Abstract Optical fiber communications have been become one of the most popular researches since 1970s. In this field, there are many studies on the coupling between semiconductor lasers and fibers and many conclusions are demonstrated. In this thesis we build a 2-D numerical model to simulate energy coupling between laser diodes (LDs) and tapered optical fibers. Our model is based on the spectral domain integral equation (SDIE) formulation which is derived from Maxwell equations and the principle of mode matching. Through this numerical model we will be able to show the field distribution in LD waveguide junctions. We may also use this tool to study the coupling parameters such as the separation distance and tapered fiber geometry.

The limit of current technology for mobile base station filters is the multimode filter, in which each cavity supports two (or possibly three) independent degenerate resonances. Shielded dielectric resonators with a rectangular cross-section are useful in this application. In the design of these filters, manufacturers are using software packages employing finite element or finite difference time domain techniques. However, for sufficient accuracy these procedures require large numbers of points or elements and can be very time consuming. Over the last decade research using the mode matching technique has been used to solve this kind of difficulty for various types of filter design and waveguide problems. In this thesis a mode matching method and computer program is developed to calculate the propagation coefficients and field patterns of the modes in a shielded rectangular dielectric rod waveguide. Propagating, complex, evanescent and backward wave modes are included and the work shows the presence of a dominant mode, and other fundamental modes, not previously identified. The effect of the shield proximity on the propagation characteristics and mode spectrum is investigated, together with the limitations on the accuracy of the mode matching method. In addition, the fields within the shielded rectangular dielectric rod waveguide, are used to calculate the attenuation coefficient of the dominant and fundamental modes. The influence on the attenuation coefficient of the proximity of the shield to the rod is also evaluated for these modes and limitations on accuracy are discussed. The calculated numerical results for the propagation and attenuation coefficient values are verified by measurement. The propagation coefficients results are typically within 2% of those measured. Verification of the attenuation coefficient results is achieved by comparing calculated and measured Q at the resonant frequencies of a number of shielded rectangular dielectric rod resonators. The difference between calculated and measured Q values is on average less than 4%. In the absence of a full solution of the shielded rectangular dielectric rod resonator, these results provide useful design information for this structure. In addition, the work reported in this thesis provides a basis for a full electromagnetic solution of this type of resonator. This would encompass the cubic dielectric resonator in a cubical cavity.

Finite-Difference (FD) based complex modes solver and Complex Mode Matching Method (CMMM) is one of the most popular combinations in modeling and simulation of opti- cal waveguides. This thesis covers the basic theories behind the approaches and impor- tant implementation details. Weighted Optical Path Distance is proposed to speed up convergence and improve numerical accuracy to deal with asymmetric structures. An improved formula is derived for Complex Mode Matching Method expansion process based on matrix optimization. The latter part applies the above approach in the mod- eling of bending structures and grating structures. Typical structures, including bend- ing structures, straight-bend-straight structures, long-period gratings, gratings with de- posited layer, gratings with deep corrugations, are investigated and analyzed. / Thesis / Master of Science in Electrical and Computer Engineering (MSECE)

During the past 60 years fluid-structure interaction in a wide range of three dimensional circular cylinder problems have been studied. Initial problems considered a rigid wall structure which were solved using impedance model comparisons. Soon after, further solution techniques were used, such as computer simulation, transfer matrix methods and finite element techniques. However such problems were only valid for low frequencies when compared with experiments, this was because that did not include higher order modes. The importance of higher order modes was then established and studies have since included these modes. More recently, mode matching methods have been used to find the amplitudes of waves in structures comprising two or more ducts. This has been done with using an orthogonality relation to find integrals which occur from the application this method. This methodology is demonstrated in as background information and is applied to prototype problems formed of rigid ducts. The rigid duct theory led to the consideration of elastic shells, of which several shell modelling equations were available from the vibration theory. In this thesis, the Donnell-Mustari equations of motion are used to model thin, elastic, fluid-loaded shells of circular cross-section. It is demonstrated that generalised orthogonality relations exist for such shells. Two such relations are found: one for shells subject to axisymmetric motion and one for shells subject to non-axisymmetric motion. These generalised orthogonality relations are new to the field of acoustics and are specific to shells modelled with the Donnell-Mustari equations of motion. The mode matching method is used to find the amplitudes of waves propagating in prototype problems and the generalised orthogonality relations are used to find integrals which occur through this method. Expressions for energy for all considered structure types are used to find the resulting energy for each prototype problem and results for equivalent problems are compared. In addition, verification of the resulting amplitudes is done by ensuring that the matching conditions are suitably satisfied. It is anticipated that the method will have application to the understanding and control of the vibration of cylindrical casings such as those enclosing turbo-machinery. Another application of the method would be the tuning of cylindrical casings, such as those featured on car exhaust systems or HVAC (heating, ventilation and air conditioning) systems.

