Master of Science / Department of Physics / Brian Washburn / Zenghu Chang / Attosecond pulse generation is a powerful tool to study electron dynamics in atoms and molecules. However, application of attosecond pulses is limited by the low photon flux of attosecond sources. Theoretical models predict that the harmonic efficiency scales as λ[lambda]-6 in the plateau region of the HHG spectrum, where λ [lambda] is the wavelength of the driving laser. This indicates the possibility of generating more intense attosecond pulses using short wavelength driving lasers. The purpose of this work is to find a method to generate intense single attosecond pulses using a 400 nm driving laser. In our experiments, 400 nm femtosecond laser pulses are used to generate high harmonics. First, the dependence of the high harmonic generation yield on the ellipticity of 400 nm driving laser pulse is studied experimentally, and it is compared with that of 800 nm driving lasers. A semi-classical theory is developed to explain the ellipticity dependence where the theoretical calculations match experiment results very well. Next, 400 nm short pulses (sub-10 fs) are produced with a hollow core fiber and chirped mirrors. Finally, we propose a scheme to extract single attosecond pulses with the Generalized Double Optical Gating (GDOG) method.

This thesis is composed of three main parts. Each chapter is concerned with characterizing some properties of a random ensemble or stochastic process. The properties of interest and the methods for investigating them di er between chapters. We begin by establishing some asymptotic results regarding zeros of random harmonic mappings, a topic of much interest to mathematicians and astrophysicists alike. We introduce a new model of harmonic polynomials based on the so-called "Weyl ensemble" of random analytic polynomials. Building on the work of Li and Wei [28] we obtain precise asymptotics for the average number of zeros of this model. The primary tools used in this section are the famous Kac-Rice formula as well as classical methods in the asymptotic analysis of integrals such as the Laplace method. Continuing, we characterize several topological properties of this model of harmonic polynomials. In chapter 3 we obtain experimental results concerning the number of connected components of the orientation-reversing region as well as the geometry of the distribution of zeros. The tools used in this section are primarily Monte Carlo estimation and topological data analysis (persistent homology). Simulations in this section are performed within MATLAB with the help of a computational homology software known as Perseus. While the results in this chapter are empirical rather than formal proofs, they lead to several enticing conjectures and open problems. Finally, in chapter 4 we address an industry problem in applied mathematics and machine learning. The analysis in this chapter implements similar techniques to those used in chapter 3. We analyze data obtained by observing CAN tra c. CAN (or Control Area Network) is a network for allowing micro-controllers inside of vehicles to communicate with each other. We propose and demonstrate the e ectiveness of an algorithm for detecting malicious tra c using an approach that discovers and exploits the natural geometry of the CAN surface and its relationship to random walk Markov chains. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2018. / FAU Electronic Theses and Dissertations Collection

by See Kai-hung. / Title in Chinese: / Includes bibliographical references / Thesis (M.Ph.)--Chinese University of Hong Kong, 1986

by Leung Pui-tang. / Parallel title in Chinese characters. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1988. / Bibliography: leaves 92-94.

This thesis presents the theory, implementation and applications of the harmonic sinusoid modeling of pitched audio events. Harmonic sinusoid modeling is a parametric model that expresses an audio signal, or part of an audio signal, as the linear combination of concurrent slow-varying sinusoids, grouped together under harmonic frequency constraints. The harmonic sinusoid modeling is an extension of the sinusoid modeling, with the additional frequency constraints so that it is capable to directly model tonal sounds. This enables applications such as object-oriented audio manipulations, polyphonic transcription, instrument/singer recognition with background music, etc. The modeling system consists of an analyzer and a synthesizer. The analyzer extracts harmonic sinusoidal parameters from an audio waveform, while the synthesizer rebuilds an audio waveform from these parameters. Parameter estimation is based on a detecting-grouping-tracking framework. The detecting stage finds and estimates sinusoid atoms; the grouping stage collects concurrent atoms into harmonic groups; the tracking stage collects the atom groups at different time to form continuous harmonic sinusoid tracks. Compared to standard sinusoid model, the harmonic model focuses on harmonic groups of atoms rather than on isolated atoms, therefore naturally represents tonal sounds. The synthesizer rebuilds the audio signal by interpolating measured parameters along the found tracks. We propose the first application of the harmonic sinusoid model in digital audio editors. For audio editing, with the tonal events directly represented by a parametric model, we can implement standard audio editing functionalities on tonal events embedded in an audio signal, or invent new sound effects based on the model parameters themselves. Possibilities for other applications are suggested at the end of this thesis.

