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Alle optischen Systeme haben den gleichen Zweck: Sie manipulieren Eigenschaften des Lichts, durch Interaktion mit Materie. In dieser Arbeit werden zwei wichtige Teilaspekte aus diesem Kontext untersucht, im linearen und im nicht-linearen Bereich. In Teil I werden die bekannten Bragg-Reflexionen in neuem Licht betrachtet. Bragg Reflexion findet statt, wenn Licht mit einem periodischen Medium interagiert. Die Bragg-Bedingung verknüpft den Gitterabstand in einem Kristall mit der Wellenlänge, die von ihm reflektiert wird. In dieser Arbeit werden die Bragg Reflexionen in gewellten Wellenleitern untersucht. Es wird gezeigt, dass die Bragg-Bedingung nicht ausreicht, um die Streuung in diesen Wellenleitern zu verstehen. Es wird numerisch und analytisch demonstriert, dass unebene Ränder eine neue Reflexionsbedingung schaffen, die über das einfache Bragg-Bild hinausgeht. Dieser Streueffekt, der Square Gradient Bragg-Mechanismus ist aus statistischen Streuansätzen bekannt. Er hängt mit der Krüummung des Randes zusammen und hat einen starken Einfluss auf die Wellenleitung in diesen Systemen. In dieser Arbeit wird die erste allgemeine Theorie für den Square Gradient Bragg Streumechanismus vorgestellt, die es ermöglicht, Voraussagen für einzelne Wellenleiter mit beliebig deformierten Rändern zu treffen. Eine weitere wichtige Eigenschaft des Lichts wird in Teil II dieser Arbeit untersucht: Die Verschränkung zwischen zwei Photonen. Verschränkung ist ein intuitiv nicht verständliches Phänomen, weil es in der uns umgebenden klassischen Welt kein Analogon hat. Insbesondere verletzt es unsere implizite Annahme eines lokalen Realismus, weil voneinander entfernte Teilchen scheinbar instantan miteinander wechselwirken können. In dieser Arbeit wird eine neue und verstimmbare Quelle für verschränkte Photonen entworfen. Die Photonenpaare werden in nicht-linearen Kristallen erzeugt, aber ihre Verschränkung wird rein geometrisch erzwungen. Dieser geometrische Ansatz erlaubt es, die Frequenz der Photonen einzustellen. Hier übertrifft diese neue Quelle ihre Vorgänger, die ausführlich besprochen werden. Die Verschränkung der erzeugten Photonen wird experimentell nachgewiesen. / Any optical experiment, any optical technology is only about one thing: Manipulating the properties of light through interaction with matter. This thesis will address two important issues in this broad context, in the linear and in the non-linear regime. In Part I, the well-known Bragg reflection is revised. Bragg reflection takes place whenever light interacts with a periodic structure. The famous Bragg condition relates the lattice spacing in a crystal to the wavelength which is effectively reflected by that lattice. In this thesis the Bragg reflection in dielectric waveguides is investigated. It is shown that the Bragg condition is not sufficient to describe the scattering situation in waveguides with corrugated boundaries. It is demonstrated, analytically and numerically, that corrugated boundaries cause a new type of reflection condition, which goes beyond the Bragg picture. This scattering mechanism, the Square Gradient Bragg Scattering, is known from statistical scattering approaches. It is connected to the curvature of the boundary and has a strong influence on the wave propagation in these systems. Here the first general theory for Square Gradient Bragg Scattering is presented, which allows for making predictions for single corrugated waveguides with arbitrary boundaries. Another important property of light is investigated in Part II of this thesis: The entanglement of two photons. Entanglement is a counter-intuitive phenomenon, because it has no classical analogy. It especially violates our assumption of local realism, because distant particles seemingly act on each other instantaneously. In this thesis a new tunable and portable source of photon pairs is designed. The photon pairs are created in non-linear crystals, but their entanglement is enforced in a purely geometrical manner. This geometrical approach makes the setup tunable. This is where the new design supersedes its predecessor, which will be discussed in detail. The entanglement of the generated photons is demonstrated experimentally.