Agriculture faces significant challenges with current climate change and a growing global population. Increasing dry periods, even in Sweden, require increased field irrigation to secure harvests while water availability decreases. Research in remote sensing has led to significant technological advancements where soil moisture can now be detected with precision at 100x100 meters. This study aims to evaluate how well satellite analysis of soil moisture aligns with field experiments and its usefulness for irrigation decisions. Through the collection and analysis of data from both field measurements and satellites, the agreement between these has been examined where statistical measures such as NNSE, RMSE, and MAE have been used. A challenge with satellite analysis is its limitation to measuring soil moisture only in the top layer (3-5 cm) of the soil, which does not estimate the water content in the root zone required for irrigation decisions. To address this, the cumulative function matching method (CDF-method) was used to estimate the water content in the root zone based on satellite measurements of the top soil layer. The results show that satellite data aligns with field measurements for various locations in Sweden, with NNSE values between 0.08-0.61 and an accuracy (MAE) of 4.51-6.99 % water content. Furthermore, the results indicate that water content in the root zone can be estimated from surface soil moisture using the CDF matching method with an accuracy of 1.28-6.41 %. However, this method requires cross-validation in the field where the estimation is to be performed, and the use of satellite analysis for irrigation decisions is limited to the field level. To effectively utilize satellite analysis as a global decision support, methods for estimating water content in the root zone need to be developed to be more applicable for the different soil types.

<p>This dissertation investigates whether dual credit students' academic performance in subsequent university courses is comparable to that of non-dual-credit students. The study uses data from a Midwest regional public university over a ten-year period and employs propensity score matching and proportional odds ordinal logistic regression to create balanced comparison groups and analyze the results. The findings indicate that students who completed the prerequisite course as dual credit have similar grades in subsequent university courses as those who completed the prerequisite course as a university student. The study also identifies significant predictors of academic performance in subsequent university courses, such as sex, historically underserved groups status, high school GPA, and course subject, regardless of dual credit status. However, first-generation status, SAT scores, and the time between courses are not statistically significant predictors. These results suggest that dual credit students are as prepared for subsequent university courses as non-dual-credit students. Nevertheless, academic outcomes differ based on certain factors, which should be considered when designing student success initiatives and allocating resources.</p>

<p>The main contributions of this thesis include two points: firstly, we originally establish Complex STM to semi-analytically calculate the mode profiles of multi-layer planar waveguide terminated with both PML and PRB ; secondly, although CMMM has been generally applied to the simulation of waveguide facets, Bragg gratings, etc[52-53], we for the first time demonstrate that CMMM can also be utilized for the modeling of couplings of radiation field outgoing perpendicularly to the waveguide axis with an incident wave launched in the examples of high-index-contrast waveguide crossings and corners. CMMM is proved to be able to estimate the field profiles and power flows accurately through the validation with FDTD.</p> / <p>Optical waveguides are basic building blocks of high-density photonic integrated circuits and play crucial roles in optical access networks, biomedical system, sensors and so on. Various kinds of dielectric waveguides apply the total internal reflection condition to transmit optical field [9] and even more complicated structures based on waveguide interconnects, Bragg grating, photonic crystals are actively developed by corporations and academic institutes. Especially, the fast developing pace of Metal-Organic Chemical Vapor Deposition (MOCVD), Molecular Beam Epitaxy (MBE) and other fabrication techniques has predicted the increasing complication and thus more advanced function of modern optics integrated circuits. Under such circumstances, convenient and accurate modeling and simulation schemes are necessary for the exploration, designing and optimization of photonic devices, systems and networks before the time-consuming and expensive fabrication process.</p> <p>The thesis summarizes several frequency-domain modeling schemes for the calculation of mode profile or beam propagation in 2D dielectric waveguide. The thesis mainly covers conventional Smooth Transition Method (STM), High Order Finite Difference (HOFD) scheme, Complex STM, and Complex Mode Matching Method (CMMM) based on the 2D waveguide model terminated with Perfect Matching Layer (PML) and Perfect Reflection Boundary (PRB). The mode spectrums and modal patterns obtained from Complex STM are compared with those of HOFD, and the simulation of waveguide crossings and corners with CMMM is validated with Finite-Difference-Time-Domain (FDTD) Method.</p> <p><strong> </strong></p> / Master of Applied Science (MASc)

