The Optical Parametric Oscillator (OPO) has been one of the most versatile source of non-classical states of light. Usual configurations of such devices are a macroscopic second order nonlinear crystals inside an optical cavity. Recently the use of silicon photonics techniques allowed the implementation of high quality factor microcavities and OPOs which include several technological advantages over usual configuration as a small size, bigger bandwidth, CMOS compatibility, facility to engineer the dispersion properties and compatibility with commercial optical fiber communications. Nevertheless the nonlinearity present within these systems is a third order nonlinearity for which theoretical calculations lack in the literature. Here we describe theoretically the quantum properties of the light generated in an OPO with a third order nonlinearity. We showed that the effects of phase modulation (which are not present in the second order nonlinearity) and dispersion are determinant in the way that oscillation and entanglement is produced in the system. Despite of these effects, bipartite and tripartite entanglement is predicted with the use of the Schmidt modes formalism. We also describe the system when there are more modes exited within the cavity and a frequency comb is formed. In such a situation, using again the Schmidt modes formalism, multipartite entanglement was predicted as well. / O oscilador paramétrico ótico (OPO) tem sido uma fonte muito versátil de estados não clássicos da luz. A configuração usual destes OPOs consiste em um cristal macroscópico com não linearidade de segunda ordem no interior de uma cavidade ótica. Recentemente, devido ao desenvolvimento da fotonica de silício, foi possível a implementação de micro- cavidades óticas e OPOs que possuem varias vantagens sobre OPOs usuais. Não entanto a não linearidade destes sistemas é de terceira ordem. Neste trabalho, descrevemos teoricamente as propriedades quânticas da luz gerada num OPO com não linearidade de terceira ordem. Mostra-se que os efeitos de modulação de fase (não presentes na não linearidade de segunda ordem) e a dispersão são determinantes para a geração e o emaranhamento produzido no sistema. Emaranhamento bi e tri partito foi predito teoricamente usando o formalismo de modos de Schmidt. Também foi feita uma descrição quando mais modos da cavidade são excitados gerando um pente de frequência. Nesta situação. e utilizando novamente o formalismo de modos de Schmidt, foi predito emaranhamento multimodo destes sistemas.

Synchronization of an ensemble of oscillators is a phenomenon present in systems of different fields, ranging from social and physical to biological and technological systems. The most successful approach to describe how synchrony emerges in these systems is given by the Kuramoto model. This model as it stands, however, assumes oscillators of fixed natural frequencies and a homogeneous all-to-all coupling strength. The Kuramoto model has been analytically discussed to address the synchronization phenomena of coupled oscillators in the thermodynamic limit (N --> ∞). However, there needs to be a modi cation to address the inevitable in uence of external fields on the pattern of various real life synchronization phenomena which, in general; involves a finite number of oscillators. This research introduces a time dependent coupling strength K(t) which is from the modulation of external elds in the form of, for example, a periodic impulse, in the nite oscillators assembly. A sinusoidal function with some arbitrary values of amplitude and frequency is added to the fixed coupling strength as a perturbation of external elds. Temporal evolution of order parameter r(t) and phase θ(t), both of which measure the degree of synchronization of an assembly of oscillators simultaneously, are compared between uniform and time dependent cases. Graphical comparison are made using a 2 oscillator system, a building block of any finite oscillators case. Also, similar comparisons are performed for a system of 32 oscillators which are chosen randomly as a representative of a nite number of oscillators (2 < N < ∞). A temporal variation of the relative phase angle θ(t) = θ2(t) - θ1(t) in 2 and 32 oscillators systems using uniform and time dependent cases is also a part of this research. This work also introduces a time-dependent coupling strength in the form of a step function. The main objective of using such a function is to keep the synchronized behavior of the oscillators persistently. This behavior can be achieved with the perception that occasional boosting with higher coupling strength K(t) should be enough to sustain synchronous behavior of oscillators which, in general, are tuned with lower K(t). / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2018. / FAU Electronic Theses and Dissertations Collection

In the design of voltage-controlled oscillators (VCOs) for communication systems, timing jitter is of major concern since it is the largest contributor to the bit-error rate. The latest deep submicron processes provide the possibility of higher oscillator speed at the cost of increased device noise and a higher 1/f noise corner. Therefore it is crucial to characterize the upconverted 1/f noise for practical applications. This dissertation presents a simple model to relate the time domain jitter and frequency domain phase noise in the presence of non-negligible 1/f noise sources. It will simplify the design, simulation, and testing of the PLL, since with this technique only the open loop VCO needs to be considered. Design methodologies for white noise dominated ring oscillators and PLLs are also developed by analyzing the upconverted thermal noise in time domain using a LTI model. The trade-off and relationship between jitter, speed, power dissipation and VCO geometry are evaluated for different applications. This model is supported by the measured data from 24 ring oscillators with different geometry fabricated in TSMC 0.18um process. The theory developed in this dissertation is applied to the design of PLL- and DLL- based true random number generators (TRNG) for application in the area of“smart cards". New architectures of dual-oscillator sampling and delay-line sampling are proposed for random number generation, which has the advantage of lower power dissipation and lower cost over traditional approaches. Both structures are implemented in test chips fabricated in AMI 1.5um process. The PLL-based TRNG passed the NIST SP800-22 statistical test suite and the DLL-based TRNG passed both the NIST SP800-22 statistical test suite and the Diehard battery of tests.