Several microwave devices and antennas that are based on negative-refractive-index transmission-line (NRI-TL) metamaterials are presented in this thesis, which exhibit superior performance features compared to their conventional counterparts. These are a Wilkinson balun, a 1:4 series power divider, a four-element printed dipole array, a leaky-wave antenna, and an electrically small folded-monopole antenna. The Wilkinson balun employs +90° and −90° NRI-TL metamaterial lines at the output branches of a Wilkinson divider, to achieve a six-fold increase in the measured differential output phase bandwidth compared to that of an analogous balun employing transmission lines, while occupying only 55% of the area. The 1:4 series power divider comprises four non-radiating 0° NRI-TL metamaterial lines, each with a compact length of λ0/8, to provide equal power split to all four output ports. Compared to a conventional series power divider employing one-wavelength long transmission lines, the metamaterial divider provides a 154% increase in the measured through-power bandwidth, while occupying only 54% of the area. The metamaterial series power dividing concept is also applied to a four-element fully-printed dipole array that is designed to radiate at broadside, in order to demonstrate that the array exhibits reduced beam squinting characteristics. It is shown that the metamaterial-fed array has a measured scan-angle bandwidth that is 173% greater than an array that is fed using a conventional low-pass loaded line. The reduced-beam squinting property that NRI-TL metamaterial lines offer is subsequently exploited to create a leaky-wave antenna that radiates a near-fixed beam in the forward +45° direction, with an average measured beam squint of only 0.031°/MHz. This is achieved by operating the antenna in the upper right-handed band where the phase and group velocities are the closest to the speed of light. Finally, an electrically small antenna comprising four 0° NRI-TL metamaterial unit cells is presented which supports a predominantly even-mode current, thus enabling it to be modeled as a multi-arm folded monopole. This significantly increases its radiation resistance, which allows it to be matched to 50 Ω, while maintaining a high measured efficiency of 70%.

The majority of signals, that need to be processed, are analog, which are continuous and can take an infinite number of values at any time instant. Precision of the analog signals are limited due to influence of distortion which leads to the use of digital signals for better performance and cost. Analog to Digital Converter (ADC), converts the continuous time signal to the discrete time signal. Most A/D converters are classified into two categories according to their sampling technique: nyquist rate ADC and oversampled ADC. The nyquist rate ADC operates at the sample frequency equal to twice the base-band frequency, whereas the oversampled ADC operates at the sample frequency greater than the nyquist frequency. The sigma delta ADC using the oversampling technique provides high resolution, low to medium speed, relaxed anti-aliasing requirements and various options for reconfiguration. On the contrary, resolution of the sigma delta ADC can be traded for high speed operation. Data sampling techniques plays a vital role in the sigma delta modulator and can be classified into discrete time sampling and continuous time sampling. Furthermore, the discrete time sampling technique can be implemented using the switched-capacitor (SC) integrator and the switched-current (SI) integrator circuits. The SC integrator technique provides high accuracy but occupies a larger area. Unlike the SC integrator, the SI integrator offers low input impedance and parasitic capacitance. This makes the SI integrator suitable for low supply voltage and high frequency applications. From a detailed literature study on the multi-bit sigma delta modulator, it is analyzed that, theneeds a highly linear digital to analogue converter (DAC) in its feedback path. The sigma delta modulators are very sensitive to linearity of the DAC which can degrade the performance without any attenuation. For this purpose T.C. Leslie and B. Singh proposed a Hybrid architecture using the multi-bit quantizer with a single bit DAC. The most significant bit is fed back to the DAC while the least significant bits are omitted. This omission requires a complex digital calibration to complete the analog to digital conversion process which is a small price to pay compared to the linearity requirements of the DAC. This project work describes the design of High-Speed Hybrid Current modeModulator with a single bit feedback DAC at the speed of 2.56GHz in a state-of-the-art 65 nm CMOS process. It comprises of both the analog and digital processing blocks, using T.C. Leslie and B. Singh architecture with the switched current integrator data sampling technique for low voltage, high speed operation. The whole system is verified mathematically in matlab and implemented using signal flow graphs and verilog a code. The analog blocks like switched current integrator, flash ADC and DAC are implemented in transistor level using a 65 nm CMOS technology and the functionality of each block is verified. Dynamic performance parameters such as SNR, SNDR and SFDR for different levels of abstraction matches the mathematical model performance characteristics.

