Computer simulation of electromagnetic behaviour of a device is a common practice in modern engineering. Maxwell's equations are solved on a computer with help of numerical methods. Contemporary devices constantly grow in size and complexity. Therefore, new numerical methods should be highly efficient. Many industrial and research applications of numerical methods need to account for the frequency dependent materials. The Finite-Difference Time-Domain (FDTD) method is one of the most widely adopted algorithms for the numerical solution of Maxwell's equations. A major drawback of the FDTD method is the interdependence of the spatial and temporal discretisation steps, known as the Courant-Friedrichs-Lewy (CFL) stability criterion. Due to the CFL condition the simulation of a large object with delicate geometry will require a high spatio-temporal resolution everywhere in the FDTD grid. Application of subgridding increases the efficiency of the FDTD method. Subgridding decomposes the simulation domain into several subdomains with different spatio-temporal resolutions. The research project described in this dissertation uses the Huygens Subgridding (HSG) method. The frequency dependence is included with the Auxiliary Differential Equation (ADE) approach based on the one-pole Debye relaxation model. The main contributions of this work are (i) extension of the one-dimensional (1D) frequency-dependent HSG method to three dimensions (3D), (ii) implementation of the frequency-dependent HSG method, termed the dispersive HSG, in Fortran 90, (iii) implementation of the radio environment setting from the PGM-files, (iv) simulation of the electromagnetic wave propagating from the defibrillator through the human torso and (v) analysis of the computational requirements of the dispersive HSG program.

Heart rate variability analysis can be used for a diagnosis of the cardiac diseases. The HRV analysis methods are divided into linear and nonlinear methods. Time-domain method is one of the simplest method and belongs to linear methods. Detrended fluctuation analysis DFA is nonlinear method made relatively recently. In this paper, it has been done the comparison of these two methods based on the changes detection in HRV caused by an ischemia.

In the present thesis, computational methods for theanalysis and design of photonic bandgap structure areconsidered. Many numerical methods have been used to study suchstructures. Among them, the plane wave expansion method is veryoften used. Using this method, we show that inclusions ofelliptic air holes can be used effectively to obtain a largercomplete band gap for two-dimensional (2D) photonic crystals.An optimal design of a 2D photonic crystal is also consideredin the thesis using a combination of the plane wave expansionmethod and the conjugate gradient method. We find that amaximum complete 2D band gap can be obtained by connectingdielectric rods with veins for a photonic crystal with a squarelattice of air holes in GaAs. For some problems, such as defect modes, the plane waveexpansion method is extremely time-consuming. It seems that thefinite-difference time-domain (FDTD) method is promising, sincethe computational time is proportional to the number of thediscretization points in the computation domain (i.e., it is oforderN). A FDTD scheme in a nonorthogonal coordinate systemis presented in the thesis to calculate the band structure of a2D photonic crystal consisting of askew lattice. The algorithmcan easily be used for any complicated inclusion configuration,which can have both the dielectric and metallic constituents.The FDTD method is also applied to calculate the off-plane bandstructures of 2D photonic crystals in the present thesis. Wealso propose a numerical method for computing defect modes in2D crystals (with dielectric or metallic inclusions). Comparedto the FDTD transmission spectra method, our method reduces thecomputation time and memory significantly, and finds as manydefect modes as possible, including those that are not excitedby an incident plane wave in the FDTD transmission spectramethod. The FDTD method has also been applied to calculateguided modes and surface modes in 2D photonic crystals using acombination of the periodic boundary condition and theperfectly matched layer for the boundary treatment. Anefficient FDTD method, in which only real variables are used,is also proposed for the full-wave analysis of guided modes inphotonic crystal fibers. / QC 20100629

