<p>In this study, we developed and improved the numerical mode matching (NMM) method which has previously been shown to be a fast and robust semi-analytical solver to investigate the propagation of electromagnetic (EM) waves in an isotropic layered medium. The applicable models, such as cylindrical waveguide, optical fiber, and borehole with earth geological formation, are generally modeled as an axisymmetric structure which is an orthogonal-plano-cylindrically layered (OPCL) medium consisting of materials stratified planarly and layered concentrically in the orthogonal directions.</p><p>In this report, several important improvements have been made to extend applications of this efficient solver to the anisotropic OCPL medium. The formulas for anisotropic media with three different diagonal elements in the cylindrical coordinate system are deduced to expand its application to more general materials. The perfectly matched layer (PML) is incorporated along the radial direction as an absorbing boundary condition (ABC) to make the NMM method more accurate and efficient for wave diffusion problems in unbounded media and applicable to scattering problems with lossless media. We manipulate the weak form of Maxwell's equations and impose the correct boundary conditions at the cylindrical axis to solve the singularity problem which is ignored by all previous researchers. The spectral element method (SEM) is introduced to more efficiently compute the eigenmodes of higher accuracy with less unknowns, achieving a faster mode matching procedure between different horizontal layers. We also prove the relationship of the field between opposite mode indices for different types of excitations, which can reduce the computational time by half. The formulas for computing EM fields excited by an electric or magnetic dipole located at any position with an arbitrary orientation are deduced. And the excitation are generalized to line and surface current sources which can extend the application of NMM to the simulations of controlled source electromagnetic techniques. Numerical simulations have demonstrated the efficiency and accuracy of this method.</p><p>Finally, the improved numerical mode matching (NMM) method is introduced to efficiently compute the electromagnetic response of the induction tool from orthogonal transverse hydraulic fractures in open or cased boreholes in hydrocarbon exploration. The hydraulic fracture is modeled as a slim circular disk which is symmetric with respect to the borehole axis and filled with electrically conductive or magnetic proppant. The NMM solver is first validated by comparing the normalized secondary field with experimental measurements and a commercial software. Then we analyze quantitatively the induction response sensitivity of the fracture with different parameters, such as length, conductivity and permeability of the filled proppant, to evaluate the effectiveness of the induction logging tool for fracture detection and mapping. Casings with different thicknesses, conductivities and permeabilities are modeled together with the fractures in boreholes to investigate their effects for fracture detection. It reveals that the normalized secondary field will not be weakened at low frequencies, ensuring the induction tool is still applicable for fracture detection, though the attenuation of electromagnetic field through the casing is significant. A hybrid approach combining the NMM method and BCGS-FFT solver based integral equation has been proposed to efficiently simulate the open or cased borehole with tilted fractures which is a non-axisymmetric model.</p> / Dissertation

This thesis, for the first time in the literature, presents an automatic mode-matching system that uses the phase relationships between the residual quadrature and drive signals in a gyroscope to achieve and maintain the frequency matching condition, and also the system allows controlling the system bandwidth by adjusting the closed loop parameters of the sense mode controller, independently from the mechanical sensor bandwidth. There are two mode-matching methods, using the proposed mode-matching system, presented in this thesis. In the first method, the frequency matching between the resonance modes of the gyroscope is automatically accomplished by changing the proof mass potential. The main motivation behind the first method is to tune the sense mode resonance frequency with respect to the drive mode resonance frequency using the electrostatic tuning capability of the sense mode. In the second method, the mode-matched gyroscope operation is accomplished by using dedicated frequency tuning electrodes that only provides a capability of tuning the sense mode resonance frequency generating an electrostatic spring effect on the sense frame, independently from the proof mass potential. This study mainly focuses on the second method because the proof mass potential variation is not desired during the gyroscope operation since the proof mass potential directly affects the drive and sense mode dynamics of the gyroscope. Therefore, a single-mass fully-decoupled gyroscope including the dedicated frequency tuning electrodes are designed. To identify mode shapes and mode frequencies of the designed gyroscope, FEM simulations are performed. The designed gyroscopes are fabricated using SOI-based SOG process. The fabrication imperfections are clarified during the formation of the structural layer