Fiber tapers have attracted much attention and have been successfully employed in various applications, ranging from resonators, filters, interferometers to sensors. This thesis studies the properties of fiber tapers for the purpose of making tapered-based devices and sensors in aerospace related application where small size and light weight are critical. This thesis includes theoretical derivation and experimental verifications of distributed mode coupling in tapered single-mode fibers (SMFs) with high-resolution optical frequency-domain reflectometry (OFDR) technique. The studies are realized with OFDR through phase detection of a Mach-Zehnder interferometer (MZI), which measures local refractive index change relative to the reference arm. The wavelength shifts converted by the phase change give the group index differences between the fundamental mode and higher-order modes of fiber tapers. The energy re-distribution is observed in Rayleigh backscatter amplitude as a function of fiber length with a ~13µm resolution over the entire fiber taper, and group index difference between core and cladding modes is measured with a spatial resolution of ~2cm by using autocorrelation data processing. The thermal and mechanical properties of fiber tapers have also been characterized with OFDR. The cross-correlation wavelength shift is related to the refractive index change of the modes. It is shown that residual stress induced by the tapering process results in the inhomogeneous thermal property, which can be significantly reduced by an annealing treatment. A fiber taper with a waist diameter of ~6µm has a force sensitivity of ~620.83nm/N, ~500 times higher than that of SMF. Furthermore, polarization-preserving character of tapered polarization-maintaining fibers (PMFs) is evaluated by OFDR-based distributed birefringence along tapered PMFs. Three tapered-based micro-fiber devices have been used as effective mode selecting components to build narrow-linewidth tunable Erbium-doped fiber ring lasers. The fabrication is easy and at a low cost. 1) a tapered fiber tip forms multimode interference mechanism; 2) a two-taper MZI has been demonstrated by splitting/combining the fundamental mode and higher-order modes through fiber tapers and is tuned by bending one taper waist; 3) a novel tunable fiber Fabry-Perot filter, consisting of a hollow-core photonic bandgap fiber and a micro-fiber, is employed in the reflection mode.

The objective of this thesis is to present a theoretical and experimental investigation of the dynamics of micro and nano-electromechanical systems electrothermally tuned and electrostatically actuated, and explore their potential for practical applications. The first part of the dissertation presents the tuning of the frequency of clamped-clamped micro and nano-resonators, straight and curved. These resonators are electrothermally or electrostatically tuned. The effect of geometric parameters on the frequency variation is investigated experimentally and theoretically using a reduced order model based on the Euler-Bernoulli beam theory. High tunability is demonstrated for micro and nano beams, straight and initially curved. The second part discusses the dynamical behavior of a curved (arch) beam electrothermally tuned and electrostatically actuated. We show that the first resonance frequency increases up to twice its fundamental value and the third resonance frequency decreases until getting very close to the first resonance frequency triggering the veering phenomenon. We study experimentally and analytic ally, using the Galerkin procedure, the dynamic behavior of the arch beam. Next, upon changing the electrothermal voltage, the second symmetric natural frequency of the arch is adjusted to near twice, three times, and four times the fundamental natural frequency. This gives rise to a potential two-to-one, three-to-one, and four-to-one autoparametric resonances between the two modes. These resonances are demonstrated experimentally and theoretically. The third part of the dissertation is concerned with the incorporation of the electrothermally tuned and electrostatically actuated microresonators into potential applications: filtering and sensing. First, we experimentally prove an exploitation of the nonlinear softening, hardening, and veering phenomena of an arch beam, to demonstrate a flat, wide, and tunable bandwidth and center frequency by controlling the electrothermal actuation voltage. Second, a pressure sensor based on the convective cooling of the air surrounding an electrothermally heated resonant bridge is demonstrated experimentally. The concept is demonstrated using both straight and arch microbeam resonators driven and sensed electrostatically. The change in the surrounding pressure is shown to be accurately tracked by monitoring the change in the resonance frequency of the structure.