Size reduction is a key issue in the development of contemporary integrated photonics. This thesis is mainly devoted to study some integrated photonic components in sub-wavelength or nanometric scales, both theoretically and experimentally. The possible approaches to reduce the sizes or to increase the functionalities of photonic components are discussed, including waveguides and devices based on silicon nanowires, photonic crystals, surface plasmons, and some near-field plasmonic components. First, some numerical methods, including the finite-difference time-domain method and the full-vectorial finite-difference mode solver, are introduced. The finite-difference time-domain method can be used to investigate the interaction of light fields with virtually arbitrary structures. The full-vectorial finite-difference mode solver is mainly used for calculating the eigenmodes of a waveguide structure. The fabrication and characterization technologies for nano-photonic components are reviewed. The fabrications are mainly based on semiconductor cleanroom facilities, which include thin film deposition, electron beam lithography, and etching. The characterization setups with the end-fire coupling and the vertical grating coupling are also described. Silicon nanowire waveguides and related devices are studied. Arrayed waveguide gratings with 11nm and 1.6nm channel spacing are fabricated and characterized. The dimension of these arrayed waveguide gratings is around 100 μm, which is 1--2 order of magnitude smaller than conventional silica based arrayed waveguide gratings. A compact polarization beam splitter employing positive/negative refraction based on a photonic crystal of silicon pillars is designed and demonstrated. Extinction ratio of ~15dB is achieved experimentally in a wide wavelength range. Surface plasmon waveguides and devices are analyzed theoretically. With surface plasmons the light field can be confined in a sub-wavelength dimension. Some related photonic devices, e.g., directional couplers and ring resonators, are studied. We also show that some ideas and principles of microwave devices, e.g., a branch-line coupler, can be borrowed for building corresponding surface plasmon based devices. Near-field plasmonic components, including near-field scanning optical microscope probes and left handed material slab lenses, are also analyzed. Some novel designs are introduced to enhance the corresponding systems. / QC 20100908

The absence of appropriate media to cultivate photons efficiently at the micro or nano scale has hindered taking the full advantage of processing information with light. The proposal of such a medium for light, known as photonic crystals (PCs)--multi-dimensional artificially periodic dielectric media--brings the possibility of a revolution in communications and sensing much closer. In such media, one can manipulate light at a scale on the order of the wavelength or even shorter. Applications of PCs other than in communication include bio-sensing because of the peculiar properties of PCs such as the capability of enhance field-matter interaction and control over the group velocity. As a result, PC waveguide (PCW) structures are of interest and it is expected that PC sensors offer the feasibility of multi-analyte and compact sensing schemes as well as the ability of the detection of small absolute analyte quantities (nanoliters) and low-concentration samples (picomoles), which may be advantages over conventional approaches such as fiber optic and slab waveguide sensors. Depending on the nature of the analyte, either dispersive or absorptive sensing schemes may be implemented. Light propagation is controlled fully only with 3D PCs. One of the problems arising due to reducing the dimension to 2D is that PCs become strongly polarization sensitive. In many cases, one wants to implement polarization insensitive devices such that the PC provides a full band gap for all polarizations. To address this problem, a novel type of PC called annular PC is proposed and analyzed. The capability of tuning the TE and TM polarizations independently within the same structure provides great flexibility to produce polarization-independent or polarization-dependent devices as desired. PCW bends are expected to be the essential building blocks of photonic integrated circuits. Sharp corners having small radii of curvature can be obtained. To enhance the low-loss and narrow-band transmission through these bends, PC heterostructures waveguide concept is introduced. We show that in PCWs formed by joining different types of PCs in a single structure, light can flow around extremely sharp bends in ways that are not possible using conventional PCWs based on a single type of PC.

