O assunto principal deste trabalho é qualificar, quantificar e implementar o comportamento numérico de estruturas discretizadas através do método dos elementos finitos. Serão abordados apenas os elementos lineares unidimensionais dinâmicos, porém a aplicabilidade da formulação proposta pode se estender para elementos bi e tridimensionais lineares dinâmicos. Inicia-se com uma introdução ao tema. Com certo desenvolvimento matemático, pode-se isolar analiticamente a parcela relacionada ao erro numérico. Elevando a ordem do erro de truncamento, obtém-se precisão elevada na resposta numérica. Inspirado no integrador temporal de Newmark, projetam-se elementos que apresentam estabilidade incondicional para os chamados efeitos espúrios. O efeito evanescente é um fenômeno espúrio onde a onda se propaga ao longo da estrutura acompanhada de um amortecimento puramente numérico ao longo do domínio do espaço. Outro efeito analisado é a reflexão espúria. Quando dois elementos adjacentes têm comprimentos diferentes, surge uma onda de reflexão (ou duas, no caso do elemento de viga) na interface deles. Tal onda, também de origem puramente matemática, existe devido à diferença entre as massas e as rigidezes absolutas dos elementos envolvidos, independente do fato de que eles tenham as mesmas características físicas. A relação entre o incremento de tempo e o período de oscilação é convenientemente empregada como principal parâmetro para quantificar a discretização no domínio temporal. No domínio do espaço, a relação empregada é entre o comprimento do elemento e o comprimento de onda. / The main subject of this work is to qualify, quantify and implement the numerical behavior of discrete structures through the finite element method. It will be investigated only the dynamic onedimensional linear elements, but the applicability of the proposed formulation can be extended to the bi and tri-dimensional cases. It begins with an introduction to the theme. With some mathematical development, the related numerical error can be isolated analytically. Once the truncation error is isolate, a high precision numerical response is obtained. Inspired in the Newmark time integrator, unconditionally stable elements for spurious effects are idealized. The evanescent effect is a spurious phenomenon where the wave propagates along the structure subjected to a numerical damping in the spatial domain. Another effect analyzed here is the spurious wave reflection. When two adjacent elements have different lengths, a reflected wave exists (two waves for the beam element) at their interface. This wave, which meaning is purely mathematical, exists due to the difference of their absolute mass and stiffness between the finite elements involved, even when both elements have the same physical properties. The rate between the time increment and the period of oscillation is conveniently employed as the main parameter to quantify the time discretization. In the spatial domain, the used parameter is the relation between the element and the wave length.

O assunto principal deste trabalho é qualificar, quantificar e implementar o comportamento numérico de estruturas discretizadas através do método dos elementos finitos. Serão abordados apenas os elementos lineares unidimensionais dinâmicos, porém a aplicabilidade da formulação proposta pode se estender para elementos bi e tridimensionais lineares dinâmicos. Inicia-se com uma introdução ao tema. Com certo desenvolvimento matemático, pode-se isolar analiticamente a parcela relacionada ao erro numérico. Elevando a ordem do erro de truncamento, obtém-se precisão elevada na resposta numérica. Inspirado no integrador temporal de Newmark, projetam-se elementos que apresentam estabilidade incondicional para os chamados efeitos espúrios. O efeito evanescente é um fenômeno espúrio onde a onda se propaga ao longo da estrutura acompanhada de um amortecimento puramente numérico ao longo do domínio do espaço. Outro efeito analisado é a reflexão espúria. Quando dois elementos adjacentes têm comprimentos diferentes, surge uma onda de reflexão (ou duas, no caso do elemento de viga) na interface deles. Tal onda, também de origem puramente matemática, existe devido à diferença entre as massas e as rigidezes absolutas dos elementos envolvidos, independente do fato de que eles tenham as mesmas características físicas. A relação entre o incremento de tempo e o período de oscilação é convenientemente empregada como principal parâmetro para quantificar a discretização no domínio temporal. No domínio do espaço, a relação empregada é entre o comprimento do elemento e o comprimento de onda. / The main subject of this work is to qualify, quantify and implement the numerical behavior of discrete structures through the finite element method. It will be investigated only the dynamic onedimensional linear elements, but the applicability of the proposed formulation can be extended to the bi and tri-dimensional cases. It begins with an introduction to the theme. With some mathematical development, the related numerical error can be isolated analytically. Once the truncation error is isolate, a high precision numerical response is obtained. Inspired in the Newmark time integrator, unconditionally stable elements for spurious effects are idealized. The evanescent effect is a spurious phenomenon where the wave propagates along the structure subjected to a numerical damping in the spatial domain. Another effect analyzed here is the spurious wave reflection. When two adjacent elements have different lengths, a reflected wave exists (two waves for the beam element) at their interface. This wave, which meaning is purely mathematical, exists due to the difference of their absolute mass and stiffness between the finite elements involved, even when both elements have the same physical properties. The rate between the time increment and the period of oscillation is conveniently employed as the main parameter to quantify the time discretization. In the spatial domain, the used parameter is the relation between the element and the wave length.