of the gyroscope. Next, the closed loop controllers are designed for the drive amplitude control, sense force-feedback, quadrature cancellation, and mode-matching regarding the phase relationship between the quadrature and drive signals. Mode-matching is achieved by using a closed loop controller that provides a DC tuning potential. The mode-matching system consisting of vacuum packaged sensor, drive amplitude control, sense force-feedback, quadrature cancellation, and mode-matching modules is implemented on a printed circuit board (PCB), and then the system level tests are performed. Tests illustrate that the mode-matching system operates in a desired manner. Test results demonstrate that the performances of the studied MEMS gyroscopes are improved up to 2.6 times in bias instability and 2 times in ARW under the mode-matched condition compared to the mismatched (~200 Hz) condition, reaching down to 0.73 &deg / /hr and 0.024 &deg / /&radic / hr, respectively. At the mode-matched gyroscope operation, the better performance is obtained to be bias instability of 0.87

The scalability and cost of microelectromechanical systems (MEMS) optical switches are now the important factors driving the development of MEMS optical switches technology. The employment of MEMS in the design and fabrication of optical switches through the use of micromachining fabricated micromirrors expands the capability and integrity of optical backbone networks. The focus of this dissertation is on the design, fabrication, and implementation of a new type of MEMS optical switch that combines the advantages of both 2-D and 3-D MEMS switch architectures. This research presents a new digital MEMS switch architecture for 1×N and N×N optical switches. The architecture is based on a new microassembled smart 3-D rotating inclined micromirror (3DRIM). The 3DRIM is the key device in the new switch architectures. The 3DRIM was constructed through a microassembly process using a passive microgripper, key, and inter-lock (PMKIL) assembly system. An electrostatic micromotor was chosen as the actuator for the 3DRIM since it offers continuous rotation as well as small, precise step motions with excellent repeatability that can achieve repeatable alignment with minimum optical insertion loss between the input and output ports of the switch. In the first 3DRIM prototype, a 200×280 microns micromirror was assembled on the top of the electrostatic micromotor and was supported through two vertical support posts. The assembly technique was then modified so that the second prototype can support micromirrors with dimensions up to 400×400 microns. Both prototypes of the 3DRIM are rigid and stable during operation. Also, rotor pole shaping (RPS) design technique was introduced to optimally reshape the physical dimensions of the rotor pole in order to maximize the generated motive torque of the micromotor and minimize the required driving voltage signal. The targeted performance of the 3DRIM was achieved after several PolyMUMPs fabrication runs. The new switch architecture is neither 2-D nor 3-D. Since it is composed of two layers, it can be considered 2.5-D. The new switch overcomes many of the limitations of current traditional 2-D MEMS switches, such as limited scalability and large variations in the insertion loss across output ports. The 1×N MEMS switch fabric has the advantage of being digitally operated. It uses only one 3DRIM to switch the light signal from the input port to any output port. The symmetry employed in the switch design gives it the ability to incorporate a large number of output ports with uniform insertion losses over all output channels, which is not possible with any available 2-D or 3-D MEMS switch architectures. The second switch that employs the 3DRIM is an N×N optical cross-connect (OXC) switch. The design of an N×N OXC uses only 2N of the 3DRIM, which is significantly smaller than the N×N switching micromirrors used in 2-D MEMS architecture. The new N×N architecture is useful for a medium-sized OXC and is simpler than 3-D architecture. A natural extension of the 3DRIM will be to extend its application into more complex optical signal processing, i.e., wavelength-selective switch. A grating structures have been selected to explore the selectivity of the switch. For this reason, we proposed that the surface of the micromirror being replaced by a suitable gratings instead of the flat reflective surface. Thus, this research has developed a rigorous formulation of the electromagnetic scattered near-field from a general-shaped finite gratings in a perfect conducting plane. The formulation utilizes a Fourier-transform representation of the scattered field for the rapid convergence in the upper half-space and the staircase approximation to represent the field in the general-shaped groove. This method provides a solution for the scattered near-field from the groove and hence is considered an essential design tool for near-field manipulation in optical devices. Furthermore, it is applicable for multiple grooves with different profiles and different spacings. Each groove can be filled with an arbitrary material and can take any cross-sectional profile, yet the solution is rigorous because of the rigorous formulations of the fields in the upper-half space and the groove reigns. The efficient formulation of the coefficient matrix results in a banded-matrix form for an efficient and time-saving solution.