Disertacijoje sprendžiama lėtinimo sistemų kraštinių ir galinių laidininkų įtakos modelių tikslumui įvertinimo problema. Pagrindiniai tyrimo objektai – daugialaidžių ir meandrinių mikrojuostelinių linijų matematiniai modeliai, skaitiniai analizės metodai. Darbo tikslas – sukūrus modelius, grįstus baigtinių skirtumų laiko srities metodu, ištirti galinių ir kraštinių laidininkų netolygumų įtaką meandrinių mikrojuostelinių vėlinimo linijų laiko ir dažninėms charakteristikoms, pasiūlyti meandrinių vėlinimo linijų konstrukcijų tobulinimo priemones. Darbe sprendžiami uždaviniai: matematinių pavienės, susietųjų ir daugialaidžių mikrojuostelinių linijų modelių sudarymas ir savybių tyrimas, taikant baigtinių skirtumų bei baigtinių skirtumų laiko srities analizės metodus; daugialaidžių mikrojuostelinių linijų sintezės ir meandrinių mikrojuostelinių vėlinimo linijų analizės algoritmų bei jų elektrinių charakteristikų skaičiavimo metodikų sudarymas. Disertaciją sudaro įvadas, keturi skyriai, bendrosios išvados, naudotos literatūros ir autoriaus publikacijų disertacijos tema sąrašai. Įvadiniame skyriuje formuluojama tiriamoji problema, aptariamas darbo aktualumas, aprašomas tyrimų objektas, formuluojamas darbo tikslas bei uždaviniai, aprašoma tyrimų metodika, darbo mokslinis naujumas, rezultatų praktinė reikšmė, ginamieji teiginiai. Įvado pabaigoje pristatomi pranešimai konferencijose disertacijos tema bei pateikiama disertacijos struktūra. Pirmajame skyriuje pateikiama literatūros... [toliau žr. visą tekstą] / There are investigated accuracy issues of edges and ends evaluation problems of meander slow-wave systems in the dissertation. Objects of research – mathematical models of multiconductor and meander microstrip delay lines, numerical analysis methods. Aim of the work – after creating mathematical models, based on finite difference time domain method, explore ends and edges discontinuity effects on meander microstrip delay lines time and frequency characteristics, propose structural improvement measures of meander delay line. The dissertation approaches major tasks such as: mathematical individual, coupled, multiconductor microstrip lines models composition for performance and their properties investigation using finite difference and finite difference time domain methods of analysis; synthesis algorithm of multiconductor microstrip lines and analysis algorithm of meander microstrip delay line and methodology of their electrical characteristics calculation creation. The thesis consists of four parts including introduction, 4 chapters, conclusions, references. The introduction reveals investigated problem, importance of the thesis and object of research. It also describes the purpose and tasks of the dissertation, research methodology, scientific novelty and the practical significance of results examined in the thesis and defended statements. The introduction ends in presenting the author’s publications on the subject of the defended dissertation, offering the material of made... [to full text]

There are investigated accuracy issues of edges and ends evaluation problems of meander slow-wave systems in the dissertation. Objects of research – mathematical models of multiconductor and meander microstrip delay lines, numerical analysis methods. Aim of the work – after creating mathematical models, based on finite difference time domain method, explore ends and edges discontinuity effects on meander microstrip delay lines time and frequency characteristics, propose structural improvement measures of meander delay line. The dissertation approaches major tasks such as: mathematical individual, coupled, multiconductor microstrip lines models composition for performance and their properties investigation using finite difference and finite difference time domain methods of analysis; synthesis algorithm of multiconductor microstrip lines and analysis algorithm of meander microstrip delay line and methodology of their electrical characteristics calculation creation. The thesis consists of four parts including introduction, 4 chapters, conclusions, references. The introduction reveals investigated problem, importance of the thesis and object of research. It also describes the purpose and tasks of the dissertation, research methodology, scientific novelty and the practical significance of results examined in the thesis and defended statements. The introduction ends in presenting the author’s publications on the subject of the defended dissertation, offering the material of made... [to full text] / Disertacijoje sprendžiama lėtinimo sistemų kraštinių ir galinių laidininkų įtakos modelių tikslumui įvertinimo problema. Pagrindiniai tyrimo objektai – daugialaidžių ir meandrinių mikrojuostelinių linijų matematiniai modeliai, skaitiniai analizės metodai. Darbo tikslas – sukūrus modelius, grįstus baigtinių skirtumų laiko srities metodu, ištirti galinių ir kraštinių laidininkų netolygumų įtaką meandrinių mikrojuostelinių vėlinimo linijų laiko ir dažninėms charakteristikoms, pasiūlyti meandrinių vėlinimo linijų konstrukcijų tobulinimo priemones. Darbe sprendžiami uždaviniai: matematinių pavienės, susietųjų ir daugialaidžių mikrojuostelinių linijų modelių sudarymas ir savybių tyrimas, taikant baigtinių skirtumų bei baigtinių skirtumų laiko srities analizės metodus; daugialaidžių mikrojuostelinių linijų sintezės ir meandrinių mikrojuostelinių vėlinimo linijų analizės algoritmų bei jų elektrinių charakteristikų skaičiavimo metodikų sudarymas. Disertaciją sudaro įvadas, keturi skyriai, bendrosios išvados, naudotos literatūros ir autoriaus publikacijų disertacijos tema sąrašai. Įvadiniame skyriuje formuluojama tiriamoji problema, aptariamas darbo aktualumas, aprašomas tyrimų objektas, formuluojamas darbo tikslas bei uždaviniai, aprašoma tyrimų metodika, darbo mokslinis naujumas, rezultatų praktinė reikšmė, ginamieji teiginiai. Įvado pabaigoje pristatomi pranešimai konferencijose disertacijos tema bei pateikiama disertacijos struktūra. Pirmajame skyriuje pateikiama literatūros... [toliau žr. visą tekstą]

