Nonlinear optics is a rapidly growing field of research, in which the light-matter interaction between intense light field from lasers and strong optical nonlinearity of the materials is investigated. The capability to create a material system with high nonlinearity and furthermore control it for tailor-made properties is captivating and unlocks the potential for more interesting applications.In Chapter 1, an electrically tunable nonlinear optical device working at near-infrared wavelength is theoretically and experimentally demonstrated. Ultrahigh optical second-order nonlinearity from TiN-based coupled metallic quantum wells can be electrically tuned by external electric field. Tunability of second-order susceptibility χ(2) reaches a 63% modulation depth with an average tunability of 10.5% per volt. In addition, electro-optic modulation of second-harmonic signal is presented by continuous tuning of χ(2) over a long period of time with high stability. These results provide a new material platform with actively controllable strong nonlinearity for future nonlinear photonic systems. In Chapter 2, a material system with strong and broadband optical second-order nonlinearity in the near-infrared is theoretically and experimentally demonstrated. Multiple units of TiN-based coupled metallic quantum wells with slightly shifted nonlinear response peaks are uniquely designed and epitaxially grown to form a multilayered stack. By measuring near-infrared to visible second-harmonic generation, second-order susceptibility χ(2) reaches 740 pm/V at 900 nm and spreads 200 nm, covering wavelength range from 800 nm to 1000 nm. Our discoveries open up the possibility to create materials with tailored broadband optical nonlinearity. In Chapter 3, a material platform excels in both optical second- and third- order nonlinearity at telecom wavelength is theoretically and experimentally demonstrated. In this TiN-based coupled metallic quantum wells structure, electronic sub-bands are engineered to support doubly resonant inter-sub-band transitions for exceptionally high second-order nonlinearity and provide single-photon transitions for remarkable third-order nonlinearity within the 1400–1600 nm bandwidth. Second-order susceptibility χ(2) reaches 2840 pm/V at 1440 nm, while Kerr coefficient n2 arrives at 2.8×10-10 cm2/W at 1460 nm. The achievement of simultaneous strong second- and third- order nonlinearity in one material at telecom wavelength creates opportunities for multi-functional advanced applications in the field of nonlinear optics.

The human sensorimotor cortex contains topologically organized maps of the body and movements, usually referred to as Penfield’s homunculus. The initial homun-cular map was depicted using electrical stimulation in patients undergoing brain surgery. For the last 25 years, noninvasive functional magnetic resonance imaging (fMRI) has allowed researchers to map brain organization and function with high spatial resolution (on the order of millimeters). However, less research has been conducted to model the temporal dynamics of fMRI for its low temporal resolution (on the order of seconds). To map topological organization in visual, auditory, and sensorimotor cortices, the phase-encoded paradigm uses time delays in periodic fMRI signals to encode and decode the representations of different brain regions. Phase-encoded fMRI data are typically ana-lyzed by Fourier transform, and an overall signal-to-noise ratio and a single phase of periodic signals are estimated from the entire time series. However, this method cannot fully characterize the temporal dynamics and stability of periodic signals and phases.

This dissertation includes three fMRI studies that aim to map the cortical repre-sentations of body parts (face and hand) and unravel the spatiotemporal brain dynamics during a reach-to-eat task. I proposed a data processing pipeline that uses independent component analysis to separate periodic noise from periodic signals, and use time-frequency analysis and circular statistics to model the spread of phase angle of fMRI time series and determine the stability of periodic signals. These analyses provide additional statistical measures, not obtainable using conventional linear methods, to validate the observed periodic fMRI signals. These methods are fundamental steps to construct a more accurate and comprehensive functional brain atlas of the human sensorimotor cortex.