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The goal of this project was to develop and utilise instrumentation for Vibrational Sum-Frequency Spectroscopy (VSFS) for the study of metallic interfaces treated with surfactants commonly used as corrosion inhibitors. This work is motivated primarily by the mechanistic knowledge gap surrounding the adsorption of such molecules, and the general lack of detail about the in situ interface. In particular, a corrosion inhibitor dodecyltrimethylammnonium chloride, abbreviated as DDTMAC, (an exemplar inhibitor of carbon steel in acidic environ- ments) has been focussed on, and its adsorption on gold and on carbon steel has been studied by VSFS and other complementary means, such as x-ray photoelectron spectroscopy (XPS), quartz crystal microgravimetry (QCM), and ellipsometry. VSFS is a second order non-linear optical technique, and possesses interface specificity (in- sensitive to bulk phases), making it a uniquely powerful for studying surfaces treated with such molecules, both ex and in situ. In VSFS, two photons strike a surface simultaneously (to within one picosecond), generating a third photon, and this third photon carries geometric and conformational information about the interface it was generated from. If incoming photon energies are swept, it also provides vibrational fingerprinting. The instrumentation described in this work uses an ultrashort (spectrally broad) probe pulse in the mid-IR region, and a longer, narrower pump pulse at 800 nm to produce broadband spectra rapidly (as opposed to tuning the probe pulse), meaning time resolved measurements of the in situ interface are possible. This instrumentation has been developed using ultrafast laser facilities in the Photon Science Institute at the University of Manchester, based on Ti:Sapphire sources, with a spectral The instrumentation has been tested using the benchmark system of self-assembled monolayers (SAMs) of octadecanethiol on gold, using the CH3 stretch mode region, and geometric informa- tion has been obtained about such a monolayer. This benchmark system has then been further studied using a more conventional surface probe, XPS, and geometric information has been verified. Following successful benchmarking, the VSFS instrument was applied to gold surfaces treated with DDTMAC. Initial measurements were ex situ, and once again verified using XPS, and coverage was determined to be comparable to the ODT benchmark at high concentrations for much shorter immersion times. Further measurements were applied to the in situ interface with the development of a liquid cell, exploiting the inherent surface specificity of VSFS, and it was noted that the in situ interface significantly differed from the ex situ surface. In situ measurements were then verified using common in situ probes, ellipsometry and quartz crystal microgravimetry (QCM), and coverage and thickness were calculated. This toolbox was then applied to the engineering interface of carbon steel treated with DDTMAC, both in water and in 1 molar hydrochloric acid, ex situ and in situ, and the symmetry and conformation of adlayers of DDTMAC was studied. We observed centrosymmetry at the in situ interface (with evolving weak resonances on a strong non-resonant background indicat- ing changes in ordering), and asymmetry at the ex situ interface resulting in much stronger resonances. This indicates disruption to the ordering of the overlayer upon removal from solution. The localised conformation and geometry of such adlayers was also studied using Sum-Frequency Microscopy in a collaboration with the University of Houston, and a domain structure of DDTMAC adsorption on the gold and steel surface was observed ex situ. Finally, VSFS in conjunction with near-ambient pressure XPS (NAP-XPS) was applied to study the initial adsorption of water on the native oxide film of a polycrystalline zinc surface for atmospheric corrosion applications. With VSFS, the OD resonance of deuterated water was probed (i.e. the non-hydrogen-bonded dangling OD bond at the air-water interface), and then the amount of water uptake was quantified using NAP-XPS, as a function of relative humidity. These measurements indicate that water adsorption occurs in an initially centrosymmetric layer, inaccessible to VSFS but not NAP-XPS, and subsequent water adsorption occurs in the form of droplets (islands) which grow as a function of relative humidity.

I present several new methods for the characterisation of ultrashort pulses using interferometry. A generalisation of the concatenation algorithm for spectral shearing interferometry enables interferograms taken at multiple shears to be combined. This improves the precision of the reconstructed phase in the presence of detector noise, and enables the relative phase between disjoint spectral components to be obtained without decreasing the spectral resolution. The algorithm is applied to experimental data from two different implementations of spectral shearing interferometry for ultrashort optical pulses. In one, the shears are acquired sequentially, and in the other they are acquired simultaneously. I develop a form of spatio-temporal ultrashort pulse characterisation which performs both spatial and spectral shearing interferometry simultaneously. It requires a similar geometrical setup to common implementations of spectral phase interferometry for direct electric-field reconstruction, but provides complete amplitude and phase characterisation in time and one spatial dimension. I develop the theory of lateral shearing interferometry for spectrally resolved wavefront sensing of extended ultraviolet and soft x-ray pulses generated using high-harmonic generation. A comprehensive set of wavefront measurements of harmonics 13-25 in Krypton show good agreement with theory, validating the technique. I propose and numerically demonstrate quantum-path interferometry mediated by a weak control field for high harmonic generation. This is a general technique for measuring the amplitude and relative phases of each contributing quantum path. The control field perturbatively modulates the phase of each path. The differing sensitivity of each path to the parameters of the control field allows their contributions to be distinguished from one another.

This thesis describes the use of counterpropagating pulse trains to quasi-phase-match high-harmonic generation (HHG). Two novel techniques for generating trains of ultrafast pulses are described and demonstrated. The first method makes use of a birefringent crystal array to split a single pulse into a sequence of pulses. The second method makes use of the time-varying polarisation of a chirped pulse passed through a multiple-order wave plate to generate a train of pulses by the addition of a polariser. It is demonstrated that this second technique can be used to make pulse trains with non-uniform pulse separation by using an acousto-optic programmable dispersive filter to manipulate the higher-order dispersion encountered by the chirped pulse. The crystal array method is used to demonstrate quasi-phase-matching of HHG in a gas-filled capillary, using one and two counterpropagating pulses. Enhancements of up to 60% of the intensity of the 27th harmonic of the 800,nm driving laser light are observed. Information on the spatial and dynamic properties of the HHG process is obtained from measurements of the coherence length in the capillary. Simulations of HHG in a capillary waveguide have been performed. These agree well with the results of the quasi-phase-matching experiments. The effect of mode-beating on the generation process in a capillary and its use as a quasi-phase-matching mechanism are investigated.