Fiber tapers have attracted much attention and have been successfully employed in various applications, ranging from resonators, filters, interferometers to sensors. This thesis studies the properties of fiber tapers for the purpose of making tapered-based devices and sensors in aerospace related application where small size and light weight are critical. This thesis includes theoretical derivation and experimental verifications of distributed mode coupling in tapered single-mode fibers (SMFs) with high-resolution optical frequency-domain reflectometry (OFDR) technique. The studies are realized with OFDR through phase detection of a Mach-Zehnder interferometer (MZI), which measures local refractive index change relative to the reference arm. The wavelength shifts converted by the phase change give the group index differences between the fundamental mode and higher-order modes of fiber tapers. The energy re-distribution is observed in Rayleigh backscatter amplitude as a function of fiber length with a ~13µm resolution over the entire fiber taper, and group index difference between core and cladding modes is measured with a spatial resolution of ~2cm by using autocorrelation data processing. The thermal and mechanical properties of fiber tapers have also been characterized with OFDR. The cross-correlation wavelength shift is related to the refractive index change of the modes. It is shown that residual stress induced by the tapering process results in the inhomogeneous thermal property, which can be significantly reduced by an annealing treatment. A fiber taper with a waist diameter of ~6µm has a force sensitivity of ~620.83nm/N, ~500 times higher than that of SMF. Furthermore, polarization-preserving character of tapered polarization-maintaining fibers (PMFs) is evaluated by OFDR-based distributed birefringence along tapered PMFs. Three tapered-based micro-fiber devices have been used as effective mode selecting components to build narrow-linewidth tunable Erbium-doped fiber ring lasers. The fabrication is easy and at a low cost. 1) a tapered fiber tip forms multimode interference mechanism; 2) a two-taper MZI has been demonstrated by splitting/combining the fundamental mode and higher-order modes through fiber tapers and is tuned by bending one taper waist; 3) a novel tunable fiber Fabry-Perot filter, consisting of a hollow-core photonic bandgap fiber and a micro-fiber, is employed in the reflection mode.

The objective of this research is to investigate low-complexity, efficient electronic equalizers to increase the data rate and possibly extend the reach of multi-mode fiber (MMF) links. Specifically, we begin by baselining the performance limits of conventional receivers. A robust, in-house mode solver was developed as part of this research and is currently being used by one of the largest fiber manufacturers in their internal R &D work. A detailed performance assessment of the impact of decision feedback equalizers has been conducted using an extensive model of the installed fiber base. The finite-length DFE results were instrumental in influencing the IEEE 802.3aq standardization effort. In particular, we were able to achieve a reach of 220m but the original goal of 300m was unattainable on 99% of the installed fiber base using DFEs of moderate complexity. A low-cost equalizer that has excellent performance, the bi-directional DFE, was applied to the MMF channel for the first time. The performance of the infinite-length BiDFE was characterized without any constraints on the signal-to-noise ratio and on the receiver front-end, as has been previously done in the literature. A new joint optimization technique that helps the finite-length BiDFE perform significantly better than the infinite-length DFE was developed. It was shown that given a finite number of filter coefficients, the BiDFE utilizes them better than the conventional DFE. Furthermore, a reach of 350-400m at a data rate of 10 Gbps was shown to be feasible with equalizers of complexity similar to that currently available. A multiple-input, multiple-output (MIMO) characterization of the MMF channel was developed through the simultaneous use of both center and offset launch together with the two-segment photo-detector. The potential benefit of MIMO processing for MMF links was demonstrated by computing Shannon capacity bounds. It was established that the 2x2 MIMO channel performs about 1.4 dBo better than the conventional 1x1 link at 10 Gbps with practical joint launch. The MIMO scheme still has a performance improvement of 1dBo at 20 Gbps thereby indicating that 20 Gbps transmission is feasible. Performance evaluation of multi-km MMF links was conducted using a comprehensive model that accounts for mode coupling effects. It was determined that ignoring mode coupling can result in under-estimation of the optimum DFE penalty by as much as 1~dBo for 1km links.