Power distribution networks (PDNs) are conducting structures employed in semiconductor systems with the aim of providing circuits with reliable and constant operating voltage. This network has non-neglible electrical parasitics. Consequently, when digital circuits inside the chip switch, the supply voltage delivered to them does not remain ideal and exhibits spatial and temporal voltage fluctuations. These fluctuations in the supply voltage, known as the power-supply noise (PSN), can affect the functionality and the performance of modern microprocessors. The design of this PDN in the chip is an important part in ensuring power integrity. Modeling and simulation of the PSN in on-chip PDNs is important to reduce the cost of processors. These PDNs have irregular geometries, which affect the PSN. As a result, they have to be modeled. The problem sizes encountered in this simulation are usually large (on the order of millions), necessitating computationally efficient simulation approaches. Existing approaches for this simulation do not guarantee at least one of the following three required properties: computationally efficiency, accuracy, and numerically robustness. Therefore, there is a need to develop accurate, numerically robust, and efficient algorithms for this simulation. For many interconnects (e.g., transmission lines, board connectors, package PDNs), only their frequency responses and SPICE circuits (e.g., nonlinear switching drivers, equivalent circuits of interconnects) terminating them are known. These frequency responses are usually available only up to a certain maximum frequency. Simulating the electrical behavior of these systems is important for the reliable design of microprocessors and for their faster time-to-market. Because terminations can be nonlinear, a transient simulation is required. There is a need for a transient simulation of band-limited frequency-domain data characterizing a multiport passive system with SPICE circuits. The number of ports can be large (greater than or equal to 100 ports). In this simulation, unlike in traditional circuit simulators, normal properties like stability and causality of transient results are not automatically met and have to be ensured. Existing techniques for this simulation do not guarantee at least one of the following three required properties: computationally efficiency for a large number of ports, causality, and accuracy. Therefore, there is a need to develop accurate and efficient time-domain techniques for this simulation that also ensure causality. The objectives of this Ph.D. research are twofold: 1) To develop accurate, numerically robust, and computationally efficient time-domain algorithms to compute PSN in on-chip PDNs with irregular geometries. 2) To develop accurate and computationally efficient time-domain algorithms for the causal cosimulation of band-limited frequency-domain data with SPICE circuits.