Terahertz waveguides are the focus of considerable research interest due to their potential for sensing, imaging and communications applications. Two of the most promising designs are the metal wire waveguide and the parallel-plate waveguide. The metal wire waveguide exhibits excellent low loss and low dispersion characteristics. However, the radiation is only weakly coupled to the wire and the beam extends a great distance from the waveguide, which can lead to high bending loss. In my research I show that this large beam extent also gives a high degree of flexibility in the geometry required to couple radiation into the waveguide or between waveguide sections. I also show that the traditional formalism of bending loss is incomplete, and that there is an optimum radius of curvature to reduce loss. The relationship between the beam extent and the radius of the wire presents the possibility of a tapered waveguide to confine the radiation as it propagates. I here present experimental data and simulations results to verify this subwavelength confinement at the tip of a tapered metal wire waveguide, which is of great interest for near-field imaging applications. The parallel-plate waveguide is another design frequently employed due to its low loss and low dispersion characteristics. Resonant structures may also be easily incorporated into the waveguide for sensing and filtering applications. One such structure is a single rectangular groove, which serves as a notch filter with a very narrow linewidth when the transverse-electric (TE) mode of the waveguide is excited, though its physical origin is poorly understood. In this work I present a detailed experimental and theoretical study of the rectangular resonant cavity in a TE-mode parallel-plate waveguide, particularly with respect to its potential as a microfluidic refractive index sensor. This study is extended to include the possibility of two grooves, in both coupled and non-coupled geometries, and their efficacy as multichannel or high-resolution single-channel microfluidic sensors.

The scalability and cost of microelectromechanical systems (MEMS) optical switches are now the important factors driving the development of MEMS optical switches technology. The employment of MEMS in the design and fabrication of optical switches through the use of micromachining fabricated micromirrors expands the capability and integrity of optical backbone networks. The focus of this dissertation is on the design, fabrication, and implementation of a new type of MEMS optical switch that combines the advantages of both 2-D and 3-D MEMS switch architectures. This research presents a new digital MEMS switch architecture for 1×N and N×N optical switches. The architecture is based on a new microassembled smart 3-D rotating inclined micromirror (3DRIM). The 3DRIM is the key device in the new switch architectures. The 3DRIM was constructed through a microassembly process using a passive microgripper, key, and inter-lock (PMKIL) assembly system. An electrostatic micromotor was chosen as the actuator for the 3DRIM since it offers continuous rotation as well as small, precise step motions with excellent repeatability that can achieve repeatable alignment with minimum optical insertion loss between the input and output ports of the switch. In the first 3DRIM prototype, a 200×280 microns micromirror was assembled on the top of the electrostatic micromotor and was supported through two vertical support posts. The assembly technique was then modified so that the second prototype can support micromirrors with dimensions up to 400×400 microns. Both prototypes of the 3DRIM are rigid and stable during operation. Also, rotor pole shaping (RPS) design technique was introduced to optimally reshape the physical dimensions of the rotor pole in order to maximize the generated motive torque of the micromotor and minimize the required driving voltage signal. The targeted performance of the 3DRIM was achieved after several PolyMUMPs fabrication runs. The new switch architecture is neither 2-D nor 3-D. Since it is composed of two layers, it can be considered 2.5-D. The new switch overcomes many of the limitations of current traditional 2-D MEMS switches, such