Photonic microwave or millimeter wave (MMW) sources that produce highly stable and broadly tunable microwave frequencies of low phase noise are anticipated for many applications ranging from broadband wireless access networks and satellite communication systems to emerging broadband photonics-based phased-array antennas and radars.

The goal of this dissertation is to investigate and control the characteristics of the generated photonic microwave frequencies induced by an optically injected semiconductor laser. Two ways of controlling the dynamics are considered: through the control of the operational parameters of the optically injected laser system and through the control of the intrinsic parameters of the injected semiconductor laser. Controlling the operating parameters shows limit cycles of period one (P1) and period two (P2) that have reduced sensitivity to intrinsic laser noise and small-signal fluctuations in the operating conditions. The intrinsic parameters of the semiconductor laser, particularly the gain saturation factor, are shown to have significant effects on the characteristics of the nonlinear dynamics in both the stable-locking and periodic regions. Therefore, this dissertation shows the optimal operating points of the optically injected semiconductor laser for photonic microwave applications.

This study of prostate cancer patients who underwent radiation therapy (RT) examined how total sleep time changed from the time of simulation to four months after the completion of RT and investigated whether specific variables predicted initial levels of sleep disturbance and characteristics of the trajectories of sleep disturbance. Eighty-two men completed a number of measures (i.e., wrist actigraphy, General Sleep Disturbance Scale, Center for Epidemiologic Studies-Depression scale, Spielberger State-Trait Anxiety Inventories, Brief Pain Inventory) over six months. Descriptive statistics and hierarchical linear modeling were used for data analysis. Large amounts of inter-individual variability were found in the trajectories of sleep disturbance. At baseline, sleep disturbance were associated with ethnicity, KPS score, total dose of RT, pain at baseline. The trajectories of sleep disturbance in this group of men with prostate cancer were associated with total dose of RT, pain at baseline, total sleep time at baseline, state anxiety at baseline. This study is the first using actigraphy to identify predictors of inter-individual variability in sleep disturbance in men with prostate cancer undergoing RT. Additional research is warranted to confirm this study's findings and to develops and test interventions in this vulnerable group of oncology patients.

In this thesis, we focus on graphene-based surface plasmon-polaritons at terahertz frequencies and their possible applications. The primary motivation is to efficiently couple free-space terahertz radiation into an ultra-compact and low-loss waveguide. Characteristics of surface plasmon-polaritons on monolayer and double-layer graphene are first re-derived and reviewed. Then we propose two novel waveguide structures: graphene-metal structure and graphene-wrapped fibers. Possible modes that can be supported by the structures are analyzed and how to excite them is addressed. Also, promising applications are briefly described. Our work reveals that graphene-metal structure is a good starting point for exploration of both new physics and innovative devices, and that graphene-wrapped fibers can also be of substantial interest as the quality of graphene is improved.

Nonlinear dynamics of semiconductor lasers is applied for microwave frequency division. Optical injection is used to drive a slave laser into the dynamical period-two state. A fundamental microwave frequency and its suhharmonic are generated in the power spectrum. Both frequencies will be simultaneously locked when an external microwave near either frequency is applied on the bias. In our experiment, precise microwave frequency division is demonstrated by modulating the laser at the fundamental of 18.56 GHz. A locked subharmonic at 9.28 GHz with a low phase variance of 0.007 rad(2) is obtained from a 10-dBm input. A large locking range of 0.61 GHz is measured under a 4-dBm modulation. Similarly, precise frequency multiplication is demonstrated by modulating at 9.65 GHz. At an input power of -5 dBm, a multiplied signal at 19.30 GHz is obtained with a phase variance of 0.027 rad(2) and a locking range of 0.22 GHz.