This thesis explores the automatic extraction of musical information from live performances - with the intention of using that information to create novel, responsive and adaptive performance tools for musicians. We focus specifically on two forms of musical analysis - harmonic analysis and beat tracking. We present two harmonic analysis algorithms - specifically we present a novel chroma vector analysis technique which we later use as the input for a chord recognition algorithm. We also present a real-time beat tracker, based upon an extension of state of the art non-causal models, that is computationally efficient and capable of strong performance compared to other models. Furthermore, through a modular study of several beat tracking algorithms we attempt to establish methods to improve beat tracking and apply these lessons to our model. Building upon this work, we show that these analyses can be combined to create a beat-synchronous musical representation, with harmonic information segmented at the level of the beat. We present a number of ways of calculating these representations and discuss their relative merits. We proceed by introducing a technique, which we call Performance Following, for recognising repeated patterns in live musical performances. Through examining the real-time beat-synchronous musical representation, this technique makes predictions of future harmonic content in musical performances with no prior knowledge in the form of a score. Finally, we present a number of potential applications for live performances that incorporate the real-time musical analysis techniques outlined previously. The applications presented include audio effects informed by beat tracking, a technique for synchronising video to a live performance, the use of harmonic information to control visual displays and an automatic accompaniment system based upon our performance following technique.

Hui Yuen Yung. / Thesis submitted in: August 1998. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 70-73). / Text in English; abstract also in Chinese. / Hui Yuen Yung. / Acknowledgements --- p.vi / Abstract --- p.vii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Second harmonic generation --- p.5 / Chapter 2.1 --- Introduction --- p.5 / Chapter 2.2 --- Maxwell's equations in dielectric media --- p.6 / Chapter 2.3 --- Second harmonic generation --- p.7 / Chapter 2.4 --- Phase matching --- p.8 / Chapter 2.5 --- Quasi phase matching --- p.10 / Chapter 2.6 --- Inversion symmetry --- p.11 / Chapter 3 --- Third order nonlinear optical processes in optical fibers --- p.14 / Chapter 3.1 --- Introduction --- p.14 / Chapter 3.2 --- Optical fibers --- p.15 / Chapter 3.3 --- Third order interaction between waves of same frequency --- p.16 / Chapter 3.4 --- Third order interaction between waves of different frequencies --- p.19 / Chapter 4 --- Multiphoton ionization interference effect --- p.23 / Chapter 4.1 --- Historical development --- p.23 / Chapter 4.2 --- Multiphoton ionization interference effect --- p.26 / Chapter 4.3 --- Periodic ionization --- p.27 / Chapter 4.4 --- Periodic electric field --- p.28 / Chapter 4.5 --- Physical interpretation --- p.29 / Chapter 5 --- Experimental setup --- p.32 / Chapter 5.1 --- Introduction --- p.32 / Chapter 5.2 --- Laser system --- p.32 / Chapter 5.3 --- Optical fibers --- p.33 / Chapter 5.4 --- Coupling light into fibers --- p.34 / Chapter 5.5 --- Detection system --- p.36 / Chapter 5.6 --- Optical layout --- p.36 / Chapter 6 --- Second harmonic generation in optical fibers --- p.40 / Chapter 6.1 --- Introduction --- p.40 / Chapter 6.2 --- Self-preparation in optical fibers --- p.41 / Chapter 6.3 --- Polarization dependence --- p.42 / Chapter 6.4 --- Seeding optical fibers --- p.42 / Chapter 6.5 --- Seeding by varying green light intensity --- p.45 / Chapter 6.6 --- Square dependence of second harmonic generation in optical fibers --- p.46 / Chapter 7 --- Erasure of x(2) grating in optical fibers --- p.56 / Chapter 7.1 --- Introduction --- p.56 / Chapter 7.2 --- Experiment --- p.58 / Chapter 7.3 --- Results --- p.59 / Chapter 7.3.1 --- Erasure by different propagating mode --- p.59 / Chapter 7.3.2 --- Erasure in germanium-doped fiber --- p.60 / Chapter 7.3.3 --- Erasure in erbium-doped fiber --- p.61 / Chapter 7.4 --- Discussion --- p.61 / Chapter 8 --- Conclusion --- p.68 / Chapter 8.1 --- Summary of our work --- p.68 / Chapter 8.2 --- Outlook --- p.69 / Chapter 8.2.1 --- Multiphoton ionization in polymer --- p.69 / Chapter 8.2.2 --- Erasure by blue light --- p.69 / Bibliography --- p.70