as limited scalability and large variations in the insertion loss across output ports. The 1×N MEMS switch fabric has the advantage of being digitally operated. It uses only one 3DRIM to switch the light signal from the input port to any output port. The symmetry employed in the switch design gives it the ability to incorporate a large number of output ports with uniform insertion losses over all output channels, which is not possible with any available 2-D or 3-D MEMS switch architectures. The second switch that employs the 3DRIM is an N×N optical cross-connect (OXC) switch. The design of an N×N OXC uses only 2N of the 3DRIM, which is significantly smaller than the N×N switching micromirrors used in 2-D MEMS architecture. The new N×N architecture is useful for a medium-sized OXC and is simpler than 3-D architecture. A natural extension of the 3DRIM will be to extend its application into more complex optical signal processing, i.e., wavelength-selective switch. A grating structures have been selected to explore the selectivity of the switch. For this reason, we proposed that the surface of the micromirror being replaced by a suitable gratings instead of the flat reflective surface. Thus, this research has developed a rigorous formulation of the electromagnetic scattered near-field from a general-shaped finite gratings in a perfect conducting plane. The formulation utilizes a Fourier-transform representation of the scattered field for the rapid convergence in the upper half-space and the staircase approximation to represent the field in the general-shaped groove. This method provides a solution for the scattered near-field from the groove and hence is considered an essential design tool for near-field manipulation in optical devices. Furthermore, it is applicable for multiple grooves with different profiles and different spacings. Each groove can be filled with an arbitrary material and can take any cross-sectional profile, yet the solution is rigorous because of the rigorous formulations of the fields in the upper-half space and the groove reigns. The efficient formulation of the coefficient matrix results in a banded-matrix form for an efficient and time-saving solution.

The objective of our research is to develop system architectures and CMOS circuits that interface with high-Q silicon microgyroscopes to implement navigation-grade angular rate sensors. The MEMS sensor used in this work is an in-plane bulk-micromachined mode-matched tuning fork gyroscope (M² – TFG ), fabricated on silicon-on-insulator substrate. The use of CMOS transimpedance amplifiers (TIA) as front-ends in high-Q MEMS resonant sensors is explored. A T-network TIA is proposed as the front-end for resonant capacitive detection. The T-TIA provides on-chip transimpedance gains of 25MΩ, has a measured capacitive resolution of 0.02aF /√Hz at 15kHz, a dynamic range of 104dB in a bandwidth of 10Hz and consumes 400μW of power. A second contribution is the development of an automated scheme to adaptively bias the mechanical structure, such that the sensor is operated in the mode-matched condition. Mode-matching leverages the inherently high quality factors of the microgyroscope, resulting in significant improvement in the Brownian noise floor, electronic noise, sensitivity and bias drift of the microsensor. We developed a novel architecture that utilizes the often ignored residual quadrature error in a gyroscope to achieve and maintain perfect mode-matching (i.e.0Hz split between the drive and sense mode frequencies), as well as electronically control the sensor bandwidth. A CMOS implementation is developed that allows mode-matching of the drive and sense frequencies of a gyroscope at a fraction of the time taken by current state of-the-art techniques. Further, this mode-matching technique allows for maintaining a controlled separation between the drive and sense resonant frequencies, providing a means of increasing sensor bandwidth and dynamic range. The mode-matching CMOS IC, implemented in a 0.5μm 2P3M process, and control algorithm have been interfaced with a 60μm thick M2−TFG to implement an angular rate sensor with bias drift as low as 0.1°/hr ℃ the lowest recorded to date for a silicon MEMS gyro.