This work covers two main results united by multidimensional coherent spectroscopy (MDCS): one experimental and one theoretical. MDCS is a nonlinear optical technique in which a sample is probed using a series of ultrashort pulses. Measurements are made while varying the relative time delays between the pulses, and the resulting spectra yield a much richer set of information compared to traditional linear spectroscopies. The experimental work concerns the negatively charged silicon-vacancy (SiV) center in diamond. We use two-pulse correlation (TPC) spectroscopy and rephasing MDCS to probe a diamond sample with a high density of implanted SiV centers. These spectra reveal a large number of spectral peaks, which can be grouped into two families of SiV centers using the MDCS spectra. By comparing spectra from two polarizations of the incident light, we associate the two families with two orientation groups within the diamond. We link the differences in the frequencies of the spectral peaks to strain intrinsic to our sample, and use the peak locations from both families to solve for the full strain tensor local to the laser spot. By measuring TPC spectra at multiple points on the sample, we track changes in the measured strain. We observe non-zero strain on the order or 1e-5 at every measured location, and observe variation in both the normal and shear strain in the sample. We interpret the strain as likely to be due to the high implantation density of silicon in the diamond. These results could be useful when using SiV centers as a strain gauge. The theoretical work uses simulations to calculate spectra. The simulations developed here begin by recursively generating a list of Feynman diagrams for a given signal pathway and system. The contributions due to each Feynman diagram are calculated and combined to find the complete spectrum. The code is designed to be very flexible, and can be used to simulate arbitrary types of MDCS spectra and energy level diagrams. We then apply the simulations to investigate the effects of correlated dephasing due to scattering events in the Markovian limit on MDCS of interacting systems. We derive a mathematical expression to represent the dephasing rate of a coherence in terms of the dephasing rates of the coherences from the constituent energy transitions and the correlation matrix of these transitions. This expression is applied to simulate double-quantum and higher-order n-quantum spectra of multiple interacting systems. For double-quantum spectra, correlated dephasing results in a higher double-quantum dephasing rate, and anticorrelated dephasing results in a lower double-quantum dephasing rate. Similar results are found for the n-quantum dephasing rate. Generally, for certain configurations, the many-body dephasing rate can be arbitrarily low, and the n-quantum linewidth can be arbitrarily narrow, although this requires some form of anticorrelation. These results could be useful in creating quantum sensors with higher sensitivities, since one limit of the sensitivity is the decoherence time of the system.

Nowadays, a significant part of the research interest in optoelectronic devices is in making nanostructures such as heterojunctions, nanowires, quantum wells and quantum dots that dramatically change the electron behavior of the material compared to their bulk counterpart. In this dissertation, we applied ultrafast spectroscopy to study specifically the hot carrier separation and recombination dynamics in the CVD-grown monolayer molybdenum disulfide (MoS2) and graphene heterostructure, III-nitride quantum well LED structure and self-organized InGaN nanowires for photocatalysis. By using ultrafast pump-probe spectroscopy, we observed efficient electron and hole separation within a few hundred femtoseconds by interlayer charge transfer from graphene to MoS2 monolayer following initial excitation and thermalization. The transfer-back process to graphene happens in multiple timescales, the dynamics of which after the thermalization can only be modeled by a Porter-Thomas distribution for the charge transfer rate because the transfer back process after the thermalization is dominated by the material disorder. The III-nitride quantum well has been the most common LED structure since the 1990s. III-V compounds are also the only known material that can have tunable valence and conduction band levels that cover the chemical potential of a few important photochemical reactions such as water splitting and methane oxidation thus making them ideal for photocatalysis in converting solar energy into electrochemical energy. We studied the time-resolved photoluminescense (TRPL) and the time-resolved differential reflectance (TRDR) of the self-organized InGaN nanowires observed a fast decay component in the PL decay dynamics that were not observed in the DR measurements only when the InGaN is p-doped. We argue that the fast decay component in the PL decay dynamics indicates the charge separation due to the built-in polarization field near the surface of the nanowires. We also studied the temperature-dependent TRPL experiments and room temperature TRDR of the quantum disk-in-wire micro-LED structure that contains tilted quantum wells grown along the semi-polar facets. The TRPL decay curves always show faster dynamics than the TRDR. This is modeled with thermal activated non-radiative process that can be explained with Arrhenius’s Law applied to the lateral charge transport over the local indium composition fluctuation. Throughout this thesis, we study the ultrafast charge separation and relaxation by directly probing and by combining the PL and DR dynamics in different nanostructures. We have demonstrated a novel approach for detecting carrier spatial separation and the results revealed the important microscopic physics such as material disorder, band bending and local fluctuation that are crucial for future research and development.

The cyclic exchange of energy between the pump, signal, and idler fields that characterizes optical parametric amplification (OPA) places a fundamental limitation on efficiency for Gaussian-shaped beam and pulse profiles typical of real laser sources. This is because the intensity dependent conversion period of OPA results in asynchronous conversion across the spatiotemporal intensity profiles of the mixing laser fields. We introduce a new method for achieving efficient OPA by using simultaneously phase-matched idler second harmonic generation (SHG) to act as an effective loss-channel for idler photons. The dynamics are characterized by damped conversion cycles, leading to asymptotic conversion of the pump and idler to the signal and idler second harmonic fields at all points in transverse space and time. We develop a damped Duffing oscillator model that unifies the description of conventional OPA with OPAs that use linear absorption \cite{Ma:15, El-Ganainy:15, Zhong:16, Li:17, Ma:17} or SHG \cite{Flemens:21} to remove idler photons and enhance efficiency. An experimental demonstration in a CdSiP\textsubscript{2}-based device enables 68\% pump depletion with 44\% pump to signal energy conversion efficiency--a several fold increase over conventional OPA efficiency. We then show that SHG can replace loss to induce non-Hermitian features such as regions of broken and unbroken PT-symmetric phase demarcated by an exceptional point in three-wave mixing nonlinear interactions. This enables a new paradigm where the behavior associated with the PT-symmetric phase of a non-Hermitian subsystem can be used to control the containing Hermitian system through the coherent couplings. These findings suggest a new approach for the engineering of dynamics where energy recovery and sustainability are of importance in photonics and laser science. Finally, we demonstrate self-dispersion managed adiabatic difference frequency generation (ADFG). While ADFG has been demonstrated to produce single-cycle pulses in the mid-IR \cite{Krogen:17}, this is not without the challenge of implementing a complicated dispersion management scheme to compensate for the complex dispersion imparted by the device. We engineer and characterize an aperiodically poled LiNbO\textsubscript{3} device that generates an octave-spanning bandwidth in the mid-IR (2-4 \textmu m) that imparts no net dispersion to the generated light.