La tesis estudia cinco formulaciones del método de modos acoplados para analizar guías con medios magnéticos en su interior. La formulación indirecta, de tipo general, se ha aplicado al análisis de desfasadores toroidales obteniéndose resultados similares a los obtenidos mediante un método numérico puro como es el de diferencias finitas. La tesis introduce igualmente una formulación del método de adaptación que junto con el método de modos acoplados permite analizar discontinuidades simples. La combinación de los métodos anteriores con la matriz de dispersión generalizada ha permitido analizar discontinuidades en guías de onda con ferritas transversalmente magnetizadas con discontinuidades en las tres direcciones del sistema de coordenadas.

[pt] Esta tese apresenta um estudo sobre métodos semianalíticos para modelagem de guias de ondas com contornos complexos. Os campos eletromagnéticos dentro de meios não homogêneos e anisotrópicos são resolvidos por meio de harmônicos cilíndricos como base para outras abordagens numéricas, como o método de perturbação regular (RPM), o método de perturbação de material em cavidade (CMPM) e o método de casamento de pontos (PMM). As novas soluções semianalíticas que exploramos aqui podem ser empregadas para a análise de comunicação sem fio ao longo de túneis, bem como para a modelagem de sensores realistas de perfilagem durante a perfuração em problemas geofísicos de baixa frequência. Estudamos o potencial do RPM ao combiná-lo com os princípios da transformação óptica (TO) para analisar um guia de onda coaxial excêntrico preenchido com materiais anisotrópicos. Além disso, estendemos o CMPM clássico proposto por Harrington para lidar com meios anisotrópicos para resolver os números de onda de corte dos campos modais no mesmo guia de onda de maneira aproximada, mas numericamente eficiente. Outra solução de perturbação é proposta combinando as correções de baixa ordem do RPM no CMPM para fornecer correções de alta ordem para os números de onda de corte dos modos suportados pelo guia. Uma formulação matemática de um método semianalítico baseado em PMM para resolver guias de onda preenchidos com meios anisotrópicos e com camadas arbitrárias também é apresentada. Uma versão melhorada deste método é introduzida para modelar estruturas guiadas cilíndricas de múltiplas camadas não circulares. Essas soluções baseadas em casamento de pontos representam boas alternativas para abordagens de força bruta, como métodos de elementos finitos e de diferenças finitas. / [en] This thesis presents a study on semi-analytic methods for modeling waveguides with complex-shaped boundaries. The electromagnetic fields inside inhomogeneous and anisotropic media are solved via cylindrical harmonics as a basis for other numerical approaches, including the regular perturbation method (RPM), the cavity-material perturbation method (CMPM), and the point-matching method (PMM). The novel semi-analytic solutions we have explored here can be employed for the analysis of wireless communication along tunnels and boreholes as well as for the modeling of realistic logging-whiledrilling (LWD) sensors and their environments at low-frequency geophysical problems. We studied the potential of the RPM when combining it with the transformation optics (TO) principles to analyze an eccentric coaxial waveguide filled with anisotropic materials. Furthermore, we have extended the classical CMPM proposed by Harrington to handling anisotropic media for solving the cutoff wavenumbers of the modal fields in the same eccentric coaxial waveguide in an approximated but numerically efficient manner. Another perturbation solution is proposed here and combines the low-order corrections from RPM into the CMPM for providing high-order corrections to the cutoff wavenumbers of the modes supported in this guide. A mathematical formulation of a semi-analytic point-matching method for solving more complex anisotropic-filled waveguides with an arbitrary number of layers is also presented. An improved version of this method is introduced for modeling noncircular multi-layered cylindrical guided structures. Such point-matching-based solutions represent good alternatives to brute-force approaches such as finiteelement and finite-difference methods and motivate further investigations. We present a series of validation results showing the accuracy, efficiency, and potential limitations of the explored methods.

