science and Engineering department of the University of Arizona at Tucson. Ce travail porte sur l'étude théorique et numérique des cristaux phononiques non-linéaires. Les non-linéarités étudiées sont celles dues aux constantes élastiques d'ordre deux (quadratiques) et trois (cubiques) des matériaux constituant les cristaux. Les effets non-linéaires sont étudiés grâce á des méthodes d'éléments finis en simulant la propagation d'une onde élastique á travers les cristaux. Un premier projet de recherche a porté sur l'étude d'une structure osseuse, et plus spécifiquement sur la dispersion des ondes élastiques dans une structure constituée d'une alternance de couches de collagène et d'hydroxy apatite. Les simulations montrent qu'il existe un lien étroit entre l'hydratation des os et leur capacité à dissiper l'énergie. La seconde étude réalisée concerne un résonateur élastique. Une structure constituée d'inclusions d'acier dans de la silice présente un comportement de commutateur (switch) lorsque les non-linéarités cubiques de l'acier sont prises en compte. Cet effet fortement non-linéaire apparaît lorsque l'amplitude de l'onde incidente dépasse un certain seuil. Un modèle analytique complet est fourni. La dernière étude réalisée montre la conception de matériaux composites possédant de fortes non-linéarités cubiques mais de faibles non-linéarités quadratiques. La dérivation des lois de mélange des paramètres élastiques d'un matériau non-linéaire dans un matériau linéaire est effectuée à l'ordre trois. Les équations montrent une forte amplification des paramètres non-linéaires du matériau résultant pour certaines concentrations. Les simulations permettent de conclure que le résonateur mentionné ci-dessus peut effectivement étre réalisé. Pour cette thèse, un outil numérique innovant basé sur la méthode des éléments finis de type Galerkin Discontinu (DG) est développé pour la simulation de la propagation d'ondes élastiques, dans des systèmes linéaires et non-linéaires et dans des milieux finis et semi-infinis. L'implémentation de ce code DG pour des simulations 2D et 3D tire parti des infrastructures de calcul actuelles (processeurs graphiques, clusters) grâce à la propriété de parallélisation massive des algorithmes DG. Cette thèse s'est déroulée dans le cadre d'une cotutelle entre l'École Centrale de Lille et le département de Science et ingénierie des matériaux de l'Université d'Arizona, à Tucson.

Lors de deux dernières décennies, la nano-structuration a permis une augmentation conséquente des performances thermoélectriques. Bien qu’à l’ origine le silicium (Si) ait une faible efficacité thermoélectrique, son efficacité sous forme de nanostructure, et notamment de nanofils, a provoqué un regain d’intérêt envers la conduction thermique au sein de ces nanostructures de Si. Bien que la conductivité thermique y ait été réduite de deux ordres de grandeur, les mécanismes de conduction thermique y demeurent flous. Une meilleure compréhension de ces mécanismes permettrait non seulement d’augmenter l’efficacité thermoélectrique mais aussi d’ouvrir la voie à un contrôle des phonons thermiques, de manière similaire à ce qui se fait pour les photons. L’objectif de ce travail de thèse était donc de développer une plateforme de caractérisation, d’étudier le transport thermique au sein de différentes nanostructures de Si et enfin de mettre en exergue la contribution du transport cohérent de phonons à la conduction thermique. Dans un premier temps, nous avons développé un système de mesure allant de pair avec une procédure de fabrication en salle blanche. La fabrication se déroule sur le site de l’institut de Sciences Industrielles et combine des manipulations chimiques, de la lithographie électronique, de la gravure plasma et du dépôt métallique. Le système de mesure est base sur la thermoreflectance : un changement de réflectivité d’un métal a une longueur d’onde particulière traduit un changement de température proportionnel. Nous avons dans un premier temps étudié le transport thermique au sein de simples membranes suspendues, suivi par des nanofils, le tout étant en accord avec les valeurs obtenues dans la littérature. Le transport thermique au sein des nanofils est bien diffus, à l’exception de fils de moins de 4 μm de long a la température de 4 K ou un régime partiellement balistique apparait. Une étude similaire au sein de structures périodiques 1D a démontré l’impact de la géométrie et l’aspect partiellement spéculaire des réflexions de phonons a basse température. Une étude sur des cristaux phononiques (PnCs) 2D a ensuite montré que même si la conduction est dominée par le rapport surface sur vole (S/V), la distance inter-trous devient cruciale lorsqu’elle est suffisamment petite. Enfin, il nous a été possible d’observer dans des PnCs 2D un ajustement de la conductivité thermique base entièrement sur la nature ondulatoire des phonons, réalisant par-là l’objectif de ce travail. / In the last two decades, nano-structuration has allowed thermoelectric efficiency to rise dramatically. Silicon (Si), originally a poor thermoelectric material, when scaled down, to form nanowires for example, has seen its efficiency improve enough to be accompanied by a renewed interest towards thermal transport in Si nanostructures. Although it is already possible to reduce thermal conductivity in Si nanostructures by nearly two orders of magnitude, thermal transport mechanisms remain unclear. A better understanding of these mechanisms could not only help to improve thermoelectric efficiency but also open up the path towards high-frequency thermal phonon control in similar ways that have been achieved with photons. The objective of this work was thus to develop a