Thulium (Tm) based high repetition rate compact optical frequency comb sources operating in the 2 µm regime with femtosecond pulse durations enable a wide range of applications such as precise micro-machining, spectroscopy and metrology. Applications such as metrology and spectroscopy rely on the stability of mode-locked lasers (MLLs) which provide extreme precision, yet, the complex dynamics of such highly nonlinear systems result in unstable events which could hinder the normal operation of a MLL. MLL as a nonlinear system inherently exists a wide variety of complex attractors, which are sets of states that the system tends to evolve toward, exhibiting unique behaviors. Complex phenomena including pulsating solitons, chaotic solitons, period-doubling, soliton explosion, etc., have been predicted theoretically and observed experimentally in the past decade. However, most experimental observations rely on conventional characterization methods, which are limited to the scanning speed of the spectrometer and the electronic speed of photodetector and digitizer, so that the details of the non-repetitive events can be buried. In recent years, a technique called dispersive Fourier transform (DFT) has been developed and allows consecutive recordings of the pulse-to-pulse spectral evolution of a femtosecond pulse train, opening a whole new world of nonlinear dynamics in MLL. In this dissertation, we first demonstrate the ability of scaling the repetition rate of a Tm MLL to repetition rate as high as 1.25 GHz through miniaturizing the cavity. Our approach of maintaining comparable pulse energies while scaling the repetition rates allows a high-quality femtosecond mode-locking performance with low noise performance in Tm soliton lasers. Then we experimentally study the transition dynamics between consecutive multi-pulsing states through adjusting pump power with a constant rate in an erbium-doped fiber laser, specifically the build-up and annihilation of soliton pulses between a double pulsing and a three-pulse state utilizing DFT. To investigate real-time laser dynamics in Tm based laser systems, we propose and develop a DFT system that up-converts the signal to the 1 µm regime via second harmonics generation (SHG) and stretches the signal in a long spool of single-mode fiber to realize DFT. This approach overcomes the limitation of bandwidth of 2 µm photodetector and high intrinsic absorption of 2 µm light in fused silica fibers. The SHG-DFT system is used to study dynamics of both explosions in a chaotic state between stable single-pulsing and double-pulsing state, and explosions induced by soliton collision in a dual-wavelength vector soliton state. We also study dynamics of transient regimes in a Tm-doped fiber ring laser that can be switched between conventional soliton and dissipative soliton, revealing how spectral filtering plays a role in obtaining stable stationary states.

Transition metal dichalcogenides (TMDs) have received considerable attention in the past decade for their optoelectronic applications in photovoltaics, lasers, and quantum information. In the monolayer limit, these materials exhibit extraordinary properties, including efficient light-matter coupling, ultrafast charge transfer, long-lived interlayer excitons with high binding energies, and many-body excitonic interactions. In this thesis, we present the development and application of multidimensional coherent imaging spectroscopy (MDCIS), a four-wave mixing (FWM) based nonlinear spectroscopic imaging technique, to TMD monolayers and heterostructures. Based on multidimensional coherent spectroscopy (MDCS), MDCIS allows us to distinguish between homogeneous and inhomogeneous contributions to the material linewidths and distinguish coherent and incoherent coupling mechanisms in TMD heterostructures. The imaging aspect allows us to capture the spatial variation of the aforementioned physical processes across TMDs. We first discuss our results applying MDCS to an MoSe2/WSe2 heterostructure, for which we characterize the coherent and incoherent coupling mechanisms present in these materials. We quantify the timescales of rapid electron (91+/-9 fs) and hole (148+/-28 fs) transfer between the two materials. Furthermore, we visualize strong coherent coupling between excitons in the MoSe2 and WSe2 layers by observing oscillations of the coupling peaks in one-quantum MDCS and measuring a mixing energy of 73 meV in zero-Quantum MDCS. We also observe many-body signatures of the interlayer excitons and, in conjunction with photoluminescence measurements, measure their binding energy to be 254 meV. To accelerate nonlinear imaging, we develop a lock-in amplifier that uses a box-weighted instead of an exponentially-weighted lowpass filter. The transfer function of the box lock-in has tunable notches in the frequency domain that enable sufficient suppression of adjacent modulations present on the detector. We use Monte-Carlo simulations to quantify the signal-to-noise ratio and suppression of adjacent modulations, demonstrating the superiority of the box lock-in over the conventional exponential lock-in at short pixel-dwell times. We further experimentally demonstrate this advantage by imaging a monolayer of MoSe2 on a distributed Bragg reflector. Furthermore, we present results using MDCIS to study the potential of MoSe2 monolayers and MoSe2/WSe2 heterostructures for quantum information applications. We map the distribution of homogeneous and inhomogeneous linewidths across an MoSe2 monolayer, identifying promising areas with low inhomogeneity and long dephasing times that bear the potential for qubits. We also visualize the strain across the MoSe2 monolayer and comment on the detrimental effects strain may have in device applications. Similarly, we map strain across an MoSe2/WSe2 heterostructure and quantify the spatial homogeneity of coherent coupling (81 % of the sample) and charge transfer (91 % of the sample). We further map the distribution of interlayer exciton lifetimes. These quantities display a surprising robustness in the presence of strain, strengthening the case for TMD heterostructures as an applications platform for quantum information and photovoltaics. Lastly, we demonstrate how to further accelerate the nonlinear imaging techniques in this thesis by smart scanning and sampling schemes in the time-domain. We obtain FWM images, dephasing maps, and decay maps within minutes, opening the avenue for moving these techniques out of the lab and into a fabrication/manufacturing setting for advanced materials characterization.