Several microwave devices and antennas that are based on negative-refractive-index transmission-line (NRI-TL) metamaterials are presented in this thesis, which exhibit superior performance features compared to their conventional counterparts. These are a Wilkinson balun, a 1:4 series power divider, a four-element printed dipole array, a leaky-wave antenna, and an electrically small folded-monopole antenna. The Wilkinson balun employs +90° and −90° NRI-TL metamaterial lines at the output branches of a Wilkinson divider, to achieve a six-fold increase in the measured differential output phase bandwidth compared to that of an analogous balun employing transmission lines, while occupying only 55% of the area. The 1:4 series power divider comprises four non-radiating 0° NRI-TL metamaterial lines, each with a compact length of λ0/8, to provide equal power split to all four output ports. Compared to a conventional series power divider employing one-wavelength long transmission lines, the metamaterial divider provides a 154% increase in the measured through-power bandwidth, while occupying only 54% of the area. The metamaterial series power dividing concept is also applied to a four-element fully-printed dipole array that is designed to radiate at broadside, in order to demonstrate that the array exhibits reduced beam squinting characteristics. It is shown that the metamaterial-fed array has a measured scan-angle bandwidth that is 173% greater than an array that is fed using a conventional low-pass loaded line. The reduced-beam squinting property that NRI-TL metamaterial lines offer is subsequently exploited to create a leaky-wave antenna that radiates a near-fixed beam in the forward +45° direction, with an average measured beam squint of only 0.031°/MHz. This is achieved by operating the antenna in the upper right-handed band where the phase and group velocities are the closest to the speed of light. Finally, an electrically small antenna comprising four 0° NRI-TL metamaterial unit cells is presented which supports a predominantly even-mode current, thus enabling it to be modeled as a multi-arm folded monopole. This significantly increases its radiation resistance, which allows it to be matched to 50 Ω, while maintaining a high measured efficiency of 70%.

Probabilistic simultaneous polynomial reconstruction algorithm of Bleichenbacher-Kiayias-Yung is extended to the polynomials whose degrees are allowed to be distinct. Furthermore, it is observed that probability of the algorithm can be increased. Specifically, for a finite field $F$, we present a probabilistic algorithm which can recover polynomials $p_1,ldots, p_r in F[x]$ of degree less than $k_1,k_2,ldots,k_r$, respectively with given field evaluations $p_l(z_i) = y_{i,l}$ for all $i in I$, $|I|=t$ and $l in [r]$ with probability at least $1 - (n - t)/|F|$ and with time complexity at most $O((nr)^3)$. Next, by using this algorithm, we present a probabilistic decoder for interleaved Reed-Solomon codes. It is observed that interleaved Reed-Solomon codes over $F$ with rate $R$ can be decoded up to burst error rate $frac{r}{r+1}(1 - R)$ probabilistically for an interleaving parameter $r$. It is proved that a Reed-Solomon code RS$(n / k)$ can be decoded up to error rate $frac{r}{r+1}(1 - R&#039 / )$ for $R&#039 / = frac{(k-1)(r+1)+2}{2n}$ when probabilistic interleaved Reed-Solomon decoders are applied. Similarly, for a finite field $F_{q^2}$, it is proved that $q$-folded Hermitian codes over $F_{q^{2q}}$ with rate $R$ can be decoded up to error rate $frac{q}{q+1}(1 - R)$ probabilistically. On the other hand, it is observed that interleaved codes whose subcodes would have different minimum distances can be list decodable up to radius of minimum of list decoding radiuses of subcodes. Specifically, we present a list decoding algorithm for $C$, which is interleaving of $C_1,ldots, C_b$ whose minimum distances would be different, decoding up to radius of minimum of list decoding radiuses of $C_1,ldots, C_b$ with list size polynomial in the maximum of list sizes of $C_1,ldots, C_b$ and with time complexity polynomial in list size of $C$ and $b$. Next, by using this list decoding algorithm for interleaved codes, we obtained new list decoding algorithm for $qh$-folded Hermitian codes for $q$ standing for field size the code defined and $h$ is any positive integer. The decoding algorithm list decodes $qh$-folded Hermitian codes for radius that is generally better than radius of Guruswami-Sudan algorithm, with time complexity and list size polynomial in list size of $h$-folded Reed-Solomon codes defined over $F_{q^2}$.

This dissertation studies three classes of estimators for the asymptotic variance parameter of a stationary stochastic process. All estimators are based on the concept of data "re-use" and all transform the output process into functions of an approximate Brownian motion process. The first class of estimators consists folded standardized time series area and Cramér-von Mises (CvM) estimators. Detailed expressions are obtained for their expectation at folding levels 0 and 1; those expressions explain the puzzling increase in small-sample bias as the folding level increases. In addition, we use batching and linear combinations of estimators from different levels to produce estimators with significantly smaller variance. Finally, we obtain very accurate approximations of the limiting distributions of batched folded estimators. These approximations are used to compute confidence intervals for the mean and variance parameter of the underlying stochastic process. The second class --- folded overlapping area estimators --- are computed by averaging folded versions of the standardized time series corresponding to overlapping batches. We establish the limiting distributions of the proposed estimators as the sample size tends to infinity. We obtain statistical properties of these estimators such as bias and variance. Further, we find approximate confidence intervals for the mean and variance parameter of the process by approximating the theoretical distributions of the proposed estimators. In addition, we develop algorithms to compute these estimators with only order-of-sample-size work. The third class --- reflected area and CvM estimators --- are computed from reflections of the original sample path. We obtain the expected values and variance of individual estimators. We show that it is possible to obtain linear combinations of reflected estimators with smaller variance than the variance of each constituent estimator, often at no cost in bias. A quadratic optimization problem is solved to find an optimal linear combination of estimators that minimizes the variance of the linearly combined estimator. For all classes of estimators, we provide Monte Carlo examples to show that the estimators perform as well in practice as advertised by the theory.