Les métamatériaux sont des milieux prometteurs pour l'imagerie acoustique. Grâce à ces milieux, il est possible de concevoir des lentilles à faces parallèles pouvant dépasser la limite conventionnelle de résolution d'une lentille et par conséquent améliorer les systèmes d'imagerie. Malgré l'intérêt grandissant des chercheurs pour les métamatériaux, le comportement des ondes acoustiques dans ces milieux n'est pas totalement connu. Nous proposons de développer la problématique de la propagation des ondes acoustiques dans un milieu de type métamatériau en détail dans ce manuscrit. Cette étude a permis d'extraire un critère discriminant un métamatériau d'un matériau classique et d'apporter un regard nouveau sur l'amplification des ondes évanescentes dans les métamatériaux.Nous explorons une piste peu empruntée en vue du dimensionnement de métamatériaux : les milieux aléatoires. Nous nous focalisons sur les milieux à deux dimensions dont les phases sont fluides. Dans cette optique, une phase de validation de techniques d'homogénéisation dynamique existantes est réalisée \textit{via} la comparaison des réponses acoustiques d'un écran de diffuseurs répartis aléatoirement obtenues par des simulations numériques FDTD avec celles prédites par des modèles analytiques. L'étude de ces modèles, utiles au dimensionnement de structures aléatoires présentant des réponses acoustiques ciblées, nous a amené à examiner avec attention leur comportement quasi-statique. Une technique d'homogénéisation permettant de prendre en compte explicitement les interactions entre diffuseurs est proposée dans ce contexte. Développée dans le cadre de la diffusion simple et multiple, elle relie les propriétés mécaniques effectives aux moyennes des champs acoustiques dans un volume représentatif.Finalement, l'analyse du comportement d'un milieu aléatoire \og réaliste \fg~possédant théoriquement des bandes fréquentielles à réfraction négative, grâce à des diffuseurs résonants à basses fréquences, a été menée. Différents régimes de fonctionnement atypiques sont identifiés à l'aide de simulations numériques. La confrontation des réponses de ce milieu avec celles d'un cristal phononique est ensuite présentée et révèle une étonnante similitude entre les deux arrangements. / Metamaterials are promising media for acoustic imaging. For example, such media give the possibility to build flat lenses exhibiting sub-diffraction-limit resolution, thereby improving imaging setup. Despite the growing interest of the researcher for metamaterials, acoustic wave propagation is still not widely known. This work addresses the topic of wave propagation in metamaterials. In this work, we have defined a criterion which differentiate metamaterial from classical material and provide a new insight in the amplification of evanescent waves.We explore how to design metamaterials with random media. We focus on two dimensional media with fluid components. A validation process of existing dynamic homogenization techniques is done via the comparison between the responses of a screen of scatterers obtained by numerical simulations from FDTD with those predict by the analytical models. The study of those models, useful for designing random media with atypical responses, lead us to consider their quasi-static limit. In this context, we propose a homogenization technique which includes explicitly the interactions between scatterers. It is developed for multiple and simple scattering and link the effective properties to the averages of the acoustic fields in a representative volume.Finally, the analysis of the acoustic responses of a realistic random medium having theoretical negative refraction frequency bandwidth, thanks to low frequency resonant scatterers is done. Different atypical responses are identified from the numerical simulations. The comparison between the responses of this medium and those of phononic crystals is presented and shows a surprising similarity of the two arrangements.

Reliability and sensitive information protection are critical aspects of integrated circuits. A novel technique using near-field evanescent wave coupling from two subwavelength gratings (SWGs), with the input laser source delivered through an optical fiber is presented for tamper evidence of electronic components. The first grating of the pair of coupled subwavelength gratings (CSWGs) was milled directly on the output facet of the silica fiber using focused ion beam (FIB) etching. The second grating was patterned using e-beam lithography and etched into a glass substrate using reactive ion etching (RIE). The slightest intrusion attempt would separate the CSWGs and eliminate near-field coupling between the gratings. Tampering, therefore, would become evident. Computer simulations guided the design for optimal operation of the security solution. The physical dimensions of the SWGs, i.e. period and thickness, were optimized, for a 650 nm illuminating wavelength. The optimal dimensions resulted in a 560 nm grating period for the first grating etched in the silica optical fiber and 420 nm for the second grating etched in borosilicate glass. The incident light beam had a half-width at half-maximum (HWHM) of at least 7 µm to allow discernible higher transmission orders, and a HWHM of 28 µm for minimum noise. The minimum number of individual grating lines present on the optical fiber facet was identified as 15 lines. Grating rotation due to the cylindrical geometry of the fiber resulted in a rotation of the far-field pattern, corresponding to the rotation angle of moiré fringes. With the goal of later adding authentication to tamper evidence, the concept of CSWGs signature was also modeled by introducing random and planned variations in the glass grating. The fiber was placed on a stage supported by a nanomanipulator, which permitted three-dimensional displacement while maintaining the fiber tip normal to the surface of the glass substrate. A 650 nm diode laser was fixed to a translation mount that transmitted the light source through the optical fiber, and the output intensity was measured using a silicon photodiode. The evanescent wave coupling output results for the CSWGs were measured and compared to the simulation results.