隨著全球化的發展，對外投資不僅在國際經貿中所扮演的角色愈來愈重要，型態也愈來愈多元，呈現出與過去大不相同的特性與風貌。這樣的發展趨勢，再度引起學者對廠商對外投資的影響效果產生興趣。過去有關對外投資影響效果的文獻，主要是以探討對外投資對地主國經濟發展的影響為主，探討對母國或母公司影響的文獻則不多，特別是開發中國家的廠商對外投資對母國影響的研究更是付之闕如。為了彌補此方面文獻之不足，本研究利用台灣製造業1987-2003年的廠商資料來探討廠商對外投資對其技術升級之影響。 廠商對外投資對母國經濟影響的相關議題在台灣一直受到持續的關注，1991年政府開放廠商赴大陸投資之後，該議題更是引發熱切的討論。部分學者擔憂廠商對外投資後將造成國內產業的空洞化；但有另一部分的學者則主張，台灣只要持續技術升級及產業升級就可避免空洞化的危機。有鑑於此，本研究利用三個經濟指標，研發支出、生產力與效率，及技能提升(skill-upgrading)來檢驗不具競爭優勢的產業或附加價值鏈外移，是否有利於台灣進行技術升級。 本研究首先建立了一個理論模型來探討廠商對外投資對其國內研發活動的影響。研究結果顯示，廠商對外投資對其國內的研發支出可能同時產生兩個相反的影響效果，即互補效果及替代效果。互補效果主要來自於廠商對外投資後的「規模擴大效果」，而替代效果的發生則會因廠商對外投資動機之不同，而有不同的來源管道。 本研究實證模型的創新之處在於利用propensity score matching的配對方式搭配difference-in-differences的估計方法來控制實證研究中常會出現的自我選擇誤差(self-selection bias)及互為因果(causality)的問題。本研究採用了四種不同的配對方式來建構對外投資廠商的配對樣本，並發現Nearest available matching within calipers的配對方式可以產生最佳的配對效果，在不犧牲太多樣本數的情況下，顯著縮小對外投資廠商在對外投資前與無對外投資廠商的特性差距。 本研究的實證結果發現，僅管對外投資廠商，特別是赴開發中國家投資的廠商可能對母國的就業造成不利的衝擊，但卻能夠顯著提高母國的研發支出、技術效率及勞工技能，顯示廠商對外投資確實有助於台灣的技術升級。研究結果認為台灣政府應重新思考產業政策及社會福利政策的制定方向，以解決這些新的經濟議題。 / Foreign direct investment has played an increasingly important role in the world economy and, as a consequence, an immense amount of research has investigated its determinants and effects. However, while previous studies have focused on the impact of inward FDI on the host countries, there has been relatively little research on the impact of outward foreign direct investment (OFDI) on the home countries in general, and on developing economies (LDCs) in particular. To fill this gap in the literature, this thesis investigates the home-country effects of the OFDI activity of Taiwanese manufacturing firms. To be specific, the impact of OFDI on the investing firms’ domestic R&D spending, productivity and efficiency, employment and skill-upgrading is examined. A theoretical model is developed to examine the relationship between OFDI and domestic R&D activity. It is shown that OFDI could induce two opposing effects on domestic R&D spending, namely, a complementary effect and a substitution effect. The complementary effect arises mainly due to the “sales-increasing effect” of overseas investment. Substitution effects might arise from different channels depending on FDI motives. Firm-level panel data covering the period 1987-2003 are used in the empirical analysis. The novelty in this thesis is the application of a propensity score matching approach combined with the difference-in-differences method to control for the possible selection bias related to the empirical analysis. Four different matching methods are used to construct matched samples of Taiwan’s OFDI firms. The empirical results reveal that, although Taiwanese overseas investment, especially the investment in LDCs, reduces domestic employment, it stimulates investing firms’ domestic R&D spending, technology efficiency and skill intensity. This implies that while the OFDI activity of Taiwanese firms has brought about a positive effect on their technological upgrading, which is beneficial to the industrial development and resource allocation of the economy, the recent increase in the unemployment in Taiwan could to some extent be attributed to the OFDI activity. It also suggests that the Taiwanese government might need to reconsider its industrial policy as well as social welfare policy in order to deal with these new economic issues.