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.

The unique frequency range and robustness of surface acoustic wave (SAW) devices has been a catalyst for their adoption as integral components in a range of consumer and military electronics. Furthermore, the strain and piezoelectric fields associated with SAWs are finding novel applications in nanostructured devices. In this thesis, the interaction of SAWs with periodic elastic structures, such as photonic or phononic crystals (PnCs), is studied both computationally and experimentally. To predict the behaviour of elastic waves in PnCs, a finite-difference time-domain simulator (PnCSim) was developed using C++. PnCSim was designed to calculate band structures and transmission spectra of elastic waves through two-dimensional PnCs. By developing appropriate boundary conditions, bulk waves, surface acoustic waves, and plate waves can be simulated. Results obtained using PnCSim demonstrate good agreement with theoretical data reported in the literature. To experimentally investigate the behaviour of SAWs in PnCs, fabrication procedures were developed to create interdigitated transducers (IDTs) and PnCs. Using lift-off photolithography, IDTs with finger widths as low as 1.8 um were fabricated on gallium arsenide (GaAs), corresponding to a SAW frequency of 397 MHz. A citric acid and hydrogen peroxide wet-etching solution was used to create shallow air hole PnCs in square and triangular lattice configurations, with lattice constants of 8 um and 12 um, respectively. The relative transmission of SAWs through these PnCs as a function of frequency was determined by comparing the insertion losses before and after etching the PnCs. In addition, using a scanning Sagnac interferometer, displacement maps were measured for SAWs incident on square lattice PnCs by Mathew (Creating and Imaging Surface Acoustic Waves on GaAs, Master’s Thesis). Reasonable agreement was found between simulations and measurements. Additional simulations indicate that SAW waveguiding should be possible with a PnC consiting of air holes in GaAs. The phononic properties of a commonly used photonic plate were also determined. Band structure simulations of the plate displayed no complete elastic band gaps. However, transmission simulations indicated that a pseudo-gap may form for elastic waves polarized in the sagittal plane. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2009-12-23 16:24:33.164

Novel wave phenomena in two- and three-dimensional (2D and 3D) phononic crystals were investigated experimentally using ultrasonic techniques. Resonant tunneling of ultrasonic waves was successfully observed for the first time by measuring the transmission of ultrasound pulses through a double barrier consisting of two 3D phononic crystals separated by a cavity. This effect is the classical analogue of resonant tunneling of a quantum mechanical particle through a double potential barrier, in which transmission reaches unity at resonant frequencies. For phononic crystals, the tunneling peak was found to be less than unity, an effect that was explained by absorption. The dynamics of resonant tunneling was explored by measuring the group velocities of the ultrasonic pulses. Very slow and very fast velocities were found at frequencies close to and at the resonance, respectively. These extreme values are less than the speed of sound in air and greater than the speed of sound in any of the crystal’s constituent materials. Negative refraction and focusing effects in 2D phononic crystals were also observed. Negative refraction of ultrasound was demonstrated unambiguously in a prism-shaped 2D crystal at frequencies in the 2nd pass band where the wave vector and group velocity are opposite. The Multiple Scattering Theory and Snell’s law allowed theoretical predictions of the refraction angles. Excellent agreement was found between theory and experiment. The negative refraction experiments revealed a mechanism that can be used to focus ultrasound using a flat phononic crystal, and experiments to demonstrate the focusing of ultrasound emitted by several point sources were successfully carried out. The importance of using phononic crystals with circular equifrequency contours, as well as matching the size of the contours inside and outside the crystal, was established. Both conditions were satisfied by a flat phononic crystal of steel rods, in which the liquid inside the crystal (methanol) was different from the outside medium (water). The possibility of achieving subwavelength resolution using this phononic crystal was investigated with a subwavelength line source (a miniature strip-shaped transducer, approximately lambda/5 wide, where lambda is sound wavelength in water). A resolution of 0.55lambda was found, which is just above the diffraction limit lambda/2.