Optical frequency combs, unique light sources that coherently link optical frequencies with microwave electrical signals, have heralded several scientific frontiers such as frequency metrology, optical clockwork, precision navigation, and high speed communication over the past decades. Parametric oscillation in ultrahigh Q microresonators, facilitated by the high quality factors and the small mode volumes, is an alternative physical process that offers the opportunity of optical frequency comb generation in compact footprints with smaller weight and lower power consumption. In particular, the observation of dissipative Kerr soliton (DKS) formation and soliton-induced Cherenkov radiation offers a reliable route towards self-referenced broadband optical frequency microcomb. DKS is localized attractor where the Kerr nonlinearity is compensated by the cavity dispersion and the cavity loss is balanced by the parametric gain. Thus the cavity dispersion and the pump-resonance detuning are two determining parameters in the existence of DKS in ultrahigh Q microresonators. Among numerous material platforms, Si3N4 planar waveguide system draws great attention for its high nonlinearity, wide transparent window, low propagation loss and its CMOS-compatibility. For Si3N4 microresonators, dispersion is typically engineered by designing waveguide geometry. However, conventional method of using multi-mode waveguide results in additional perturbation to the Kerr frequency comb generation dynamics. Furthermore, despite of all the advantages, DKS suffers from low conversion efficiency, restrict pump-resonance detuning requirement and difficult dispersion design, which could be supplemented by normal dispersion frequency microcomb. In this thesis, I focus on frequency microcomb studies in novel designs of tapered Si3N4 planar waveguide geometry achieving higher-order-mode suppression. I not only work on unravelling the fundamental dynamics of DKS in anomalous dispersion regime, but I also investigate a novel pulse formation mechanism in normal dispersion device. Benefiting from their high intrinsic phase coherence and individual comb line powers, I further extend my research to absolute distance metrology with a single soliton comb that achieves nm-level precision, and terabits/s free-space optical communication with a flat normal dispersion comb.

Intracavity Phase Interferometry (IPI) is a detection technique that exploits the inherent sensitivity of a laser's frequency to the parameters of its cavity. Intracavity interferometry is orders of magnitude more sensitive than its extracavity alternatives. This dissertation improves on previous free-space proof-of-concept designs. By implementing the technique in fiber optics, using optical parametric oscillation, and investigating non-Hermitian quantum mechanics and dispersion tailoring enhancement techniques, IPI has become more applicable and sensitive. Ring and linear IPI configurations were realized in this work, both operating as bidirectional fiber optical parametric oscillators. The benefit of using externally pumped synchronous optical parametric oscillation is the removal of the sensor dead band region and simplification of the sensing cavity. These two lasers, along with the theoretical work found in this Dissertation, will facilitate future fundamental studies of sensor noise and sensitivity enhancement.

Chalcopyrite crystals in the II-IV-V2 family have received significant interest due to their high nonlinearity, composition-tunable bandgaps, wide transparency windows, and high damage threshold. These semiconductors have been explored for electromagnetic (EM) screening, spintronic and photovoltaic applications, making them good optical and optoelectronic materials. This thesis uses terahertz spectroscopy to understand optical, electronic, and vibrational dynamical processes in CdGeP2, ZnGeP2 and CdSiP2 chalcopyrite semiconductors. We have employed Terahertz time-domain spectroscopy to investigate temperature-dependent ground-state properties of bulk chalcopyrite crystals that can be related to electronic transport and electron-lattice interactions. The complex spectra provide refraction and absorption from which electron-phonon coupling and average phonon energies are extracted. AC conductivity spectra provide carrier densities and electron scattering times, the temperature dependence of which are associated with unintentional shallow dopants. Temperature dependence of the scattering time is converted into carrier mobility and modeled with microscopic transport mechanisms such as polar optical phonon, acoustic phonons, deformation potential, ionized impurity, and dislocation scattering. Hence, analysis links the terahertz response to properties that can only be obtained using high-frequency AC Hall-effect measurements, Raman scattering, and conventional continuous-wave spectroscopy. Ultrafast photoexcited charge-carrier dynamics are investigated using time-resolved terahertz spectroscopy. Analysis of the differential THz transient reveals a two-component exponential relaxation, with decay times that increase with pump fluence due to state filling. Inverting the transients recaptures the canonical rate-equation for the system and from which the recombination dynamics are attributed to the entire excitation range. To support the recombination information, THz photoconductivity determines the excited-state carrier transport as a function of temperature. Both elevated temperatures and increased excitation density decreases excited-state carrier mobility and are attributed to carrier-carrier interactions and scattering from phonons. These model semiconductors, which have application in photonics, allow for further demonstration of pulsed-THz-based spectroscopy to capture both charge transport and dynamics. Additionally, several charge transport and carrier-lattice properties for CdGeP2, ZnGeP2, and CdSiP2 have been reported that can assist with the design and optimize of devices that comprise them.

Mode-locked fiber lasers have attracted significant scientific and commercial interest since they offer a compact and highly stable platform with straightforward operation for exploiting ultrafast and nonlinear phenomena. They have enabled a vast range of applications that span from distinct disciplines such as medical diagnostics, molecular spectroscopy, and high-power precise mechanical cutting, to optical metrology. Various gain media have been utilized to achieve laser emission at different wavelengths. We have developed unique thulium/holmium (Tm/Ho) doped mode-locked fiber laser systems to address the needs of low-noise ultrafast optical sources in the wavelength vicinity of 2 μm at higher repetition rates. Since the 2 μm wavelength regime has recently attracted more attention with the emergence of thulium gain fibers, the rich underlying cavity dynamics, novel pulse operation regimes and nonlinear phenomena in compact fiber configurations have not been fully explored yet. In this thesis, research is conducted on novel Tm fiber laser cavity configurations and on the formation of unique, polarization-based pulsing regimes. Particularly, this research is focused on the exploration of novel ultrafast and nonlinear phenomena, and the development of optical sources emitting unprecedented ultrafast pulse trains beyond conventional equal-intensity distribution using Tm/Ho doped gain media. The research presented features four main results: 1) development of a high repetition rate and low-noise Tm/Ho doped mode-locked fiber laser platform as an attractive optical source for a wide variety of applications 2) investigation of a novel mode-locked state in which the ultrafast pulse train is composed of co-generated, consecutive, equal intensity and orthogonally polarized pulses in order to achieve dual RF comb generation for dual-comb spectroscopy applications, 3) exploration of controllable ultrafast waveform generation utilizing vector soliton and harmonic mode-locking mechanisms for optical telecommunication applications, and 4) demonstration of unique transitional mode-locked states showing exceptional features such as powerful irregular bursts of ultrafast pulses and rogue wave behavior without damaging the laser elements. The aim of these projects has been to explore the novel optical properties of Tm/Ho co-doped fiber lasers in order to achieve advanced functionalities in commonly practiced applications such as telecommunication, metrology and spectroscopic applications.