Choy Kwok Wai = 利用全光極化在本體聚合物中產生準相匹配二次諧波 / 蔡國偉. / Thesis submitted in: August 2005. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 132-133). / Text in English; abstracts in English and Chinese. / Choy Kwok Wai = Li yong quan guang ji hua zai ben ti ju he wu zhong chan sheng zhun xiang pi pei er ci xie bo / Cai Guowei. / Acknowledgements --- p.ii / Abstract --- p.iii / Chinese Abstract --- p.V / Table of Contents --- p.vi / List of Figures --- p.ix / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Principle and origin of nonlinear optics --- p.2 / Chapter 1.2 --- Tensor properties and Inversion symmetry --- p.3 / Chapter 1.3 --- Relationship between microscopic and macroscopic nonlinear susceptibility for a poled polymer --- p.5 / Chapter 1.4 --- Second Harmonic Generation by nonlinear polarization --- p.7 / Chapter 1.5 --- Outline of the thesis --- p.9 / Figures --- p.10 / Chapter Chapter 2 --- Poling and relaxation of nonlinear optical polymeric systems --- p.11 / Chapter 2.1 --- Guest-Host nonlinear optical polymeric systems --- p.11 / Chapter 2.2 --- Poling techniques --- p.13 / Chapter 2.2.1 --- Thermal-assisted Electric Poling --- p.13 / Chapter 2.2.2 --- Photo-assisted Electric Poling --- p.15 / Chapter 2.2.3 --- All-optical Poling --- p.17 / Chapter 2.3 --- Quasi-phase-matching in bulk polymers by All-optical Poling --- p.20 / Chapter 2.4 --- Photorefractive effect in polymers --- p.22 / Chapter 2.5 --- Relaxation study of NLOP system --- p.23 / Figures --- p.27 / Chapter Chapter 3 --- Experimental Method --- p.33 / Chapter 3.1 --- Experimental Setup --- p.33 / Chapter 3.1.1 --- Laser system --- p.33 / Chapter 3.1.2 --- Data acquisition system --- p.34 / Chapter 3.1.3 --- Reference arm --- p.34 / Chapter 3.1.4 --- Optical Path --- p.35 / Chapter 3.2 --- Sample Preparation --- p.36 / Chapter 3.2.1 --- Polymer Films Preparation --- p.36 / Chapter 3.2.2 --- Bulk Polymers Preparation --- p.38 / Chapter 3.3 --- Poling and Thermal history of samples --- p.41 / Figures --- p.43 / Chapter Chapter 4 --- Growth and decay of optical nonlinearity in all-optically poled polymers --- p.53 / Chapter 4.1 --- Poling profiles for DR-1 and DANS doped bulk polymer by All-optical poling --- p.53 / Chapter 4.1.1 --- Poling profiles for DR-1 doped bulk polymer and polymer films by All-optical poling --- p.53 / Chapter 4.1.2 --- Possibilities of degradation of the samples during the experiment --- p.56 / Chapter 4.1.3 --- Effects of probing beam intensity and the duration of probing on the growth and decay of X(2) --- p.57 / Chapter 4.1.4 --- Poling profiles for DANS doped bulk polymer by All-optical poling --- p.57 / Chapter 4.2 --- Dependence of the poling profiles on various parameters in all-optical poling --- p.59 / Chapter 4.2.1 --- Dependence on the temperature --- p.59 / Chapter 4.2.2 --- Dependence on the relative intensities between the two seeding beams --- p.60 / Chapter 4.2.3 --- Dependence on the relative phase between the two seeding beams --- p.64 / Chapter 4.2.4 --- Tensorial properties of X(2) --- p.67 / Chapter 4.2.5 --- Dependence on the thickness of the sample --- p.68 / Chapter 4.3 --- Comparison of different relaxation models --- p.69 / Figures --- p.71 / Chapter Chapter 5 --- Growth and decay of optical nonlinearity in poled polymers with charge-generating additives --- p.89 / Chapter 5.1 --- Orientational enhancement in NLOP systems --- p.89 / Chapter 5.2 --- Space-charge field by charge-transporting molecules and sensitizer --- p.89 / Chapter 5.3 --- Poling profile of the bulk DR-1 polymer with charge-generating ingredients --- p.91 / Chapter 5.4 --- Poling profile of the bulk DANS polymer with the presence of charge-transporting molecules and sensitizers --- p.100 / Figures --- p.107 / Chapter Chapter 6 --- Growth and decay of optical nonlinearity in a nano-structured composite system --- p.113 / Chapter 6.1 --- Historical background --- p.113 / Chapter 6.2 --- Preparation of the composites films --- p.116 / Chapter 6.2.1 --- Preparation of the silver nano-particles --- p.116 / Chapter 6.2.2 --- Preparation of the composite films --- p.117 / Chapter 6.3 --- Poling profiles of polymer films with silver nano-particles --- p.118 / Figures --- p.124 / Chapter Chapter 7 --- Conclusions --- p.129 / References --- p.132