[pt] Células de medição (MCs) são amplamente utilizadas na engenharia de micro-ondas para a caracterização eletromagnética dos materiais. Neste trabalho, apresentamos uma formulação baseada na técnica de casamento de modos (MMT) para a caracterização eletromagnética de MCs para materiais anisotrópicos uniaxiais. Apresentamos e validamos uma técnica para modelagem de MCs com uma e duas portas por meio da de matrizes de espalhamento generalizadas (GSMs) extraídas do MMT. Uma vez que as soluções fechadas (isto é, não numéricas) são usadas para calcular as integrais de acoplamento das GSMs, a presente abordagem é uma alternativa computacionalmente eficiente para modelar MCs quando comparada às técnicas usuais de força bruta numérica (tais como soluções baseadas em elementos, volumes, ou diferenças finitas). Um algoritmo de inversão também é apresentado para recuperar os parâmetros constitutivos de meios complexos (materiais com perdas e anisotrópicos). Diferentemente da maioria dos trabalhos que utilizam métodos semi-analíticos, a novidade do presente método consiste em considerar MCs com seção transversal grande frente ao comprimento de onda, em vários modos podem ser progagantes. Apresentamos uma série de resultados numéricos que mostram que a técnica de inversão apresentada neste estudo pode recuperar adequadamente os parâmetros constitutivos de um material de amostra, uma vez que os parâmetros de espalhamento da MC são conhecidos. / [en] Measurement cells (MCs) are widely used in microwave engineering for the electromagnetic characterization of materials. In this work, we present a mode-matching technique (MMT) formulation for the electromagnetic characterization of MCs for uniaxial anisotropic materials. We present and validate a technique for modeling MCs with one- and two-ports via generalized scattering matrices (GSMs) extracted from the MMT. Since closed-form solutions are used for computing the coupling integrals of the GSMs, the present approach is a computationally-efficient alternative to modeling MCs when compared to usual brutal-force techniques (such as finite-elements, finitevolumes, and finite-difference solutions). An inverse algorithm is also presented to retrieve the constitutive parameters of complex media (lossy and anisotropic materials). Differently from the majority of the works using semi-analytical methods, the novelty of the present method rely on considering overmoded MCs. We present a series of numerical results that show that the inversion technique presented herein can properly retrieve the constitutive parameters of a sample material once the MC scattering parameters are known.

In this work, waveguides with simultaneous negative dielectric permittivity and magnetic permeability, otherwise known as left-handed waveguides, are investigated. An approach of formulating and solving an eigenvalue problem with finite element method resulting in the dispersion relation of the waveguides is adopted in the analysis. Detailed methodology of one-dimensional scalar and two-dimensional vector finite element formulation for the analysis of grounded slab and arbitrary shaped waveguides is presented. Based on the analysis, for waveguides with conventional media, excellent agreement of results is observed between the finite element approach and the traditional approach. The method is then applied to analyze left-handed waveguides and anomalous dispersion of modes is found. The discontinuity structure of a left-handed waveguide sandwiched between two conventional dielectric slab waveguides is analyzed using mode matching technique and the results are discussed based on the inherent nature of the materials. The scattering characteristics of a parallel plate waveguide partially filled with left-handed and conventional media are also analyzed using finite element method with eigenfunction expansion technique.

[pt] Guias de onda são amplamente utilizados na engenharia de telecomunicações para a transmissão de sinais e construção de filtros e outros dispositivos de micro-ondas. Neste trabalho, apresentamos uma formulação baseada na técnica de casamento de modos (MMT) para a análise de descontinuidades em guias de ondas cilíndricos causadas por curvaturas no eixo longitudinal da linha de transmissão. Apresentamos e validamos uma técnica para análise modal de guias de ondas curvos através da aproximação da curvatura por uma sucessão de superfícies oblíquas por meio de suas matrizes de espalhamento generalizadas (GSMs) extraídas do MMT. A presente abordagem é uma alternativa computacionalmente eficiente para modelar curvaturas em guias de ondas cilíndricos quando comparada às técnicas usuais de força bruta numérica (tais como soluções baseadas em elementos, volumes, ou diferenças finitas). Um algoritmo é apresentado para calcular os elementos da matriz GSM para diferentes configurações de junções de guias de onda. A novidade do presente método consiste em considerar a projeção dos campos eletromagnéticos em superfícies oblíquas para a aplicação do MMT. Apresentamos uma série de resultados numéricos que mostram que a técnica apresentada neste estudo pode garantir resultados com boa acurácia e precisão ao realizar a análise do comportamento modal dos campos eletromagnéticos em descontinuidades provocados por curvaturas. / [en] Waveguides are widely used in telecommunications engineering for transmitting signals and manufacturing filters and other devices in the microwave applications. In this work, we present a formulation based on the mode-matching technique (MMT) for the analysis of discontinuities in cylindrical waveguides caused by curvatures in the longitudinal axis of the transmission line. We present and validate a technique for modal analysis of curved waveguides by approximating the curvature in a succession of oblique surfaces by means of their generalized scattering matrices (GSMs) extracted from the MMT. The present approach is a computationally efficient alternative for modeling curvature in cylindrical waveguides when compared to usual numerical brute force techniques (such as element-based, volumebased, or finite difference solutions). An algorithm is presented to compute the GSM matrix elements for different configurations of waveguide junctions. The novelty of the present method consists in considering the projection of electromagnetic fields onto oblique surfaces for the application of MMT. We present a series of numerical results that show that the technique presented in this study can guarantee results with good accuracy and precision when performing the analysis of the modal behavior of electromagnetic fields at discontinuities caused by curvatures.