The realization of strong optical magnetism in nominally “non-magnetic” media could lead to novel forms of all-optical switching, energy conversion, or the generation of large (oscillatory) magnetic fields without current-carrying coils. By advancing understanding of radiant optical magnetization, the research reported in this thesis contributes progress toward these prospects. Experiments and simulations were performed of light scattering in natural dielectrics at non-relativistic optical intensities. The goal was to understand which molecular factors influenced the magnitude of induced magnetic dipole scattering in isotropic materials. The intensity dependence and spectra of cross-polarized scattering in several transparent molecular liquids (CCl4, SiCl4, GeCl4, SnCl4, SiBr4, TMOS, TEOS, TPOS) and crystalline solids (GGG, Quartz) were found to agree with predictions of quantum theory. Additionally, evidence was found for the expected proportionality between the intensity of radiant magnetization and the electric dipole transition moment, together with an inverse proportionality with respect to molecular rotation frequency. By comparing spectra in molecular liquids, it was found that spectral features in the cross-polarized scattering were uniquely attributable to high-frequency librations of magneto-electric (M-E) origin. In solids, optically-induced magnetic scattering in solids reached the same intensity as Rayleigh scattering, far below relativistic conditions. Additionally, all four channels predicted by the quantum theory for second-order (2-photon) M-E processes at the molecular level were observed in experiments on GGG crystals. Two theoretical contributions are presented in this thesis. The first is an extension of the classical Lorentz Oscillator Model from an atomic to a molecular picture. It includes the effect of torque exerted by the optical magnetic field on excited state orbital angular momentum, resulting in an enhancement in the magnetization achievable under non-relativistic conditions in molecular or condensed matter systems. Temporal dynamics are predicted for the first time, taking into account molecular composition. Secondly, the torque Hamiltonian of quantum theory is shown to obey Parity-Time (PT) symmetry, indicating that M-E effects should occur universally. Lastly, results from classical and quantum mechanical models are compared and found to be in very satisfactory agreement.

Semiconductor nanostructures have spatial inhomogeneity resulting from disorder, device design, and even experimental conditions. Inhomogeneity on one-micron length scales can be accessed with a diffraction-limited spot. Optical spectroscopies with the ability to measure on this length scale are capable of probing small samples and short-range effects that are otherwise inaccessible. In this thesis we develop a set of coherent spectroscopies based on heterodyne detection that enable measurement of ultrafast (sub-picosecond) dynamics in a diffraction-limited spot. Coherent spectroscopy techniques are known for their ability to probe many-body effects and microscopic inhomogeneity. We exploit these capabilities in several different experiments to measure effects at small length scales with extremely high sensitivity. The second-order coherence of an optical excitation has known and predicted affects on nonlinear semiconductor responses. Here we develop an experiment to compare the optical excitation of gallium arsenide quantum wells using a truly thermal light source (a luminescent diode) and a coherent light source (laser). Through careful experimentation we measure no difference in these unique excitations, and we present that the absence of an effect arises in part because the measured nonlinear response results from averaging over multiple temporal modes of the continuous thermal source. Experiments here demonstrate the ability to measure many-body effects on extremely short length scales, even less than the spot size. We measure nanometer dynamics of an excitation spot that result from the interplay between a tightly-focused ultrafast-laser spot and the collective excitation the laser induces in a semiconductor. Specifically we use spatially-resolved transient absorption to measure that a small spot of resonantly excited excitons in 10 quantum well sample decreases in size for several picoseconds before the diffusion of excitons dominates the spot-size dynamics. In a single narrow quantum well containing interfacial quantum dot states we use double-quantum multidimensional spectroscopy to measure coupling between nominally isolated localized (quantum dot) states. The coupling is only present after weak excitation of delocalized (quantum well) states in the same crystal. This experiment also demonstrates the ability of diffraction limited coherent techniques to probe length scales beyond the diffraction limit. We use multidimensional coherent spectroscopy (MDCS) to compare monolayer molybdenum diselenide samples mounted directly on sapphire versus encapsulated in hexagonal noron nitride. We measure the homogeneous linewidths of various samples and demonstrate that the linewidth of the encapsulated samples are nearly radiatively limited at 0.26 +/- 0.02 meV. The linewidth is much narrower than is expected based on the theoretical prediction for a perfect sample and the integrated absorption assuming a homogeneous sample. We attribute the narrow linewidth to localization and discuss inhomogeneity applied to highly coherent excitations. Using MDCS we measure coupling between quantum-confined polariton states. The states are spatially localized, so we are able to measure the dependence of the signal on the spatial position of the exciation spots. We also measure relaxation from the exciton into the polariton states that indicate how energy is transferred when these systems are pumped as lasers. Finally we discuss and demonstrate nonlocal four-wave mixing. We present this as a phenomenon that can be measured in materials with a high coherence length, and we present the technique as a way to determine a sample's coherence length. The fractional-Fourier transform is introduced for considering nonlinear responses in system with finite spatial extents.