Fiber tapers have attracted much attention and have been successfully employed in various applications, ranging from resonators, filters, interferometers to sensors. This thesis studies the properties of fiber tapers for the purpose of making tapered-based devices and sensors in aerospace related application where small size and light weight are critical. This thesis includes theoretical derivation and experimental verifications of distributed mode coupling in tapered single-mode fibers (SMFs) with high-resolution optical frequency-domain reflectometry (OFDR) technique. The studies are realized with OFDR through phase detection of a Mach-Zehnder interferometer (MZI), which measures local refractive index change relative to the reference arm. The wavelength shifts converted by the phase change give the group index differences between the fundamental mode and higher-order modes of fiber tapers. The energy re-distribution is observed in Rayleigh backscatter amplitude as a function of fiber length with a ~13µm resolution over the entire fiber taper, and group index difference between core and cladding modes is measured with a spatial resolution of ~2cm by using autocorrelation data processing. The thermal and mechanical properties of fiber tapers have also been characterized with OFDR. The cross-correlation wavelength shift is related to the refractive index change of the modes. It is shown that residual stress induced by the tapering process results in the inhomogeneous thermal property, which can be significantly reduced by an annealing treatment. A fiber taper with a waist diameter of ~6µm has a force sensitivity of ~620.83nm/N, ~500 times higher than that of SMF. Furthermore, polarization-preserving character of tapered polarization-maintaining fibers (PMFs) is evaluated by OFDR-based distributed birefringence along tapered PMFs. Three tapered-based micro-fiber devices have been used as effective mode selecting components to build narrow-linewidth tunable Erbium-doped fiber ring lasers. The fabrication is easy and at a low cost. 1) a tapered fiber tip forms multimode interference mechanism; 2) a two-taper MZI has been demonstrated by splitting/combining the fundamental mode and higher-order modes through fiber tapers and is tuned by bending one taper waist; 3) a novel tunable fiber Fabry-Perot filter, consisting of a hollow-core photonic bandgap fiber and a micro-fiber, is employed in the reflection mode.

The linear variable stability Transfer Function Simulation Model (TFSM), inspired by the United States Air Force's NF-16D Variable stability In-flight Simulator Test Aircraft (VISTA) and created by Henrik Pettersson, can simulate any desired aircraft. The TFSM represents a non-linear aircraft model with its stability parameters - a collection of gain constants, time constants, damping ratios, and natural frequencies. Stability parameters for aircraft generally fall into two uncoupled modes: longitudinal and lateral-directional. Unfortunately, flight tests using the TFSM exhibited undesired lateral-directional coupling in the longitudinal responses. An S-turn maneuver, formation flight test, and an uncontrolled simulation with an initial bank angle of 60 degrees were the foundation for the investigation to pinpoint the TFSM's errors. The flight tests and subsequent analysis showed that although this model is highly versatile, it has three fundamental problems. First, the original creation of the TFSM incorrectly assumed that the time rate of change for the pitch angle (in the local-horizontal reference frame) is equal to the body-axis pitch-rate for all flight conditions. Second, the TFSM's dynamics do not contain gravity terms. Third, the TFSM cannot generate the angular rates needed in a turn. Integrating the aircraft's pitch, roll, and yaw angles with the equations of motion for aircraft fixed the first problem. Unfortunately, resolving this issue only intensified the second two problems. The results from this thesis show that the last two problems are part of the TFSM and cannot be fixed explicitly. / Master of Science

Numerous mechanical systems contain surfaces in partial or full sliding contact, and therefore, prone to friction-induced vibration instability. These include systems containing mechanical switches, brakes, clutches, gears, rolling contact bearings, journal bearings, robot end-effector grasp and motion, oil drills, etc. The prominent dynamic features of a mechanical system, subject to friction-induced vibration, can be captured by an appropriate equivalent mass-on-belt model. It is the goal of this research to provide a comprehensive study of friction-induced vibrations in mechanical systems by using their equivalent mass-on-belt models. Friction-induced vibration is manifested through three mechanisms termed Stribeck effect, mode-coupling and sprag-slip. Mechanical systems prone to vibrations by one or more of the three mechanisms of instability are considered and studied in detail. The mechanical systems fall into one of two groups. A system in the first