Silicon photonics has witnessed rapid development in recent years for its fabrication compatibility with the cost-effective CMOS technology. The advancement of relevant simulation tools, however, is at a relatively slow pace. The high index contrast of the usual silicon waveguide that has imposed new challenges to the convergence and accuracy of the solution technique, the growing intricacy in solitary component design, and the increased complexity of their integration, are the impelling factors that motivate us to improve the computer-aided design, modeling, simulation, and optimization methods. The theme of the thesis is on the frequency domain simulation methods supported by the complex mode theory. The complex mode theory is introduced to the simulation domain truncated by the perfectly matching layers (PMLs) enclosed in the perfectly reflected boundaries (PRBs), wherein the discrete complex modes as eigen solutions can represent the continuous radiation fields, thus yields a unified approach for handling both guided (discrete) and radiation (continuous) waves. In this thesis, theoretical investigations have been conducted along a few different lines aiming at improving the efficiency and accuracy in complex mode expansion. Properties of high-order complex Berenger modes are firstly addressed through asymptotic solutions, and it is found that as the mode order increases, the symmetry of the cladding and substrate in the simulation domain, instead of the guiding schemes, plays a more and more decisive role regarding mode classification and modal field distribution. A weighed optical path method is then proposed to unify the high-order Berenger modes, and to enhance the symmetry of high order modes’ field distributions in the asymmetric structures, leading to the improvement in convergence speed and stability in the mode expansion. Next, an improved mode-matching method (MMM) is proposed based on an error-minimizing method instead of the conventional approach relying on the unreliable modal orthogonal property. The newly proposed method is significantly more robust as numerical errors usually jeopardize the modal orthogonality. This claim is exemplified by simulation results on silicon channel waveguide facet, bending waveguide, and silicon-germanium photo-detector waveguide. As a direct application of the improved complex mode theory, a hybrid plasmonic-photonic nano-ribbon waveguide is proposed, standing as a combination of the silicon slot and surface plasmon polariton (SPP) waveguides, is proposed and analyzed. We have found that the fundamental mode is featured at low loss as in optical waveguide as well as high confinement as in plasmonic structure. Simulations have shown that millimeter range propagation can be sustained with strong confinement. We have further studied such waveguide with an extra layer of phase changing material incorporated, attempting to realize the efficient electro-optical phase and/or loss modulation. Finally, an optical switch design is proposed by taking the full advantage of the aforementioned structure. / Thesis / Doctor of Philosophy (PhD)

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<p>A new model, referred to as the Rational Dispersion Model is proposed for modeling of dispersive materials in wide wavelength range using the Finite-Difference Time-Domain(FDTD) method. A hardware-accelerated FDTD method combined with the matrix pencil method is proposed to solve both guided and leaky modes. A circuit model based on the complex mode theory is proposed for analysis of large scale structures with non-negligible radiation effects.</p> / Doctor of Philosophy (PhD)

<p>Optical waveguide is a very important component in numerous optical structures, devices and photonic circuits. With the rapid development of fabrication technologies, increasing integrated complexity and different materials characteristics, there is higher demand on high-index contrast waveguide with arbitrary cross section and anisotropic material, which indicates the need to develop an efficient, high-performance mode solver to analyze optical waveguides to reduce the fabrication cycle and total cost. Modeling and simulation methods, including Finite Difference Time-Domain (FDTD) method, Finite Element Method (FEM), Beam Propagating Method (BPM), Mode Matching Method (MMM) and Couple Mode Theory (CMT), etc, have been popular for years. Among those methods, FEM is a good and efficient method, especially for its superiority on arbitrary meshes.</p> <p>In this thesis, both scalar and vectorial FEM mode solvers are implemented with an emphasis on dealing with the radiation and evanescent modes by enclosing the whole region with the Perfect Matched Layer (PML) and Perfect Reflecting Boundary (PRB). Thus, the unbounded and continuous radiation modes together with evanescent modes are replaced by what we called "complex modes", but still keeping the completeness and orthogonality properties.</p> / Master of Applied Science (MASc)

The world-wide development of new high-speed rail lines has led to more stringent design requirements for railway bridges, mainly because high-speed trains can cause resonance in the bridge superstructure. Dynamic simulations, often utilising time-consuming finite element analysis (FEA), have become essential for avoiding such problems. Therefore, guidelines and tools to assist structural engineers in the design process are needed. Considerable effort was spent at the beginning of the project, to develop simplified models based on two-dimensional (2D) Bernoulli-Euler beam theory. First, a closed-form solution for proportionally damped multi-span beam, subjected to moving loads was derived (Paper I). The model was later used to develop design charts (Paper II) and study bridges on existing railway lines (Paper III). The model was then extended to non-proportionally damped beams (Paper IV) in order to include the effects of soil-structure interactions. Finally, the importance of the interaction between the surrounding soil and the bridge was verified by calibrating a finite element (FE) model by means of forced vibration tests of an end-frame bridge (Paper V). Recommendations on how to use the models in practical applications are discussed throughout the work. These recommendations include the effects of shear deformation, shear lag, train-bridge and soil-structure interactions, for which illustrative examples are provided. The recommendations are based on the assumption that the modes are well separated, so that the response at resonance is governed by a single mode. The results of the work show that short span bridges, often referred to as `simple´ bridges, are the most problematic with respect to dynamic effects. These systems are typically, non-proportionally damped systems that require detailed analyses to capture the `true´ behaviour. Studying this class of dynamic system showed that they tend to contain non-classical modes that are important for the structure response. For example, the bending mode is found to attain maximum damping when its undamped natural frequency is similar to that of a non-classical mode. / <p>QC 20170213</p>

Today represents vibration analysis an inseparable part of the product design, especially aeronautical components, machine tools etc. One of the vibration analysis methods is the so-called modal analysis, which determines the modal parameters of the researched structure. This paper deals with a comparison of two commonly used approaches, namely „Single Input Multiple Output“ (SIMO) and „Multiple Input Multiple Output“ analysis (MIMO). A MIMO procedure of measurement is developed and discussed. Both analyses are executed by the same conditions on the milling machine based on parallel kinematics in order to objective comparison. The results show that the choice of the so-called reference points is very important. In case both references are appropriately selected, the MIMO analysis gives better results that the SIMO one.