Notre recherche porte sur la réponse optique des nanostructures et nous sommes certainement intéressés à la modélisation de ces structures afin d'améliorer le confinement de la lumière. Ce confinement est un des paramètres qui conduisent à l'exaltation des effets optique linéaires et non linéaires, simultanément. Notre travail est divisé en deux sections, qui présentent deux effets optiques diffèrents basées sur le confinement des champs à l’intérieur du structure. Dans la première section, la réponse optique d’une nano-antenne à ouverture en forme de nœud papillon (BNA : Bowtie nano-aperture) sera étudiée en fonction de l’indice de réfraction du milieu. L’étude discute la variation de la longueur d’onde de résonance ainsi que l’intensité du champ confiné au milieu du gap de la BNA en fonction de la distance qui sépare l’antenne d’un substrat placé en face. L’étude prend le cas d’une BNA gravée au bout d’une fibre optique métallisée. Une étude numérique complète a été réalisée par des simulations numériques basées sur la méthode des différences finies FDTD-3D (Finite Difference Time Domaine – Three dimension). Le code utilisé est développé au sein du département d’Optique de l’Institut FEMTO-ST. Notre modèle numérique décrits bien la géométrie de l’antenne ainsi que la pointe. De même les propriétés optiques de la couche métallique de la sonde sont bien décrites à travers un modèle de dispersion (model de Drude). Une étude expérimentale a été réalisée en plus pour une validation des résultats collecte théoriquement, l’étude a considéré le cas de deux BNA avec des paramètres géométrique différents, néanmoins les résultats obtenues se correspond fortement aux résultats obtenues numériquement. Dans la deuxième partie, l'effet électro-optique des nanostructures sera étudié. L’effet électro-optique ou effet Pockels consiste d’une variation linéaire de l'indice de réfraction d'un milieu non-linéaire en fonction d'un champ électrique extérieur. Cependant, la variation est reliée au tenseur de susceptibilité non linéaire du deuxième ordre, ainsi, cette effet ce produit seulement dans les matériaux non-centrosymétrique. Dans notre étude les nanostructures sont fabrique avec le Niobate de Lithium (LN) qui est considéré comme le plus avantageux diélectrique pour l’exaltation des effets non linéaire grâce à ces propriétés (acousto-optique, électro-optique, piézoélectrique …). L’étude est complétée numériquement garce a des simulations basées sur la FDTD en tenant compte de la polarisation du champ. Au début, une validation de l’utilisation de la FDTD pour estimer l’effet électro-optique intrinsèque du LN a été achevée, l’étude considère un milieu homogène (pas de confinement des champs dans le milieu) qui a pour indice de réfraction celle du LN. Pour des structure qui présentes un confinement du champ plusieurs approximation ont été suggère dans cette partie. En outre, nous présentons un nouveau modèle auto-cohérent dans lequel la variation de l'indice de réfraction est modifiée au cours de la simulation. Plusieurs structure ont été discutés (réflecteur de Bragg, structure à cavité et 2D cristal photonique) qui présentent des facteurs de confinement différents. Une étude comparative entre les différentes méthodes, montre que la différence entre les résultats de chaque hypothèse devient plus important proportionnellement au facteur de confinement. / Our research is concerned with the optical response of nano-structures by modeling them in order to enhance the confinement of light in these structures, which leads to the exaltation of linear and nonlinear optical effects.Our work is divided into two sections, which are based on the enhancement of the electric field inside the structure. In the first section, we study the optical properties of a Bowtie Nano-aperture, BNA, as a function of the refractive index of the surrounding medium. The study discusses the variation of the resonance wavelength and the intensity of the enhanced field in the gap of the BNA as a function of the distance from a sample placed in front of our BNA. The BNA is engraved at the apex of a metallic coated fiber tip. In this section a theoretical study was achieved using the Finite Difference Time Domain method FDTD in which we implement a Drude dispersion model to faithfully describe the optical properties of metals. In addition, a validating experimental study was achieved and a high accordance between both results is recorded.In the second section, the electro optical effect of nano-structures is studied. Electro-optical effect or Pockels effect is the variation of the refractive index of a nonlinear media as a function of an applied external electric field. The electro-optical effect is a linear variation of the media refractive index. However it is also related to the second order nonlinear susceptibility tensor, thus it becomes a nonlinear effect that only occurs in non-centrosymetric material. In our study we chose the case of a nano-structure fabricated with Lithium Niobate. Lithium Niobate is widely used in photonic applications due to its electro-optical, acousto-optical and nonlinear optical properties. We present a theoretical study of the electro-optical effects using the FDTD simulation method. We started by approving the ability to use the FDTD to calculate the refractive index variation in bulk Lithium Niobate then we suggest different approximations to estimate the refractive index variation when the light is confined inside the structure. In addition we suggest a new self-consistent method in which the variation of the refractive index is modified during the simulation. The study shows a comparison between different assumptions (used in previous research) and the self-consistent method for various structures, like Bragg reflectors, cavity structures and 2D photonic crystals. The study shows that the difference between the results of each assumption becomes greater when the optical confinement in the structure becomes more important.

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