group is the pseudo-rigid-body mass-on-belt representation of a compliant bistable linkage mechanism characterized by substantial geometric nonlinearity and nonlinear elasticity. A system in the second group is a mass-on-belt model that accounts for mass-belt contact stiffness. Such a system is excited primarily through mode coupling. In the first group of mechanical systems super and subcritical pitchfork bifurcation as well as Hopf bifurcation are observed. The normal force and spring pre-compression are bifurcation parameters leading to the subcritical pitchfork bifurcation and the belt velocity corresponds to the Hopf bifurcation. It is found that for a low damping and negligible spring nonlinearity, one equilibrium point dominates the steady-state response. Otherwise, the phase plane is split into two separate planes associated with the corresponding fixed point. The boundary is dictated by structural damping and spring nonlinearity. It is shown that the destabilizing mechanism in the bistable mechanisms is the Stribeck effect of friction. The dominant mode of instability for the second group of mechanical system is mode coupling instability. In this group intermittent loss of contact between the mass and the moving belt within a periodic cycle is allowed. Addition of a vibration absorber consisting of a second mass suspended from the first mass by a spring provides effective passive control of friction-induced instability due to mode-coupling. The research concludes with the study of a two mass system in which both masses are in contact with a belt and the friction force is characterized by the three regimes of lubricated contact that include boundary lubrication, mixed boundary and hydrodynamic lubrication and full hydrodynamic lubrication as sliding speed is increased. It is shown that such systems can experience periodic, quasi-periodic and chaotic vibration response.

Although optical fibers and specialty waveguides are the base of majority of today's telecom and light delivery applications, fabrication deformation, nonlinearity and attenuation limit the bandwidth of the data being transmitted or the amount of power carried by these systems. One-way to overcome these limitations without changing the fibers design or fabrication is to engineer the input light in order to excite a certain mode or a group of modes with unique optical properties. Diffractive and micro optics are highly effective for selectively coupling light to specific modes. Using micro optics, mode selective coupling can be achieved through several matching schemes: phase only, phase and amplitude, or phase, amplitude and polarization. The main scope of this work is the design and fabrication of novel optical elements that overcome the limitations of these light delivery systems, as well as the characterization and analysis of their performance both experimentally and using numerical simulation

Auxiliary power supply (APS) plays a key role in ensuring the safe operation of the main circuit elements including gate drivers, sensors, controllers, etc. in medium voltage (MV) silicon carbide (SiC)-based converter systems. Such a converter requires APS to have high insulation capability, low common-mode coupling capacitance (Ccm ), and high-power density. Furthermore, considering the lifetime and simplicity of the auxiliary power supply system design in the MV converter, partial discharge (PD) free and multi-load driving ability are the additional two factors that need to be addressed in the design. However, today’s state-of-the-art products have either low power rating or bulky designs, which does not satisfy the demands. To improve the current designs, this thesis presents a 1 MHz isolated APS design using gallium nitride (GaN) devices with MV insulation reinforcement. By adopting LCCL-LC resonant topology, the proposed APS is able to supply multiple loads simultaneously and realize zero voltage switching (ZVS) at any load conditions. Since high reliability under faulty load conditions is also an important feature for APS in MV converter, the secondary side circuit of APS is designed as a regulated stage. To achieve MV insulation (> 20 kV) as well as low Ccm value (< 5 pF), a current-based transformer with a single turn structure using MV insulation wire is designed. Furthermore, by introducing different insulated materials and shielding structures, the APS is capable to achieve different partial discharge inception voltages (PDIV). In this thesis, the transformer design, resonant converter design, and insulation strategies will be detailly explained and verified by experiment results. Overall, this proposed APS is capable to supply multiple loads simultaneously with a maximum power of 120 W for the sending side and 20 W for each receiving side in a compact form factor. ZVS can be realized regardless of load conditions. Based on different insulation materials, two different receiving sides were built. Both of them can achieve a breakdown voltage of over 20 kV. The air-insulated solution can achieve