The thesis describes primarily two experiments which investigate the coupling of structural and magnetic properties in solid-state ferromagnets on an ultrafast ($\approx$100~fs) timescale. To achieve this goal, both studies use ultrafast optical and x-ray pump-probe methods in combination, integrating information about magnetic and structural dynamics to form a more complete picture of the underlying physics. In the first experiment, the well-known shape-memory ferromagnetic Heusler alloy $\text{Ni}_2\text{MnGa}$ is studied. This compound is a multiferroic material stabilised by the correlations between electronic, magnetic, and structural order. The shape-memory effect is based on a structural phase transition between a low-temperature martensite phase and a high-temperature austenite phase. In both phases, the material is ferromagnetic. It has been observed for different stoichiometries that the martensite phase exhibits slightly incommensurate structural modulations whenever the shape-memory effect is present, but the exact connection between the two is unclear. We performed ultrafast optical measurements of the magnetisation of $\text{Ni}_2\text{MnGa}$, using 100~fs, 800~nm pulses for both the pump and the magneto-optical Kerr effect probe. We found a rapid demagnetisation with a timescale of $320\pm50$~fs, followed by a very slow recovery. At the FEMTO slicing source, we performed ultrafast x-ray diffraction on the weak (20201) satellite reflection of the (202) Bragg peak, which is a measure of the structural modulation. At high fluences of the 800~nm near-IR pump, we were able to observe a rapid and almost complete suppression of the structural modulation on a timescale of $300\pm40$~fs, very similar to the behaviour of the magnetisation. However, the longer timescale dynamics are markedly different from the one observed in the magnetisation: we observed an intermediate recovery of the structural modulation, before a second drop was caused by the thermal phase transition to the high-temperature austenite structure, which does not support the structural modulation. Our conclusion is that magnetisation and structural modulation are not strongly coupled in $\text{Ni}_2\text{MnGa}$, as the structural modulation was able to recover even while the material was demagnetised. The second experiment studied the movement of the lattice during ultrafast demagnetisation of a thin single-crystal iron film. While ultrafast demagnetisation is a very well-established effect, its microscopic mechanism remains unclear, especially with respect to the flow of angular momentum. Our goal was therefore to find a signature of the ultrafast Einstein--De Haas effect, i.e. the flow of spin angular momentum from the magnetisation to the mechanical angular momentum of the lattice. We identified that transverse shear waves would be launched from the surfaces of a rapidly demagnetising crystal, with an initial deflection whose direction depends on the magnetisation. A double-grazing x-ray diffraction geometry to measure the crystal truncation rod (CTR) of an in-plane and in-surface Bragg peak of the iron was chosen for the experiment. This choice maximises the sensitivity to the transverse strain wave and simultaneously minimises sensitivity to longitudinal strain waves caused by laser heating. The ultrafast pump-probe experiment was performed at the XPP endstation of the LCLS free-electron-laser, using a 6.9~keV x-ray probe beam and a 800~nm near-IR pump. The intensity along the (2~2~L) CTR was recorded simultaneously for each shot by using an imaging detector, with L in the range 0.02--0.09. Measurements were made for two opposite directions of magnetisation by selecting one of the two polarities of the sample electromagnet for each shot. By taking the difference of the time-resolved diffraction intensities for the two magnetisation directions along the CTR, we were able to positively identify a transverse mechanical strain wave in the data. Comparison with a detailed lattice dynamics and diffraction model allowed us to extract the timescale of the appearance of angular momentum in the lattice as around 200~fs, and the magnitude of angular momentum as corresponding to 8\% of the saturation magnetisation of iron. Using magneto-optical data for calibration, where we observed a 10\% demagnetisation under the same conditions, we conclude that a majority of about 80\% of the angular momentum lost from the spin system appear as mechanical angular momentum in the lattice; a complete transfer is also plausibe with the given experimental uncertainties. This shows that the interaction with the lattice plays an essential role in the ultrafast demagnetisation of iron.

Metamaterials operating at terahertz (THz) region of the electromagnetic spectrum have remained have remained a promising area of study not only for realizing technologies in a historically underdeveloped spectral regime, but also as a scientific tool for exploring and controlling fundamental physical phenomena at meV energy scales in a variety of condensed matter systems. In this thesis, I will present several projects in which metamaterials and more traditional condensed matter systems are integrated into hybrid metamaterial systems. We leverage these systems to realize new practical THz devices, as well as to couple to and control quantum phenomena in condensed matter systems. I will begin with an introduction to the conceptual, numerical, and experimental techniques in the THz metamaterial toolbox. The first research endeavor I will discuss is a metamaterial system that incorporates perhaps the simplest material; air. This metamaterial perfect absorber with a continuously tunable air dielectric layer allows for comprehensive exploration of metamaterial absorber systems, and demonstrates some unique phenomena owing to its lossless dielectric layer. Next I will introduce an applications oriented device; an electrically actuated broadband terahertz switch which transitions from a non-reflective, transmissive state to a fully absorptive state. It employs an all dielectric metamaterial layer to suppress reflections and trap light, and an electrically actuated phase change material, VO2 to transition between states. The final section of this dissertation will explore strong coupling effects between a metamaterial and the superconducting c-axis Josephson plasmon in the layered cuprate, La{2-x}SrxCuO4. Preliminary measurements are first presented then followed by high field THz measurements in which complex nonlinear behavior is observed.

Photonic time stretch is a well-established real-time optical technology. Using dispersion, the spectral modulation of a broadband optical pulse is stretched to alleviate the bandwidth bottleneck present in the subsequent analog-to-digital conversion and digital processing.The recent warped time stretch generalizes this concept with tailored non-uniform dispersion profiles, reshaping the wideband optical information arbitrarily and in real-time. The approach provides a design pathway for translating a-priori knowledge of signal spectra into context-optimized data acquisition and processing. This has wide-ranging applicability, including optical pulse reshaping, feature extraction, network coding, data compression and optical phase retrieval.Here, we will analyze the effects of an arbitrary dispersion profile on wideband optical signals, and show how its proper design provides full-field control over critical parameters, e.g. time-bandwidth product, SNR etc. We first show some theoretical results, then apply the warped stretch framework to digital image compression. Finally, we demonstrate a physical implementation of large and reconfigurable dispersion.