Novel wave phenomena in two- and three-dimensional (2D and 3D) phononic crystals were investigated experimentally using ultrasonic techniques. Resonant tunneling of ultrasonic waves was successfully observed for the first time by measuring the transmission of ultrasound pulses through a double barrier consisting of two 3D phononic crystals separated by a cavity. This effect is the classical analogue of resonant tunneling of a quantum mechanical particle through a double potential barrier, in which transmission reaches unity at resonant frequencies. For phononic crystals, the tunneling peak was found to be less than unity, an effect that was explained by absorption. The dynamics of resonant tunneling was explored by measuring the group velocities of the ultrasonic pulses. Very slow and very fast velocities were found at frequencies close to and at the resonance, respectively. These extreme values are less than the speed of sound in air and greater than the speed of sound in any of the crystal’s constituent materials. Negative refraction and focusing effects in 2D phononic crystals were also observed. Negative refraction of ultrasound was demonstrated unambiguously in a prism-shaped 2D crystal at frequencies in the 2nd pass band where the wave vector and group velocity are opposite. The Multiple Scattering Theory and Snell’s law allowed theoretical predictions of the refraction angles. Excellent agreement was found between theory and experiment. The negative refraction experiments revealed a mechanism that can be used to focus ultrasound using a flat phononic crystal, and experiments to demonstrate the focusing of ultrasound emitted by several point sources were successfully carried out. The importance of using phononic crystals with circular equifrequency contours, as well as matching the size of the contours inside and outside the crystal, was established. Both conditions were satisfied by a flat phononic crystal of steel rods, in which the liquid inside the crystal (methanol) was different from the outside medium (water). The possibility of achieving subwavelength resolution using this phononic crystal was investigated with a subwavelength line source (a miniature strip-shaped transducer, approximately lambda/5 wide, where lambda is sound wavelength in water). A resolution of 0.55lambda was found, which is just above the diffraction limit lambda/2.

La propagation des ondes ultrasonores à travers des cristaux phononiques CP à deux dimensions 2D constitués de diffuseurs solides dans des matrices solide et fluide est ici étudiée, ainsi que la caractérisation de ces milieux et leur application à l’imagerie acoustique. Les techniques expérimentales utilisées permettent une mesure complète des champs transmis à travers les cristaux. Les études sont menées dans des bandes fréquentielles autorisant les effets de réfraction négative indispensables à l’obtention d’une résolution inférieure à la limite de diffraction (super-résolution). De manière à compléter les analyses, différents outils théoriques sont exploités Décomposition en Ondes Planes et Eléments Finis, notamment.La première partie du document concerne la réalisation et la caractérisation de cristaux phononiques possédant des propriétés nécessaires à la réalisation de systèmes d’imagerie acoustique réfraction négative, contours équi-fréquences circulaires, accord d’indice, accord d’impédance. Cette première étude est menée sur un cristal à matrice solide, elle met en relief la possibilité de générer différents modes de Bloch au cours de la propagation. L’accord d’indice avec l’eau n’étant cependant pas obtenu, la seconde partie porte sur la réfraction négative et la focalisation des ondes à travers un CP à matrice fluide. Les propriétés du CP déterminées, le dernier chapitre s’attache à évaluer les performances des systèmes d’imagerie développés : dynamique et résolution. / This investigation deals with wave propagation in two dimensional phononic crystals (PC) made of solid scatterers embedded in solid or fluid matrices. After characterizing such composite materials, their application to acoustic imaging is brought to the forth. The ultrasonic techniques used in the experiments allow the complete measurement of the acoustic transmitted fields and the investigations concern frequency bandwidth able to exhibit negative refraction allowing Oie super-resolution effects. In order to complete the analysis, different theoretical tools are used: Plane Wave Expansion (PWE) and Finite Elements Method (FEM).The first part of this work deals with the realization and characterization of PC to be introduced into acoustic imaging devices (lenses) based on negative refraction. Special attention is given to characteristics such as circular equi-frequency contours, or index and impedance matching. However, during the acoustic wave propagation in a solid PC immersed in water, the presence of different Bloch modes contributing to the transmission of ultrasound is revealed and the index matching was not possible to obtain. Therefore the second part of the manuscript deals with negative refraction and waves focusing through a PC filled with a fluid. After determining the crystal properties, last chapter is devoted to the evaluation of the performances of acoustic imaging systems based on phononic lens.