characterization platform, study thermal transport in various Si nanostructures, and ultimately highlight the contribution of the coherent phonon transport to thermal conductivity. First, we developed an optical characterization system alongside the fabrication process. Fabrication of the structures is realized on-site in clean rooms, using a combination of wet processes, electron-beam lithography, plasma etching and metal deposition. The characterization system is based on the thermoreflectance principle: the change in reflectivity of a metal at a certain wavelength is linked to its change in temperature. Based on this, we built a system specifically designed to measure suspended nanostructures. Then we studied the thermal properties of various kinds of nanostructures. Suspended unpatterned thin films served as a reference and were shown to be in good agreement with the literature as well as Si nanowires, in which thermal transport has been confirmed to be diffusive. Only at very low temperature and for short nanowires does a partially ballistic transport regime appear. While studying 1D periodic fishbone nanostructures, it was found that thermal conductivity could be adjusted by varying the shape which in turn impacts surface scattering. Furthermore, low temperature measurements confirmed once more the specularity of phonon scattering at the surfaces. Shifting the study towards 2D phononic crystals (PnCs), it was found that although thermal conductivity is mostly dominated by the surface-to-volume (S/V) ratio for most structures, when the limiting dimension, i.e. the inter-hole spacing, becomes small enough, thermal conductivity depends solely on this parameter, being independent of the S/V ratio. Lastly, we were able to observe, at low temperature in 2D PnCs, i.e. arrays of holes, thermal conduction tuning based on the wave nature of phonons, thus achieving the objective of this work.

Le contrôle de la propagation des ondes acoustiques connait ces dernières années des applications potentielles notamment en réalisation de filtres électriques, mais aussi dans le contrôle de la vibration des structures mécaniques et l’isolation sonore. Le principe général de ce contrôle est d’attribuer aux ondes acoustiques des propriétés de propagation pouvant être modulées par une action extérieure. Dans ce contexte, l’étude menée au cours de cette thèse porte sur la possibilité de contrôler la propagation des ondes acoustiques en utilisant des matériaux piézoélectriques . Ces matériaux présentent des propriétés élastiques qui sont couplées aux grandeurs électriques à l’issu de leur processus de fabrication. La vibration d’une couche piézoélectrique est affectée par les conditions aux limites électriques imposées au niveau de ses électrodes. Un moyen simple d’imposer des conditions aux limites électriques à ce type de matériau est de connecter une impédance de charge (capacité positive, capacité négative, inductance) à ses électrodes. Les fréquences de résonnances caractéristiques de la couche piézoélectrique sont alors affectées selon la nature de cette charge. Une capacité positive permet de diminuer la fréquence de résonnance parallèle d’une couche piézoélectrique pour atteindre sa fréquence de résonnance série. En revanche, une capacité négative donne la possibilité d’augmenter la fréquence de résonnance parallèle de la couche piézoélectrique loin de la fréquence fondamentale de son mode en épaisseur. Le ca particulier d’un charge inductive offre une large possibilité de contrôler la propagation des ondes acoustiques à travers le cp piézoélectrique. Il permet d’ouvrir un gap d’hybridation dans une structure piézoélectrique unidimensionnelle, de contrôler sa position en fréquence pour provoquer l’ouverture d’une bande passante au sein du gap de Bragg, d’atténuer les ondes acoustiques dans une bande passante notamment en basses fréquences. / The ability to control the propagation of acoustic waves knows in recent years potential applications especially on the manufacture of electrical filter, but also in controlling the mechanical vibration of structures and sound insulation. To achieve this control, the properties of propagations can be changed by external load. The aim of this work is to achieve the control of acoustic waves in phononic crystal using piezoelectric materials. These materials have elastic properties coupled to the electrical properties resulting from their manufacturing process. The vibration of a piezoelectric layer is affected by the electrical boundary conditions imposed on its electrodes. A simple way to consider an electrical boundary condition on piezoelectrical material is to connect an external impedance load (positive capacitance, negative capacitance, inductance) to its electrodes. The resonance frequencies of the piezoelectric layer are then affected differently according the nature of external electric load. The positive capacitance allows to reduce the parallel resonance frequency. A negative capacitance makes it possible to increase the parallel resonance frequency of the piezoelectric layer, giving the ability to use the piezoelectric material away from away from its fundamental resonance frequency. The particular case of an inductive load has a wide possibility to control the propagation of acoustic waves through a piezoelectric pc. We demonstrate that the use of this inductive load opens a hybridization gap in a one-dimensional piezoelectric structure and enable to control the frequency position of this gap. As a result, the hybridization gap causes the opening of a bandwidth within the gap Bragg. The hybridization gap can also cause a high attenuation of acoustic waves in a pass band especially at low frequencies.