We demonstrate a versatile vortex linear light bullet as a three-dimensional vortex Airy-Bessel wave packet for the first time. It combines a temporal Airy pulse with a higher order vortex Bessel beam in the spatial domain. Its non-varying feature in linear propagation is verified by three-dimensional (3D) measurements. Advanced from previously reported linear light bullets which are limited to specific materials, the vortex Airy-Bessel wave packet works as a light bullet for any material while carrying orbital angular momentum. It is believed that the versatile vortex linear light bullet is useful in many applications such as nano-lithography, nano-surgery, etc. The study of controlled collisions between optical vortices in the time domain is also reported in this thesis.

Nanotechnology has recently enjoyed a tremendous interest, and many emerging nanoscale and low-dimensional materials and devices are under active investigation. This dissertation presents research work on the physics of the ultrafast terahertz (THz) response and the hot-carrier dynamics in two sample classes of state-of-the-art materials, namely graphene and semiconductor nanowires, by using ultrafast time-resolved THz spectroscopy. Thorough understanding of this physics is indispensable for the implementation of novel high-speed nanoelectronic and nanophotonic devices based on these materials. The dynamic THz response of a wide variety of high-quality graphene, including epitaxial and chemical-vapor-deposited, is systematically studied. In pristine epitaxial and chemical-vapor-deposited graphene, the dynamics depend critically on the doping density with relaxation times ranging from a few picoseconds in highly doped to hundreds of picoseconds in quasi-neutral layers; a microscopic density-matrix theory of carrier-carrier and carrier-phonon interactions accounts quantitatively for the experimental results. In multilayer epitaxial graphene with a few highly doped and many lightly doped layers, low-energy relaxation times of hundreds of picoseconds are measured in the lightly doped layers consistent with a first-principles theory of interlayer energy transfer via screened Coulomb interactions. In semiconducting epitaxial graphene, the relaxation of the dynamics is up to two orders of magnitude faster relative to metallic epitaxial graphene attributed to large enhancement of the phase-space available for carrier scattering due to an energy gap. In epitaxial graphene nanoribbons, a highly anisotropic response arises from two-dimensional quantum confinement with carrier lifetimes of tens of picoseconds in the high-energy subbands. The dynamic THz response of quasi-one-dimensional high-quality single-crystal germanium and germanium/silicon core/shell nanowires is also extensively investigated. The dynamics are characterized by fast few-picosecond intraband carrier relaxation followed by slower sub-nanosecond interband carrier recombination processes. Clear evidence for ballistic carrier transport on tens of nanometers is observed, and surface defect states are identified as the dominant carrier recombination and scattering mechanism limiting carrier lifetime and transport. Three possible physical origins giving rise to the observed highly anisotropic response are considered including free-carrier response, exciton response and quantum confinement effects.

Laser filamentation is a highly complex and dynamic nonlinear process that is sensitive to many physical parameters. The basic properties that define a filament consist of (i) a narrow, high intensity core that persists for distances much greater than the Rayleigh distance, (ii) a low density plasma channel existing within the filament core, and (iii) a supercontinuum generated over the course of filamentation. However, there remain many questions pertaining to how these basic properties are affected by changes in the conditions in which the filaments are formed; that is the premise of the work presented in this dissertation. To examine the effects of anomalous dispersion and of different multi-photon ionization regimes, filaments were formed in solids with different laser wavelengths. The results provided a better understanding of supercontinuum generation in the anomalous dispersion regime, and of how multi-photon ionization can affect the formation of filaments. Three different experiments were carried out on filamentation in air. The first was an investigation into the effects of geometrical focusing. A simplified theoretical model was derived to determine the transition of filamentation in the linear-focusing and nonlinear- focusing regimes. The second examined the effects of polarization on supercontinuum generation, where a polarization-dependent anomalous spectral broadening phenomenon due to molecular effects was identified. The third involved the characterization of filaments in the ultraviolet. The combination of physical mechanisms responsible for filamentation in the ultraviolet was found to be different from that in the near infrared.

Two-photon fluorescence microscopy is a popular method for imaging biological systems, offering benefits over one-photon fluorescence microscopy including increased penetration depth in tissues and reduced photobleaching. Experiments requiring selective excitation of multiple fluorophores are challenging to perform with existing two-photon fluorescence methods. Conventional two-photon microscopes employ tunable laser systems with limited temporal resolution. Other approaches include multiple-beam setups which may have complicated alignments, and ultrabroadband lasers, which simultaneously excite all fluorophores. The use of ultrafast pulse shaping methods in two-photon fluorescence microscopy offers the ability to tailor an ultrabroadband pulse to excite specific fluorophores for multicolor two-photon microscopy applications. This thesis demonstrates three applications of ultrafast pulse shaping to multicolor two-photon fluorescence microscopy. The first is the use of pulse shaping with linear unmixing of fluorescence signals to perform three-color two-photon imaging of live cells expressing fluorescent proteins. Resulting images show that the method can identify cells expressing single fluorescent proteins as well as cells expressing three fluorescent proteins simultaneously. This ultrafast pulse shaping approach has a simpler setup compared to other three-color imaging techniques, and can be easily expanded to more fluorophores. Two applications of ultrafast pulse shaping to Fluorescence Resonance Energy Transfer (FRET) microscopy are also presented. FRET microscopy is a powerful tool for observing interacting molecular species. While significant progress has been made in obtaining quantitative one-photon FRET measurements, similar progress in two-photon FRET measurements has been lacking. The techniques presented here use the selective excitation provided by pulse shaping to pave the way towards quantification of two-photon FRET. First, the use of pulse shaping to distinguish between FRET and no FRET conditions in live cells expressing fluorescent proteins is demonstrated. Differing intensity contrast results between cells imaged with different shaped pulses indicate that selective excitation can be applied to donor and acceptor fluorophores in FRET constructs and FRET can be detected. The second application discussed is the generalization of FRET stoichiometry to two-photon FRET measurements. A new theory for two-photon FRET stoichiometry is derived, and initial experimental measurements on live cells expressing fluorescent proteins are presented, yielding results that are largely consistent with expectations.