L'essor des cristaux phoniques (CP) , structures constituées d'un arrangement périodique de différents matériaux dans des domaines d'applications variés tient principalement aux propriétés exceptionnelles qui permettent le contrôle de la propagation des ondes. Des travaux récents se sont intéressés à l'accordabilité en fréquence des CP. Notamment en insérant des matériaux actifs, il a été montré qu'il était possible de moduler la position en fréquence ou la largeur de bandes interdites sans avoir à changer la géométrie du CP. Dans ce contexte, on étudie la propagation d'ondes de Lamb dans une plaque piézoélectrique homogène couverte par des électrodes disposées périodiquement sur les deux faces. Différentes conditions aux limites électriques (CLE) ont imposées sur ces électrodes afin d'agir sur la dispersion des ondes de Lamb. On montre expérimentalement et numériquement que l'application de ces CLE permet des couplages de modes de Lamb de mêmes symétries ou de symétries différentes. / One of the most important properties of phononic crystals (PCs) is their ability to prohibit the propagation of acoustic waves in specific frequency ranges called band gaps (BG). Bragg scaterring and mode hybridization are the two principal known mechanisms for BG nucleation. Recently, the interest for BG tunability has grown rapidly. This study concerns the development of a piezoelectric PC that is able to generate and control the propagation of guided Lamb waves, thus offering tunability of the band structure. A piezoelectric plate covered by ID periodic arrangement of thin electrodes is investigated. It is shown that the application of various electrical boundary conditions (EBCs) on the electrodes allows to change the effective properties of the piezoelectric plate. The dispersion of the waves is then electrically tuned and, depending on the applied EBCs, we demonstrate experimentally and numerically the possibility of opening Bragg or hydridization gaps in the subwavelength regime.

Ultrasonic wave propagation through a two-dimensional nonreciprocal phononic crystal with asymmetric aluminum rods in viscous water is studied for its application in Anderson localization and trapping of acoustic energy. A one-dimensional disorder in the otherwise 2D periodic crystal is introduced by disorienting the asymmetric rods along the rows and by keeping them equally oriented along the columns. An exponential decay of sound waves travelling along the direction of disorder is observed demonstrating Anderson localization whereas sound propagates as extended wave along the ordered direction. Localization length for the case of strong disorder with high randomness in the orientation of rods and weak disorder with weak fluctuations in the orientation of rods is evaluated. The degree of randomness in the orientation of the rods controls the localization length of the wave. Thouless's theoretical prediction for the scaling of Lyapunov exponent with disorder is experimentally observed for weak disorder at frequency in the transmission band and anomalous scaling is observed for band edge frequency. Transmission spectra of acoustic waves is also measured for opposite direction of propagation and nonreciprocity is observed for the exponentially weak transmission in the disordered direction as well as for extended states in the ordered direction. Breaking of reciprocity in the current structure is due to the broken PT symmetry. The T symmetry or the time reversal symmetry is broken by the viscous dissipation at the boundaries of scatterers and the water, and the P symmetry is broken by the asymmetric shape of the rods. Acoustic energy trapping inside a nonreciprocal phononic crystal cavity is studied by creating three configurations of cavities. These configurations are based on the orientation of the asymmetric scatterers on each side of the cavity. Only one of these configuration utilizes the nonreciprocal property of the structure. Enhancement of energy trapping in the cavity is observed for the cavity orientation utilizing nonreciprocity. The proposed enhancement of energy trapping occurs at the transmission band frequency unlike the extensively used mechanism of energy trapping at the defect modes of the band gap of the phononic crystal. All the experimental results are verified numerically using finite element based modelling in COMSOL Multiphysics. The proposed devices can be utilized for applications in one way sound transmission, noise control, isolators, circulators and energy harvesting.