Today represents vibration analysis an inseparable part of the product design, especially aeronautical components, machine tools etc. One of the vibration analysis methods is the so-called modal analysis, which determines the modal parameters of the researched structure. This paper deals with a comparison of two commonly used approaches, namely „Single Input Multiple Output“ (SIMO) and „Multiple Input Multiple Output“ analysis (MIMO). A MIMO procedure of measurement is developed and discussed. Both analyses are executed by the same conditions on the milling machine based on parallel kinematics in order to objective comparison. The results show that the choice of the so-called refer-ence points is very important. In case both references are appropriately selected, the MIMO analysis gives better results that the SIMO one.

For intermediate floors in residential and office buildings, as well as in parking garages and malls, there is a wide use of hollow core concrete slabs in Sweden today. Hollow core slabs are precast and prestressed concrete elements with cylindrical-shaped voids extending along the length of the slab. These structural elements have the advantage compared to cast-in-situ concrete slabs that they have a high strength, due to the prestressing, and that the voids allow for a lower self-weight. Additionally, the voids allow for a reduction in the use of concrete material. These characteristics offer possibilities to build long-span floors with slender designs. However, a consequence of the slenderness of the slabs is that such floors have an increased sensitivity to vibrations induced by various dynamic loads. In residential and office buildings vibrations are primarily caused by human activity, and therefore concerns related to the serviceability of such floors are raised. These vibrations are often not related to problems with structural integrity, but rather to different aspects of comfort of the residents or workers. The aim of this thesis is to provide additional information regarding the dynamic behavior of hollow core floors. An experimental modal analysis has been performed on an existing floor in an office building. The dynamic properties in the form of natural frequencies, mode shapes, damping ratios and frequency response functions were derived and analyzed from these measurements. Subsequently, several finite element models were developed, aiming to reproduce the experimental dynamic behavior of the studied floor. The measurements initially showed some unexpected dynamic responses of the floor. For this reason, more advanced methods of signal analyses were applied to the data. The analyses showed that the slab has some closely spaced modes and that the modes of the floor are complex to a certain degree. The finite element models were studied with different configurations. In particular, the effect the model size, boundary conditions, material properties and potential structural discontinuities have on the dynamic response of the slab was studied. Sufficiently good agreement has been achieved between the experimental and numerical results in terms of natural frequencies and mode shapes. The acceleration amplitude responses of the numerical models were generally higher than the ones obtained from the measurements, which leads to difficulties in matching of the frequency response functions. / Håldäck i betong används idag i stor utsträckning som bjälklag i bostads- och kontorsbyggnader, liksom i parkeringsgarage och köpcentra. Håldäcksbjälklag består av prefabricerade och förspända betongelement, med cylindriska hål som sträcker sig i plattans längsriktning. Dessa konstruktionselement har fördelen, jämfört med platsgjutna betongplattor, att de har en hög hållfasthet på grund av förspänningen och att hålen möjliggör en lägre egenvikt. Dessutom gör hålen att en mindre mängd betongmaterial behövs. Dessa egenskaper ger möjligheter att bygga golv med långa spännvidder och slank design. En konsekvens av slankheten är emellertid att sådana golv har en ökad känslighet för vibrationer som orsakas av olika dynamiska belastningar. I bostads- och kontorsbyggnader orsakas vibrationer främst av mänsklig aktivitet, och därför finns det en del oro relaterad till sådana golvs brukbarhet. Dessa vibrationer är oftast inte relaterade till frågor om strukturell integritet, utan snarare till olika aspekter av boendes eller arbetares känsla av komfort. Syftet med detta examensarbete är att bidra till kunskapen om håldäcksbjälklags dynamiska beteende. En experimentell modalanalys har utförts på ett befintligt golv i en kontorsbyggnad. De dynamiska egenskaperna i form av egenfrekvenser, modformer, dämpning och frekvenssvarsfunktioner erhölls och analyserades med hjälp av dessa mätningar. Därefter utvecklades flera finita element modeller för att reproducera det experimentellt uppmätta dynamiska beteendet hos det studerade golvet. Mätningarna visade initialt något oväntade dynamiska responser från golvet. Av denna anledning applicerades mer avancerade signalanalysmetoder på datan. Analyserna visade att plattan har några moder inom ett litet frekvensintervall och att moderna till en viss grad är komplexa. De finita element modellerna studerades med olika konfigurationer. I synnerhet studerades effekten av modellstorleken, randvillkoren, materialegenskaperna och potentiella strukturella diskontinuiteter på golvets dynamiska respons. Tillräckligt bra överensstämmelse har uppnåtts mellan de experimentella och numeriska resultaten i form av egenfrekvenser och modformer. Accelerationsamplituderna för de numeriska modellerna var i allmänhet högre än de som erhölls under mätningarna, vilket leder till svårigheter att matcha frekvenssvarsfunktionerna.