The topic of this proposal is the development of high peak power laser sources with a focus on linearly chirped pulse laser sources. In the past decade chirped optical pulses have found a plethora of applications such as photonic analog-to-digital conversion, optical coherence tomography, laser ranging, etc. This dissertation analyzes the aforementioned applications of linearly chirped pulses and their technical requirements, as well as the performance of previously demonstrated parabolic pulse shaping approaches. The experimental research addresses the topic of parabolic pulse generation in two distinct ways. First, pulse shaping technique involving a time domain approach is presented, that results in stretched pulses with parabolic profiles with temporal duration of 15 ns. After pulse is shaped into a parabolic intensity profile, the pulse is compressed with DCF fiber spool by 100 times to 80 ps duration at FWHM. A different approach of pulse shaping in frequency domain is performed, in which a spectral processor based on Liquid Crystal on Silicon technology is used. The pulse is stretched to 1.5 ns before intensity mask is applied, resulting in a parabolic intensity profile. Due to frequency to time mapping, its temporal profile is also parabolic. After pulse shaping, the pulse is compressed with a bulk compressor, and subsequently analyzed with a Frequency Resolved Optical Gating (FROG). The spectral content of the compressed pulse is feedback to the spectral processor and used to adjust the spectral phase mask applied on the pulse. The resultant pulse iv after pulse shaping with feedback mechanism is a Fourier transform, sub-picosecond ultrashort pulse with 5 times increase in peak power. The appendices in this dissertation provide additional material used for the realization of the main research focus of the dissertation. Specification and characterization of major components of equipments and devices used in the experiment are present. The description of Matlab algorithms that was used to calculate required signals for pulse shaping are shown. A brief description of the Labview code used to control the spectral processor will also be illustrated.

Device miniaturization with advanced fabrication techniques has revolutionized the semiconductor industry along with innovative concepts of carrier spin, potentially important at the fundamental physical limits of scalability. For spin-based information processing, semiconductor coupled quantum dots (CQDs) provide excellent control in spin dynamics due to 3-D confinement, discrete energy levels, and optical orientation and coupling. The research presented in this dissertation investigates spin interactions and exciton relaxation channels in semiconductor CQDs measured through optical control and time-resolved experimental techniques.Our experiments involving photoluminescence (PL) and photoluminescence excitation (PLE) methods revealed effects arising from the structural properties of semiconductor nanostructures, including quantum rings and CQDs. High resolution PL measurements on positively charged exciton states demonstrated experimental evidence of isotropic exchange interaction. Controlling exchange interaction in different spin configurations is fundamental to quantum logic operations. Hence, polarization dependent PL experiments were executed and electric field tunable exchange interaction effects were reported on the neutral exciton states. Next, time-resolved measurements were performed while pumping above the InAs wetting layer (WL) energy and probing below the WL to determine the dynamics of the optically generated electric field in CQDs. The observed, rapid onset of the optically generated electric field may provide the use of CQDs for optical switching applications.Finally, carrier relaxations in the CQDs were identified through the dynamics of the spatially indirect exciton state using a mode-locked laser excitation source and standard time-resolved single photon counting technique. Wave function distribution, carrier tunneling, and phonon scattering led to the observed lifetime and intensity modulations. With time-resolved PLE, bi-exponential lifetime decay revealed non-monotonic phonon relaxations as a result of the structure factor of the CQDs. Furthermore, with resonant excitation, carrier tunneling into charged exciton states was also eliminated. These results demonstrated tunable exciton relaxation rates in CQDs, which are useful for quantum information, optoelectronics, and photonics applications.

The femtosecond laser is an advantageous tool for manipulating matter on small scales as it can precisely remove material with minimal collateral effects. The nonlinear mechanisms mediating this damage allow for laser ablation to be confined to tens of nanometers in width. Results presented here expand upon the physics of this type of damage. A number of new damage phenomena for tightly focused femtosecond laser damage in glass are presented and physical mechanisms for their generation are suggested. The first novel phenomenon is the formation of blister-like structures leading to the ejection of thin, flat rings surrounding central damage regions, termed “grommets”. A study of damage depth from single pulse damage is also presented using a number of different measurement techniques including sample cleavage, focused ion beam cross sectioning, and acetate film imprinting. These techniques reveal damage extending far deeper into the target than was expected from the intensity distribution of the focusing optics. Experiments presented here show that a likely source for this elongation of damage is microscale self-focusing. Finally, a range of applications is presented, demonstrating the versatility and speed of single pulse nanochannel fabrication.

Vacuum scattering of electrons by an intense laser field is considered. This phenomenon is shown in many cases to be a polarization independent effect for arbitrary angle of incidence by an electron on a linearly polarized laser pulse. As the laser intensity grows and the focal volume shrinks, however, this independence fails. The corresponding electron energy and laser intensity transition is derived here for the first time. Such vacuum scattering is found to be driven by several mechanisms that occur over several scale lengths. Using both plane wave and focused laser field models, the relative importance of each is probed. In addition to extending the state of the art TEM00 to eighth order in the diffraction angle, an independent solution to the full Maxwell wave equation is also derived here based on the spectral methodology in which the imposed transverse laser fields are purely Gaussian in the focal plane. This is compared to the series expansion and found to be a distinct solution. Finally, this method is extended to allow for an arbitrary super-Gaussian transverse field profile boundary condition in the focal plane. After addressing these fundamental physics problems, some discussion of applications is given. First, the Thomson scattering cross section is derived for all laser intensities and electron energies. This allows the total amount of energy scattered by a Maxwellian electron beam to be computed: a useful experimental quantity. Following this, a simple, intuitive model is developed to calculate the brightness of a Thomson light source in a given frequency band. This is then compared to experiment and used to estimate the brightness of such a source driven by Z-Beamlet. Finally, a tunable infrared source is theoretically demonstrated. Electrons trapped in a standing electromagnetic wave tend to oscillate within the ponderomotive potential well. This bounce frequency and the laser frequency mix creating several intermodulation products that are manifested in the Thomson scattered spectra. For intensities on the order of 1017 W/cm2 , this phenomenon will scatter light along the laser polarization in the near infrared regime.