The work presented in this thesis is concerned with the propagation of acoustic waves through phononic crystal systems and their ability to attenuate sound in the low frequency regime. The plane wave expansion method and finite element method are utilised to investigate the properties of conventional phononic crystal systems. The acoustic band structure and transmission measurements of such systems are computed and verified experimentally. Good agreement between band gap locations for the investigative methods detailed is found. The well known link between the frequency range a phononic crystal can attenuate sound over and its lattice parameter is confirmed. This leads to a reduction in its usefulness as a viable noise barrier technology, due to the necessary increase in overall crystal size. To overcome this restriction the concept of an acoustically resonant phononic crystal system is proposed, which utilises acoustic resonances, similar to Helmholtz resonance, to form additional band gaps that are decoupled from the lattice periodicity of the phononic crystal system. An acoustically resonant phononic crystal system is constructed and experimental transmission measurements carried out to verify the existence of separate attenuation mechanisms. Experimental attenuation levels achieved by Bragg formation and resonance reach 25dB. The two separate attenuation mechanisms present in the acoustically resonant phononic crystal, increase the efficiency of its performance in the low frequency regime, whilst maintaining a reduced crystal size for viable noise barrier technology. Methods to optimise acoustically resonant phononic crystal systems and to increase their performance in the lower frequency regime are discussed, namely by introducing the Matryoshka acoustically resonant phononic crystal system, where each scattering unit is composed of multiple concentric C-shape inclusions.

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.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-06-07T14:31:23Z No. of bitstreams: 1 alisonarantesgoncalves.pdf: 9032611 bytes, checksum: 93776f55ce3ecc6dc5c2e6997dc1283a (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-07-13T13:23:26Z (GMT) No. of bitstreams: 1 alisonarantesgoncalves.pdf: 9032611 bytes, checksum: 93776f55ce3ecc6dc5c2e6997dc1283a (MD5) / Made available in DSpace on 2016-07-13T13:23:26Z (GMT). No. of bitstreams: 1 alisonarantesgoncalves.pdf: 9032611 bytes, checksum: 93776f55ce3ecc6dc5c2e6997dc1283a (MD5) Previous issue date: 2016-02-23 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Nesta tese estudamos a estrutura de bandas de fônons e a condutividade térmica de cristais fonônicos em temperaturas sub-Kelvin. O espectro fonônico de baixas frequências (até dezenas de GHz) foi obtido da solução da equação de onda generalizada através do método de Expansão em Ondas Planas. Os resultados para estruturas com periodicidade bidimensional da ordem de mícrons apresentam band gaps e faixas estreitas de transmissão. Este comportamento é interessante para o controle de vibrações mecânicas como em um filtro de frequências operando na frequência de GHz. A densidade de estados foi calculada com o objetivo de estudar problemas de transporte envolvendo materiais fonônicos. Além disso, calculamos a condutividade térmica cumulativa no regime de temperaturas de sub-Kelvin em micro cristais fonônicos visando possíveis aplicações em materiais termoelétricos. Esses cálculos se baseiam na teoria de transporte de Boltzmann a baixas temperaturas a fim de enfatizar o papel dos fônons de baixa frequência e negligenciar o espalhamento fônon-fônon. Em acordo com resultados recentes na literatura, mostramos que a condutividade térmica cumulativa das estruturas fonônicas cai acentuadamente em relação a suas matrizes (bulk). Dependendo da estrutura esta redução pode ser atribuída à velocidade de grupo dos fônons, à densidade de estados ou à presença de band gaps completos. / In this thesis we have studied the phononic band structure and the thermal conductivity of phononic crystals at sub-Kelvin temperatures. The low-frequency phonon spectra (up to tens of GHz) were obtained by solving the generalized wave equation with the Plane Wave Expansion method. The results for structures with two dimensional periodicity of the order of micrometers show the presence of GHz band gaps and narrow pass band. Such behavior is suitable for mechanical vibrations management like a GHz transversal phononic band pass filter. The phonon density of states was calculated aiming the study in transport problems involving phononic materials. Moreover, we have calculated the cumulative thermal conductivity at sub-Kelvin temperature regime of micro-phononic crystals aiming possible applications in thermoelectrics materials. The calculations were based in Boltzmann transport theory at low temperatures in order to highlight the role of low-frequency thermal phonons and to neglect phonon-phonon scattering. In accordance with recent results in the literature, our findings show that the cumulative thermal conductivity of the phononic crystals drops dramatically when compared with their bulk counterpart. Depending on the structural composition this reduction may be attributed to the phonon group velocity, the density of states or the presence of complete band gaps.