[pt] Esta tese apresenta uma solução semianalítica para a modelagem eletromagnética de estruturas guiadas com simetria cilíndrica no domínio da frequência. A técnica apresentada permite que uma classe abrangente de guias de ondas, acopladores, filtros, entre outros, sejam projetados de forma acurada e com custo computacional muito pequeno em termos de tempo de processamento e memória quando comparado com outras técnicas baseadas em diferenças finitas ou elementos finitos. Neste trabalho, a modelagem de estruturas guiadas relativamente complexas foi realizada usando uma decomposição em subdomínios computacionais nos quais conhecemos uma solução analítica para o problema de contorno associado. Em uma segunda etapa, as condições de contorno de acoplamento entre os subdomínios foram então impostas por meio da conservação da reação e o formalismo do método do casamento de modos. Como consequência, obtemos uma solução analítica para o problema da conexão entre guias de ondas compostos por seções circulares e coaxiais acopladas. Ao nosso conhecimento, a formulação matemática desenvolvida para o acoplamento entre subdomínios circular e coaxial é inédita, e unifica vários modelos de acoplamento modais conhecidos até então sob um formalismo generalizado. Apresentamos uma série de resultados de validação que demonstram que a técnica introduzida neste trabalho permite modelar de forma acurada e eficiente uma vasta classe de estruturas guiadas. Em adição, uma formulação matemática complementar foi introduzida para a descrição do acoplamento ortogonal entre as estruturas circulares e coaxiais acopladas com guias retangulares. Uma descrição criteriosa sobre as dificuldades matemáticas e suas consequências para a implementação numérica é também apresentada. / [en] This dissertation presents a semi-analytic solution for the electromagnetic wave modeling in guided structures with cylindrical symmetry in the frequency domain. The technique presented herein allows that a comprehensive class of waveguides, couplers, filters, among others microwave devices, to be designed accurately, and with relatively low computational cost in terms of CPU processing time and RAM memory when compared to other numerical methods based on the finite-difference or finite-element discretization of Maxwell’s equations. In this work, the electromagnetic modeling of a relatively complex guided structure was performed by using successions of computational subdomain decompositions, in which we know an analytic solution for each associated subdomain boundary problem. In a second step, the coupling boundary conditions between the subdomains were then enforced by means of the conservation of the reaction and the formalism of the mode-matching technique. As a result, we were able to obtain an analytical solution for the coupling problem of the waveguide composed by circular and coaxial sections. To the best of our knowledge, the mathematical formulation developed for the coupling between circular and coaxial subdomains is an original unprecedented scientific contribution, and it unifies several modal-coupling models known hitherto under a generalized formalism. We present a series of validation results showing that the technique introduced in this work can model accurately and efficiently a comprehensive class of electromagnetic waveguide devices. In addition, a supplementary mathematical formulation was introduced for describing the orthogonal coupling between the circular/coaxial structures with rectangular waveguides insert ports. A painstaking description of the mathematical difficulties and their consequences for numerical implementation is presented as well.