Ce travail de thèse concerne la focalisation des ondes élastiques se propageant dans une plaque mince ou à la surface d’un milieu semi-infini, au travers de lentilles acoustiques planes. Les dispositifs que nous avons étudiés sont basés sur des cristaux phononiques 2D, constitués d'inclusions d'air dans une matrice solide. Ces hétérostructures présentent un gradient de leurs propriétés élastiques le long d'une direction de la lentille. Le gradient d'indice est obtenu en modulant soit la taille des inclusions d'air, soit la distance entre deux inclusions consécutives. L’approche que nous avons adoptée est basée principalement sur la simulation numérique par éléments finis. Cependant une partie significative du travail concerne le calcul analytique de la trajectoire des rayons acoustiques ainsi que la vérification expérimentale des résultats théoriques.L’approche analytique a consisté à calculer la trajectoire des rayons acoustique dans la lentille, en tenant compte de l'anisotropie le long de chaque ligne d'inclusions. L'analyse analytique, appliquée à une onde de Lamb antisymétrique (A0), ainsi que les résultats numériques et les données expérimentales, expliquent parfaitement les caractéristiques du champ de déplacement dans la zone focale, y compris la position, la forme et les dimensions latérales de la tâche focale. Le formalisme s’applique quelle que soit la symétrie du cristal phononique et peut être étendu à des ondes élastiques présentant une autre polarisation. Nous montrons dans ce travail qu’une largeur à mi-hauteur aussi petite que 0.64 peut être obtenue lorsque la focalisation intervient au sein de la lentille.Le formalisme s’applique également à la focalisation derrière la lentille. Dans ce cas, la résolution au point focal est déterminée par le "nombre d'onde transversal maximal" à la sortie de la lentille, en bon accord avec les résultats numériques et expérimentaux. Ensuite, nous avons conçu une lentille à gradient d’indice avec des piliers résonnants érigés entre les inclusions d'air. L'analyse numérique prévoit une résolution légèrement au-delà de la limite de diffraction. Expérimentalement, nous mesurons une largeur à mi-hauteur de la tâche focale juste au-dessus de la limite de diffraction.Enfin, nous avons étudié la focalisation d’une onde de Rayleigh par une lentille à gradient d’indice. Nous avons trouvé un bon accord entre le calcul des trajectoires des rayons, les simulations numériques et les expériences. En outre, nous avons analysé la transmission de l’énergie élastique lorsque la focalisation intervient derrière la lentille. / This manuscript is about the focusing of elastic beams propagating in a plate or on the free surface of a semi-infinite medium, using flat acoustical lenses. The devices we have studied are based onto 2D phononic crystals that are made of air inclusions in a solid matrix and featuring a gradient of their elastic properties along one direction of the lens. The gradient index (GRIN) is obtained by modulating either the size of the air inclusions or the distance between two consecutive inclusions.We primarily adopted a computational approach but a significant part of the work concerns the analytical calculation of the ray trajectories as well as the experimental check of the theoretical findings. The analytical approach consists to calculate the ray trajectories of an elastic waves within the lens while accounting for the anisotropy along each lines of inclusions. The analysis applied to the lowest-order flexural Lamb wave (A0), together with both the numerical results and the experimental data, well explains the features of the displacements field in the focus area, including the location, shape and lateral width. The formalism applies whatever the symmetry of the phononic crystal is and can be extended to other polarization of the elastic wave. We show in this work that FWHM as small as 0.64 may be obtained when focusing inside the lens.The formalism applies also to the focusing behind the lens. In that case, the resolution at the focus is determined by the “maximum transverse wavenumber” at the exit of lens, in good agreement with the numerical and experimental results. Then we designed a GRIN phononic lens featuring resonant pillars in addition to the constitutive air inclusions. The numerical analysis foresees the resolution at the focus beyond the diffraction limit, while experimentally we measured the resolution to be just above the diffraction limit. Lastly, we turned to the subwavelength focusing of Rayleigh waves through GRIN lenses. We found a good agreement between the ray trajectories calculation, the numerical simulations and the experiments. We further analysed the influence of energy transmission when the focus is located behind the lens.