Optogenetic functional magnetic resonance imaging (ofMRI) is a novel technique that enables whole-brain visualization of the downstream effects of manipulating a specific neural population. This thesis presents two studies that demonstrate the advantages of ofMRI in brain circuit analysis and offer practical recommendations for ofMRI data analysis. We first describe a study where the technical advantage of ofMRI is utilized in the investigation of arousal networks. The role of central thalamus in forebrain arousal and the frequency-selective modulation of whole-brain networks are uncovered. We then address the challenges of accurate detection and characterization of hemodynamic responses with highly variable temporal dynamics in the ofMRI datasets. In order to find the optimal analysis method, a comprehensive evaluation of the commonly used approaches is presented.

Analysis of the limit-cycle, also known as period-one (P1), dynamics induced by strong optical injection to a semiconductor laser is carried out. Based on the well-established laser rate equations, an approximate solution of the P1 dynamics can be obtained by starting with a general limit-cycle solution. Our results are in good agreement with numerical and experimental results by taking the second harmonic of the P1 frequency into account. Our analysis shows that the strong coupling between the oscillating carrier density and the oscillating optical field is responsible for the high nonlinearity of these P1 dynamics.

Nonlinear dynamics of an optically injected semiconductor laser is applied to photonic microwave generation. By properly adjusting the injection conditions, the optical frequency of the slave laser is first locked to the master laser. The slave laser is then driven into a periodic dynamical state, resulting in a single-sideband (SSB) microwave modulation on the optical carrier. The frequency of the SSB can be controlled by the optical injection strength and detuning. Frequency-modulated SSB can, thus, be obtained from a modulated injection. In this work, we experimentally investigate the generated SSB in terms of its broad tunability and fast modulation response. The results suggest application of this system in radio-over-fiber and optical subcarrier multiplexing technologies when microwave frequency modulation or frequency-shift keying is employed.

Mobile food business is a business which the venders use facilities like trucks and push carts to transport and sell food on streets or private properties. The mobile food business spreads out all over the San Francisco City, and the street-food becomes more and more popular today. To build and study the point process model on linear network is one of the most powerful ways to help us get the general idea of the spatial structure of mobile food facility locations in San Francisco City. This thesis is focused on forming point process data on linear network by using the information from the Internet and identifying the spatial structure of the mobile food facility locations based on K-function, pair correlation function, mark connection function, and point process model on linear network.

Graphene is a one-atom-thick 2D system that has a unique hexagonal crystal structure of two carbon atoms per unit cell. Unlike any other 2D semiconductor material known today, intrinsic graphene has a zero bandgap with its charged carriers behaving like Dirac fermions with a zero mass, resulting in many extraordinary properties that are very different from other materials. Such properties can be controllably modified by proper impurity doping or by electrical or optical modulation, making graphene extremely attractive for novel device applications. The salient electronic, optical, and optoelectronic properties of graphene, together with its unique nanostructure, offer innovative opportunities to many potentially revolutionary applications for high-speed/high-frequency electronic and optoelectronic devices, terahertz (THz) oscillators and sensors, and ultrafast nonlinear optical elements. Realization of these exciting graphene-based devices, as well as the possibility for further innovation, relies on a good understanding of graphene’s electronic, optical and optoelectronic properties in the broad spectral range from THz to the visible. In this thesis, the electronic property of graphene is investigated first, followed by the discussion of THz property of graphene. Based on the derived models of the electronic and THz properties of graphene, we can describe the plasmonic behavior of graphene in various configurations, such as graphene-based THz waveguide. A concept THz device is demonstrated both theoretically and experimentally in the last.

In this thesis, two models are developed to describe the optical properties of graphene from the THz to the visible spectral region. We show that the optical conductivity is mainly contributed by interband carrier transitions in the visible region and by intraband carrier scattering in the THz range. Optical properties such as refractive index and transmittance can be calculated theoretically from the model in the optical range. In the THz range, the Fermi energy and the scattering rate are two important parameters in the determination of the optical conductivity. One can use these physical quantities as fitting parameters and find their values by fitting the THz model to the experimental data. The fitted results are consistent with the data and one can predict the optical conductivity and refractive index at the frequency higher than the bandwidth of our experiments. Other physical properties such as the carrier density and the mobility can also be obtained from the fitted parameters. The resultant mobilities of monolayer graphene and bilayer graphene are consistent with the results of other groups.