Les générateurs de suites binaires aléatoires constituent la partie primordiale d'un système cryptographique. La vitesse, la qualité des suites générées, la sécurité et la consommation jouent un rôle essentiel dans le choix d'un générateur. La sécurité du système cryptographique augmente si un tel système peut être réalisé dans un seul circuit.Le travail de recherche développé consiste donc en la réalisation d'un générateur de nombres aléatoires fonctionnant en basse consommation, basse vitesse. Le circuit proposé est de type analogique et valide l'ensemble des tests NIST assurant le caractère du signal. Une réalisation sur Silicium en technologie 0,35μm a été implémentée et validée via les tests NIST développés sous Matlab. De ce travail de thèse, un certain nombre de publications ont montré la plus-value recherche des résultats. / Random binary sequences generators constitute the essential part of a system Cryptographic. The speed, quality of generated suites, safety and consumption play an essential role in the selection of a generator. The security of the cryptographic system increases if such a system can be realized in a single circuit.The developed research work consists in the realization of a random number generator running in low power, low speed. The proposed circuit is analog and Valid all NIST tests ensuring the randomness of a signal.A realization on silicon in 0,35μm technology has been implemented and validated through NIST developed tests Matlab. In this thesis, a number of publications have demonstrated the added value search results.

<p>The main purpose of this thesis is to theoretically study energy levels and intra-electronic transition intensities for various f-electron systems. The f-f electronic dipole transitions are parity-forbidden for a free ion but become non-zero when the ion is subject to a crystal-field. This is commonly described within the framework of Judd-Ofelt theory which accounts for the mixing of odd parity into the wave-functions.</p><p>Some refinements and quantitative studies have been made by applying many-body perturbation theory, or the perturbed functions approach, to obtain effective dipole operators due to correlation, spin-orbit and higher order crystal-field effects not included in Judd-Ofelt theory. A software for the computation of f-electron multiplets and Stark levels was implemented and published as well.</p><p>The single- and pair-functions used for the evaluation of intensity parameters were obtained by solving various inhomogeneous Schrödinger equations. The wave-functions and energies obtained by diagonalizing an effective Hamiltonian have been used together with the oscillator strength methods to simulate absorption spectrum. Consistent crystal-field parameters applied in some of the papers were obtained by fitting crystal polarizabilities to reflect the experimental Stark levels. The same crystal model was then used to generate odd crystal field parameters needed for the f-f transition intensities. The total effect of these refinements are spectral features that usually agree well with experimental findings. Some of these methods have also been applied and seen to be quite useful for the understanding of optical fiber amplifiers frequently used in today's optical networks.</p><p>Finally, a finite-difference approach was applied for the Helium iso-electronic sequence. The exact wave-function was expanded in a sum of partial waves, and accurate ground- and excited state energies were obtained by using the iterative Arnoldi approach.</p>

The main purpose of this thesis is to theoretically study energy levels and intra-electronic transition intensities for various f-electron systems. The f-f electronic dipole transitions are parity-forbidden for a free ion but become non-zero when the ion is subject to a crystal-field. This is commonly described within the framework of Judd-Ofelt theory which accounts for the mixing of odd parity into the wave-functions. Some refinements and quantitative studies have been made by applying many-body perturbation theory, or the perturbed functions approach, to obtain effective dipole operators due to correlation, spin-orbit and higher order crystal-field effects not included in Judd-Ofelt theory. A software for the computation of f-electron multiplets and Stark levels was implemented and published as well. The single- and pair-functions used for the evaluation of intensity parameters were obtained by solving various inhomogeneous Schrödinger equations. The wave-functions and energies obtained by diagonalizing an effective Hamiltonian have been used together with the oscillator strength methods to simulate absorption spectrum. Consistent crystal-field parameters applied in some of the papers were obtained by fitting crystal polarizabilities to reflect the experimental Stark levels. The same crystal model was then used to generate odd crystal field parameters needed for the f-f transition intensities. The total effect of these refinements are spectral features that usually agree well with experimental findings. Some of these methods have also been applied and seen to be quite useful for the understanding of optical fiber amplifiers frequently used in today's optical networks. Finally, a finite-difference approach was applied for the Helium iso-electronic sequence. The exact wave-function was expanded in a sum of partial waves, and accurate ground- and excited state energies were obtained by using the iterative Arnoldi approach.

This thesis presents the CMOS integer-N frequency synthesizer for 5 GHz WCDMA applications with 1.8V power supply. The frequency synthesizer is fabricated in a TSMC 0.18£gm CMOS 1P6M technology process. The frequency synthesizer consists of a phase-frequency detector, a charge pump, a low-pass loop filter, a voltage control oscillator, an auto-band selection, and a pulse-swallow divider. In pulse-swallow divider, this thesis use true single phase clock DFF proposed by Yuan and Svensson to work on high frequency region and to save the circuit area and power. This thesis also proposes an auto-band selection circuit to control the output frequency more precise and easier, and it can also reduce the frequency drift effect caused by technology process or temperature variation.