In this research, Fresnel zone plates were studied using an accurate, full-electromagnetic simulator based on the body-of-revolution finite-difference time-domain (BOR-FDTD) method. This tool was used to investigate zone plates for two different applications: zone plates used as antennas in communication systems and zone plates used as focusing elements in free-space, focused-beam measurement systems. Through detailed studies of zone plates for these applications, a number of general characteristics of the zone plate were given a more in-depth look than they have been given in the past. For the first application, parametric studies were performed for Soret, folded, and grooved-dielectric, phase-correcting zone plates for antenna applications. These studies were used to generate new design graphs, from which general observations are made about the effect of varying different parameters on the focusing ability of a zone plate. For the grooved-dielectric, phase-correcting zone plate, these studies show that a number of factors influence the focusing ability in ways that are unexpected, based on many of the simple techniques typically used to analyze zone plates. Each of these factors is evaluated individually. For the second application, a zone plate was designed to be used as a focusing element in a free-space, focused-beam measurement system. To determine the suitability of zone plates for this application, simulations and measurements of the electric field were used to compare this zone plate to a doubly-hyperbolic lens. A complete focused-beam system, using two zone plates as focusing elements, was used to measure the permittivity of different dielectric materials. These measurements are compared to results for a system that uses doubly-hyperbolic lenses and to published values. A technique for increasing the usable bandwidth of a zone plate in a focused-beam system was proposed and tested. Finally, as a topic for future research, the question is posed: Using the BOR-FDTD method, can a similar volume of material be shaped in a way that results in improved focusing performance compared to a traditional zone plate? Some insight into this open-ended question can be gained by examining preliminary results of the optimization of zone plates using of a genetic algorithm.

[pt] O presente trabalho tem por objetivo estudar o comportamento crítico e pós-crítico de placas dobradas. Placas dobradas, tanto de aço quanto de concreto, têm sido usadas com grande freqüência em obras de engenharia, particularmente como paredes portantes e coberturas de grandes vãos. Neste último caso, placas dobradas têm uma aplicação semelhante a de cascas esbeltas, sendo, porém, mais simples de construir, dado que são compostas de superfícies planas. Neste trabalho utiliza-se o software ABAQUS para análise de placas dobradas compostas de duas placas formando um dado ângulo entre si. Estuda-se o uso destas placas como paredes portantes sob compressão, sendo conduzido um estudo paramétrico para determinar a influência dos diversos parâmetros geométricos e condições de contorno nas cargas críticas e modos críticos da placa dobrada. A seguir são determinados os caminhos pós-críticos e estuda-se a influência dos diversos parâmetros na rigidez pós-crítica e sensibilidade a imperfeições. Finalmente, estuda-se o comportamento não-linear destas placas sob flexão, sendo investigados os fenômenos de perda de estabilidade associados a este problema. / [en] The aim of the present work is to study the buckling and post-buckling behavior of folded plates. Folded plates, made of steel or concrete, have been widely used in engineering construction as load-bearing walls designed to carry floor and roof loads or roofs for large spaces. In the last case, folded plates work as a thin shell, being however easier to build since they are formed by flat surfaces joined along the fold lines. In this work the software ABAQUS is used to study the behavior of V-shaped folded plates. Initially it is analyzed the behavior of these plates when used as load-bearing walls under axial compression. A detailed parametric analysis is conducted to identify the influence of the geometrical parameters and boundary conditions on critical loads and modes. The influence of these parameters on the post-buckling response, post-critical stiffness and imperfection sensitivity is also investigated. Finally, the non-linear response of V-shaped folded plates under flexure is investigated and the possible instabilities under these loading conditions are analyzed.

This diploma thesis deals with the design of eight-bit digital to analog coverter with fully differential outputs in technology I3T25 of ON Semiconductor company. The work contains the description of basic structures and characteristics of digital to analog converters. The main focus of the work is to design a converter and auxiliary circuits at the transistor level. The functionality of designed circuits is verified by simulation environment Cadence.