a PDIV of 6 kV with Ccm of 1.2 pF. The silicone-insulated solution can achieve a PDIV of 17 kV with Ccm of 3.9 pF. / M.S. / Recently, 10 kV silicon carbide (SiC) MOSFET receives strong attention for medium voltage applications. Asit can switch at very high speed, e.g. > 50 V/ns, the converter system can operate at higher switching frequency condition with very small switching losses compared to silicon (Si) IGBT [8]. However, the fast dv/dt noise also creates the common mode current via coupling capacitors distributed inside the converter system, thereby introducing lots of electromagnetic interference (EMI) issues. Such issues typically occur within the gate driver power supplies due to the high dv/dt noises across the input and output of the supply. Therefore, the ultra-small coupling capacitor (<5 pF) of a gate driver power supply is strongly desired.[37] To satisfy the APS demands for high power modular converter system, a solution is proposed in this thesis. This work investigates the design of 1 MHz isolated APS using gallium nitride (GaN) devices with medium voltage insulation reinforcement. By increasing switching frequency, the overall converter size could be reduced dramatically. To achieve a low Ccm value and medium voltage insulation of the system, a current-based transformer with a single turn on the sending side is designed. By adopting LCCL-LC resonant topology, a current source is formed as the output of sending side circuity, so it can drive multiple loads importantly with a maximum of 120 W. At the same time, ZVS can use realized with different load conditions. The receiving side is a regulated stage, so the output voltage can be easily adjusted and it can operate in a load fault condition. Different insulation solutions will be introduced and their effect on Ccm will be discussed. To further reduce Ccm, shielding will be introduced. Overall, this proposed APS can achieve a breakdown voltage of over 20 kV and PDIV up to 16.6 kV with Ccm<5 pF. Besides, multi-load driving ability is able to achieve with a maximum of 120 W. ZVS can be realized. In the end, the experiment results will be provided.

One of the most important and interesting unsolved problems of science is the nature of glassy dynamics and the glass transition. It is quite an old problem, and starting from the early20th century there have been many efforts towards a sound understanding of the phenomenon. As a result, there are a number of theories in the field, which do not entirely contradict each other, but between which the connection is not entirely clear. In the last couple of decades or so, there has been significant progress and currently we do understand many facets of the problem. But a unified theoretical framework for the varied phenomena associated with glassiness is still lacking. Mode-coupling theory, an extreaordinarily popular approach, came from Götze and co-workers in the early eighties. The theory was originally developed to describe the two¬ step decay of the time-dependent correlation functions in a glassy fluid observed near the glass transition temperature(Tg). The theory went beyond that and made a number of quantitative predictions that can be tested in experiments and simulations. However, one of the drawback of the theory is its prediction of a strong ergodic to non-ergodic transition at a temperature TMCT; no such transition exists in real systems at the temperatures at which MCT predicts it. Consequently, the predictions of the theory like the power-law divergences of the transport quantities (e.g., viscosity and relaxation time) fail at low enough temperature and the theory can not be used below TMCT. It is well understood now that MCT is some sort of a mean-field theory of the real phenomenon, and in real systems the transition predicted by MCT is at best avoided due to finite dimensions and activated processes, neither of which is taken into account in standard MCT. Despite its draw backs, even the most severe critic of the theory will be impressed by its power and the predictions in a regime where it works. Even though the non-ergodic transition predicted by the theory is averted, the MCT mechanism for the increase of viscosity and relaxation time is actually at work in real systems. The status of MCT for glass transition is ,perhaps, similar to the Curie-Weiss theory of magnetic phase transition and it will require hard work and perhaps a conceptual breakthrough to go beyond this mean-field picture. Discussion of such a theoretical framework and its possible directions are, however, beyond the scope of this thesis. In the first part of this work, we have extended the mode coupling theory to three important physical situations: the properties of fluids under strong confinement, a sheared fluid and for the growth kinetics of glassy domains. In the second part, we have studied a different class of non equilibrium phenomenon in arrested systems, the fluctuation relations for yielding. In the first chapter, we talk about some general phenomenology of the glass transition