<p>The capability of manipulation of the flow of mechanical energy in the form of mechanical waves (including acoustic and elastic waves) has always been a challenge and a critical part in various areas of engineering. The recent advances in topological acoustic/elastic metamaterials certainly open a new pathway to the manipulation of mechanical waves, especially for the novel scattering-immune wave-guiding capability, even in the presence of defects, disorders or sharp bends along the waveguide. In this Dissertation, the theoretical background and experimental evidence of various types of elastic-wave topological metamaterials including analogues to 2D quantum valley Hall effect (QVHE) materials, 2D quantum spin Hall effect (QSHE) topological insulators are presented. First, the formulation the elastic-wave analogue to QVHE materials in a general continuous elastic phononic structure (not limited to local resonant lattices, filling the gap in the literature) is proposed, and a strategy using pressurized cells to actively control the phononic lattice is presented. By finite prestrain and geometric nonlinear effect, the space inversion symmetry of the original hexagonal lattice is broken, resulting in distinct QVHE phases (characterized by valley Chern numbers) in lattice domains with opposite pressurization. With such mechanism, the edge-state path, i.e., the domain wall connecting lattices with distinct QVHE phases, can be real-time configured. Further more, edge states with tunable frequency-wavenumber dispersion can be created at the external boundaries of the lattice by appropriate pressurization of the outermost cells. An aluminum reticular sheet built with water-jet cutting is machined in the pre-deformed pattern with a Z-shape domain wall at the center, which spatially divides the sheet into two domains with opposite QVHE phases. Using piezoelectric transducers and laser Doppler vibrometry, the measured harmonic and transient responses confirm the back-scattering-immunity of the topological edge states, and the frequency-wavenumber dispersion matches the numerical prediction. A strategy is proposed for unidirectionally generating edge states along the domain wall using two off-phase transducers, which is also experimentally demonstrated. For elastic-wave analogue to QSHE topological insulators, we focus on the ``zone-folding'' method and propose a honeycomb 2D elastic beam network with periodically altered thickness with a generalized Kekule distortion pattern. Such framework provides a parametric space with exhaustive control in the topological phase diagram of waves in the lattice compared to earlier works in the literature. The effective Hamiltonian as well as the characterized topological phase are gauge dependent, particularly they change with different reference frames. This lead to ambiguity in the topological phase of such phononic crystal. Based on this argument, it is predicted that edge states could exist at a dislocation interface connecting two piece of phononic structures of the same pattern with relative displacement. Following the same idea, but considering the available fabrication options, a phononic plate with honeycomb groove pattern engraved on both sides is built, which the depth varied according to the Kekule pattern. With proper tuning of the parameters, it realizes an analogue to the QSHE topological insulator. With <em>ab initio</em> calculation of the Berry curvature (without involving any approximations such as the perturbative approach), a new topological invariant <em>local topological charge</em> is defined and evaluated as the counterpart of the Z₂ invariant in the classical-wave-zone-folding analogue. The local topological charge has intrinsic ambiguity and its value depends on the selected reference frame. However, its <em>change </em>according to changes in the parameters, under a consistent reference frame, is well-defined. Given the fact that shifting the reference frame by certain fractions of a lattice constant was equivalent to changing one of the parameters by a certain amount, it also lead to a well-defined change in the local topological charge, which indicates topological phase transition, and one can predict the existence of edge states at the displacement-dislocation interface between two neighboring lattices having the same pattern up to a rigid-body shifting. The phononic plate is machined by a CNC mill, and the experiment is carried out using piezoelectric transducers and laser Doppler vibrometry, which confirms the existence and robustness of the topological edge states at such dislocation interface connecting identical pattern, which was unprecedented in both quantum and classical systems. The final part of this Dissertation focuses on creating classical mechanical analogues to the 1D Kitaev superconducting model and Majorana-like bound states aimed at future acoustic-wave based computation.</p>