In this thesis a number of issues related to oceanographic problems have been dealt with on the basis of applying asymptotic methods.  The first study focused on the tidal generation of internal waves, a process which is quantifed by the conversion rates. These have traditionally been calculated by using the WKB approximation. However, the systematic imprecision of this theory for the lowest modes as well as turbulence at the seabed level affect the results. To handle these anomalies we introduced another asymptotic technique, homogenization theory, which led to signifcant improvements, especially for the lowest modes.  The second study dealt with the dynamical aspects of a nonlinear oscillator which can be interpreted as a variant of the classical two-box models used in oceanography. The system is constituted by two connected vessels containing a fluid characterised by a nonlinear equation of state and a large volume differences between the vessels is prescribed. It is recognised that the system, when performing relaxation oscillations, exhibits almost-discontinuous jumps between the two branches of the slow manifold of the problem. The lowest-order analysis yielded reasonable correspondence with the numerical results.  The third study is an extension of the lowest-order approximation of the relaxation oscillations undertaken in the previous paper. A Mandelstam condition is imposed on the system by assuming that the total heat content of the system is conserved during the discontinuous jumps.  In the fourth study an asymptotic analysis is carried out to examine the oscillatory behaviour of the thermal oscillator. It is found that the analytically determined corrections to the zeroth-order analysis yield overall satisfying results even for comparatively large values of the vessel-volume ratio. / At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 3: Manuscript. Paper 4: Manuscript.

High-quality factor oscillators are often used in measurements of verysmall force since they exhibit an enhanced sensitivity in the narrow frequencyband around resonance. Forces containing frequencies outside this frequencyband are often not detectable and the total force acting on the oscillatorremains unknown. In this thesis we present methods to eciently use theavailable bandwidth around resonance to reconstruct the force from partialspectral information.We apply the methods to dynamic atomic force microscopy (AFM) wherea tip at the end of a small micro-cantilever oscillates close to a sample surface.By reconstructing the force between the tip and the surface we can deducedierent properties of the surface. In contrast, in conventional AFM only oneof the many frequency components of the time-dependent tip-surface forceallowing for only qualitative conclusions about the tip-surface force.To increase the number of measurable frequency components we developed Intermodulation AFM (ImAFM). ImAFM utilizes frequency mixing ofa multifrequency drive scheme which generates many frequencies in the response to the nonlinear character of the tip-surface interaction. ImAFM,amplitude-modulated AFM and frequency-modulated AFM can be considered as special cases of narrow-band AFM, where the tip motion can bedescribed by a rapidly oscillating part and a slowly-varying envelope function. Using the concept of force quadratures, each rapid oscillation cycle canbe analyzed individually and ImAFM measurements can be interpreted as arapid measurement of the dependence of the force quadratures on the oscillation amplitude or frequency. To explore the limits of the force quadraturesdescription we introduce the force disk which is a complete description of thetip-surface force in narrow-band AFM at xed static probe height.We present a polynomial force reconstruction method for multifrequencyAFM data. The polynomial force reconstruction is a linear approximativeforce reconstruction method which is based on nding the parameters of amodel force which best approximates the tip-surface force. Another classof reconstruction methods are integral techniques which aim to invert theintegral relation between the tip-surface force and the measured spectraldata. We present an integral method, amplitude-dependence force spectroscopy (ADFS), which reconstructs the conservative tip-surface force fromthe amplitude-dependence of the force quadratures. Together with ImAFMwe use ADFS to combine high-resolution AFM imaging at high speeds withhighly accurate force measurements in each point of an image. For the measurement of dissipative forces we discuss how methods from tomography canbe used to reconstruct forces that are a function of both tip position andvelocity.The methods developed in this thesis are not limited to dynamic AFM andwe describe them in the general context of a harmonic oscillator subject to anexternal force. We hope that theses methods contribute to the transformationof AFM from a qualitative imaging modality into quantitative microscopy andwe hope that they nd application in other measurements which exploit theenhanced sensitivity of a high-quality factor oscillator. / <p>QC 20130527</p>

This thesis is a report of the work I have done over the last five years to study thermodynamic and kinetic aspects of single-molecule behavior in the condensed phase. It is concerned specifically with the development of analytically tractable models of various phenomena that have been observed in experiments on such single-molecule systems as colloids, double-stranded DNA, multi-unit proteins, and enzymes. In fluid environments, the energetics, spatial conformations, and chemical reactivity of these systems undergo fluctuations that can be characterized experimentally in terms of time correlation functions, survival probabilities, mean first passage times, and related statistical parameters. The thesis shows how many of these quantities can be calculated in closed form from a model based on simple Brownian motion, or generalizations of it involving fractional calculus. The theoretical results obtained here have been shown to agree qualitatively or quantitatively with a range of experimental data. The thesis therefore demonstrates the effectiveness of Brownian motion concepts as a paradigm of stochasticity in biological processes.