Integration and miniaturisation in electronics has undoubtedly revolutionised the modern world. In biotechnology, emerging lab-on-a-chip (LOC) methodologies promise all-integrated laboratory processes, to perform complete biochemical or medical synthesis and analysis encapsulated on small microchips. The integration of electrical, optical and physical sensors, and control devices, with fluid handling, is creating a new class of functional chip-based systems. Scaled down onto a chip, reagent and sample consumption is reduced, point-of-care or in-the-field usage is enabled through portability, costs are reduced, automation increases the ease of use, and favourable scaling laws can be exploited, such as improved fluid control. The capacity to manipulate single cells on-chip has applications across the life sciences, in biotechnology, pharmacology, medical diagnostics and drug discovery. This thesis explores multiple applications of optical manipulation within microfluidic chips. Used in combination with microfluidic systems, optics adds powerful functionalities to emerging LOC technologies. These include particle management such as immobilising, sorting, concentrating, and transportation of cell-sized objects, along with sensing, spectroscopic interrogation, and cell treatment. The work in this thesis brings several key applications of optical techniques for manipulating and porating cell-sized microscopic particles to within microfluidic chips. The fields of optical trapping, optical tweezers and optical sorting are reviewed in the context of lab-on-a-chip application, and the physics of the laminar fluid flow exhibited at this size scale is detailed. Microfluidic chip fabrication methods are presented, including a robust method for the introduction of optical fibres for laser beam delivery, which is demonstrated in a dual-beam optical trap chip and in optical chromatography using photonic crystal fibre. The use of a total internal reflection microscope objective lens is utilised in a novel demonstration of propelling particles within fluid flow. The size and refractive index dependency is modelled and experimentally characterised, before presenting continuous passive optical sorting of microparticles based on these intrinsic optical properties, in a microfluidic chip. Finally, a microfluidic system is utilised in the delivery of mammalian cells to a focused femtosecond laser beam for continuous, high throughput photoporation. The optical injection efficiency of inserting a fluorescent dye is determined and the cell viability is evaluated. This could form the basis for ultra-high throughput, efficient transfection of cells, with the advantages of single cell treatment and unrivalled viability using this optical technique.

A near-field technique known as evanescent interferometric lithography allows for high resolution imaging. However its primary limitation is that the image exponentially decays within the photoresist due to physical limits. This thesis aims to overcome this limitation and presents a method to considerably enhance the depth of focus of images created using evanescent interferometric lithography by using a material underlay beneath the photoresist. A key enabler of this is the understanding that evanescent fields couple to surface states and operating within proximity of a resonance, the strength of the coupling allows for considerable energy extraction from the incident beam and redistribution of this energy in a photoresist cavity. This led to the analysis of the Fresnel equations, which suggested that such coupling was in fact the result of an enhanced reflectance that takes place at boundaries of carefully chosen materials. While it is known that metals and lossy dielectrics result in surface plasmon polaritons (SPP) and surface exciton polaritons (SEP) as conventional solutions to the Fresnel reflection equations for the TM polarization of light, there is no such naturally occurring surface state that allows evanescent wave enhancement with the TE polarization of light. Further investigation of the Fresnel reflection equations revealed both for TM and TE that in fact another solution exists that is but unconventional to enhance the reflectivity. This solution requires that one of the media have a negative loss. This is a new type of surface resonance that requires that one of the media be a gain medium; not one in the optical pumped sense but one that would naturally supply energy to a wave to make it grow. This new surface resonance is also a key result of this thesis. Clearly, however this is only a hypothetical solution as a real gain medium would violate the conservation of energy. However, as it is only the reflectance of this gain medium that is useful for evanescent wave enhancement, in fact a multilayered stack consisting of naturally occurring materials is one way to achieve the desired reflectivity. This would of course be only an emulation of the reflectivity aspect of the gain medium. This multilayered stack is then an effective gain medium for the reflectivity purposes when imaging is carried out at a particular NA at a particular wavelength. This proposal is also a key idea of this thesis. At λ = 193 nm, this method was used to propose a feasible design to image high resolution structures, NA = 1.85 at an aspect ratio of ~3.2. To experimentally demonstrate the enhancements, a new type of solid immersion test bed, the solid immersion Lloyd's mirror interference lithography test-bed was constructed. High quality line and space patterns with a half-pitch of 55.5 nm were created using λ = 405 nm, corresponding to a NA of 1.824, that is well in the evanescent regime of light. Image depths of 33-40 nm were seen. Next, the evanescent image was coupled to an effective gain medium made up of a thin layer of hafnium oxide (HfO) upon silicon dioxide (SiO2). This resulted in a considerable depth enhancement, and 105 nm tall structures were imaged. The work in this thesis details the construction of the solid immersion lithography test-bed, describes the implementation of the modeling tools, details the theory and analysis required to achieve the relevant solutions and understanding of the physical mechanism and finally experimentally demonstrates an enhancement that allows evanescent interferometric lithography beyond conventional limits.