High gradient acceleration is a core challenge of accelerator physics. Achieving high gradients is made challenging by issues relating to rf breakdown and pulsed surface heating, which are caused by intense surface fields in the accelerating cavities. The excitation of multiple harmonically related modes within a cavity could reduce the onset of these effects. The temperature rise from pulsed surface heating can be reduced by lowering the average magnetic surface field squared and rf breakdown could be avoided by creating an asymmetry between the anode and cathode surface electric fields. This thesis will present several different cavity designs that show a reduction in the temperature rise on the surface of over 10% for second and third harmonic cavity structures or an asymmetry in the surface electric anode and cathode fields of a factor of 2. The harmonic mode could have undesirable consequences for beam stability. A study of the longitudinal beam dynamics is included that will derive the equations governing the longitudinal motion and show that the harmonic mode will have a minor and predictable effect on the rf bucket. The Compact LInear Collider (CLIC) is a major contender for the next generation of lepton linear colliders and is made challenging by high power requirements and distribution throughout the linac. A high current drive beam is decelerated parallel to the main linac in order to create the required rf power, which can overcome some of these issues. This thesis will describe a novel design for a CLIC-like accelerating structure, using collinear acceleration through fundamental mode detuned cavities. The design will accommodate interleaved drive and test bunches, such that the drive bunches are decelerated and the test bunches are accelerated within the confines of the same cavity which can result in high transformer ratios. The analytical theory based on the circuit model will be verified by time domain simulations. A multi-harmonic detuned accelerating structure is introduced that exhibits the properties of pulsed surface heating reduction and can be used for collinear acceleration. Time domain simulations will verify the transformer ratio to within 3% of theoretical predictions and the average magnetic field squared reduction will be within 20% of the value calculated from eigenmode simulations.