problem and a few important concepts in the field. Then we briefly discuss the physical problems to be addressed in detail later on in the thesis followed by a brief account of some of the important existing theories in the field. This list is by no means exhaustive but is intended to give a general idea of the theoretical status of the problem. We conclude this chapter with a detailed derivation of MCT and its successes and failures. This derivation is supposed to serve as a reference for the details of the calculations in later chapters. The second chapter deals with a simple theory of an important problem of lubrication and dynamics of fluid at nanoscopic scales. When a fluid is confined between two smooth surfaces down to a few molecular layers and an normal force is applied on the upper surface, it is found that one layer of fluid gets squeezed out of the geometry at a time. The theory to explain this phenomenon came from Persson and Tosatti. However, due to a mathematical error, the in-plane viscosity term played no role in the original calculation. We re-do this calculation and show that the theory is actually more powerful than was suggested originally by its proponents. In the third chapter, we work out a detailed theory for the dynamics of fluid under strong planar confinement. This theory is based on mode-coupling theory. The walls in our theory enter in terms of an external potential that impose a static inhomogeneous background density. The interaction of the density fluctuation with this static background density makes the fluid sluggish. The theory explains how the fluid under strong confinement can undergo a glassy transition at a higher temperature or lower density than the corresponding bulk fluid as has been found in experiments and simulations. One of the interesting findings of the theory is the three-step relaxation that has also been found in a variety of other cases. The fourth chapter consists of a mode-coupling calculation of a sheared fluid through the microscopic approach first suggested by Zaccarelli et al[J. Phys.: Condens. Matter 14,2413(2002)]. The various assumptions of the theory are quite clear in this approach. The main aim of this calculation is to understand how FDR enters with in the theory. The only new result is the modified form of Yvon-Born-Green(YBG) equations for a sheared fluid. Then we extend the theory for the case of a confined fluid under steady shear and show that a confined fluid will show shear thinning at a much lower shear rate than the bulk fluid. When a system is quenched past a phase transition point, phase ordering kinetics begins. The properties of the system show “aging” with time, and the characteristic length scale of the quenched system grows as one waits. The analogous question for glasses has also been asked in the contexts of various numerical and experimental works. We formulate a theory in chapter five for rationalizing these findings. We find that MCT, surprisingly, offers an answer to this key question in glass forming liquids. The challenge of this theory is that care must be taken in using some equilibrium relations like the fluctuation-dissipation relation(FDR), which is one of the key steps in most of the derivations of MCT. We find that the qualitative, and some times even the quantitative, picture is in agreement with numerical findings. A similar calculation for the spin-glass case also predicts increase of the correlation volume with the waiting time, but with a smaller exponent than the structural glass case. We extended this theory to the case of shear and find that shear cuts off the growth of the length-scale of glassy correlations when the waiting time becomes of the order of the inverse shear rate. For the case of sheared fluid, if we take the limit of the infinite waiting time, the system will reach a steady state. Then, the resulting theory will describe a fluid in sheared steady state. The advantage of this theory over the existing mode-coupling theories for a sheared fluid is that FDR has not been used in any stage. This is an important development since the sheared steady state is driven away from equilibrium. Interestingly, the theory captures a suitably-defined effective temperature and gives results that are consistent with numerical experiments of steady state fluids(both glass and granular materials). We give the details of a theoretical model for jamming and large deviations in micellar gel in the sixth chapter. This theory is motivated by experiments. Through the main ingredient of the attachment-detachment kinetics and some simple rules for the dynamics, the theory is capable of capturing all the experimental findings. The novel prediction of this work is that in a certain parameter range, the fluctuation relations may be violated although the large deviation function exists. We argue that a wider class of physical systems can be understood in terms of the present theory. In the final chapter, we summarize the problems studied in this thesis and point out some future directions.