Chee Shiu Chung = 阻尼振子的線空間結構與哈密頓理論 / 朱兆中. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 88). / Text in English; abstracts in English and Chinese. / Chee Shiu Chung = Zu ni zhen zi de xian kong jian jie gou yu ha mi dun li lun / Zhu Zhaozhong. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Conservative Systems --- p.4 / Chapter 2.1 --- General Formalism --- p.4 / Chapter 2.2 --- One Simple Harmonic Oscillator --- p.7 / Chapter 2.3 --- Two Coupled Harmonic Oscillators --- p.9 / Chapter 3 --- Dissipative Systems --- p.12 / Chapter 3.1 --- Elimination of Bath --- p.12 / Chapter 3.2 --- One Oscillator with Dissipation --- p.16 / Chapter 3.3 --- Two Oscillators with Dissipation --- p.19 / Chapter 4 --- Eigenvector Expansion and Bilinear Map --- p.21 / Chapter 4.1 --- Formalism --- p.21 / Chapter 4.2 --- Inner Product and Bilinear Map --- p.23 / Chapter 4.3 --- Normalization and Phase --- p.25 / Chapter 4.4 --- Matrix Representation --- p.25 / Chapter 4.5 --- Duality --- p.28 / Chapter 5 --- Applications and Examples of Eigenvector Expansion --- p.31 / Chapter 5.1 --- Single Oscillator --- p.31 / Chapter 5.2 --- Two Oscillators --- p.32 / Chapter 5.3 --- Uneven Damping --- p.33 / Chapter 6 --- Time Evolution --- p.36 / Chapter 6.1 --- Initial-Value Problem --- p.36 / Chapter 6.1.1 --- Green's Function --- p.37 / Chapter 6.2 --- Sum Rules --- p.39 / Chapter 7 --- Time-Independent Perturbation Theory --- p.41 / Chapter 7.1 --- Non-degenerate Perturbation --- p.41 / Chapter 7.2 --- Degenerate Perturbation Theory --- p.46 / Chapter 8 --- Jordan Block --- p.48 / Chapter 8.1 --- Jordan Normal Basis --- p.48 / Chapter 8.1.1 --- Construction of Basis Vectors --- p.48 / Chapter 8.1.2 --- Bilinear Map --- p.50 / Chapter 8.1.3 --- Example of Jordan Normal Basis --- p.55 / Chapter 8.2 --- Time Evolution --- p.56 / Chapter 8.2.1 --- Time Dependence of Basis Vectors --- p.56 / Chapter 8.2.2 --- Initial-Value Problem --- p.58 / Chapter 8.2.3 --- Green's Function --- p.59 / Chapter 8.2.4 --- Sum Rules --- p.60 / Chapter 8.3 --- Jordan Block Perturbation Theory --- p.61 / Chapter 8.3.1 --- Lowest Order Perturbation --- p.61 / Chapter 8.3.2 --- Higher-Order Perturbation --- p.65 / Chapter 8.3.3 --- Non-generic Perturbations --- p.66 / Chapter 8.4 --- Examples of High-Order Criticality --- p.66 / Chapter 8.4.1 --- Fourth-order JB --- p.67 / Chapter 8.4.2 --- Third-order JB --- p.74 / Chapter 8.4.3 --- Two Second-order JB --- p.79 / Chapter 9 --- Conclusion --- p.81 / Chapter A --- Appendix --- p.83 / Chapter A.l --- Fourier Transform and Contour Integration --- p.83 / Chapter B --- Degeneracy and Criticality --- p.86 / Bibliography --- p.88