High-order sideband generation (HSG) is a recently discovered phenomenon in semiconductors simultaneously driven by a weak near infrared (NIR) laser and a strong THz electric field. The NIR field excites electrons out of the valence band into the conduction band, leaving behind holes. The strong THz field can then accelerates the electrons and holes apart before it switches directions to drive the electrons and holes back towards each other. If an electron and a hole recollide, they emit a photon. Since both particles gained energy from the THz field, the emitted photons are typically higher in energy than the original NIR photon. The narrow linewidth of both lasers result in these emitted photons being equally spaced from the NIR photon energy and each other by twice the THz frequency to generate frequency combs. More than 130 orders have been observed.

The intensities of the sidebands is typically difficult to simulate theoretically. However, a simple scaling law for the THz frequency and field strength can be used to predict the widths of the frequency combs. This provides greater tunability and control of HSG frequency combs than previously, opening technological applications of these combs. This scaling relation is complicated, however, by the motion of holes as they travel within a complicated Brillouin zone. Berry’s Curvature mixes the Bloch wavefunctions in momentum space, causing a hole to evolve into new states as it is accelerated by the THz field. When an electron recollides with a hole, these different wavefunctions are imprinted onto the intensity and polarization of the emitted sidebands. With careful polarimetry of the sidebands, information can be extracted about the material structure. For example, strain can be introduced to modify the band structure of the material, which significantly alters the measured polarizations of the sidebands. These techniques could lead to all-optical measurements of the band structure, and Berry Curvature of material systems.

In order to apply these techniques to understand novel material systems, HSG must first be observed in these materials. Any new material must be a semiconductor with a band gap near the NIR photon energy where electrons and holes can be created. However, finding systems with suitably small scattering rates and large enough coherence times remains a challenge.

Terahertz (THz) heterodyne detectors, also known as mixers, are widely used for high-resolution (with frequency resolution $\nu / \Delta \nu > 10^{6}$) detection of THz radiation in space for astrophysics and planetary science applications, and important for applications in bio-medical imaging and future THz wireless communications. Above 1 THz, heterodyne detectors based on hot-electron effects in thin superconducting films (superconducting hot-electron bolometers, or HEBs) are the current state-of-the art mixers, with an excellent sensitivity (with single-sideband noise temperature $T_{SSB} \sim 1,000$ K at 2 THz), a wide intermediate-frequency (IF) bandwidth ($\sim$3 GHz), and a small required local-oscillator (LO) power ($\sim$1 $\mu$W). However, cryogenic operating temperature (4 K or below) required for the superconducting HEBs limits their use in certain applications (e.g. deep-space missions to planets and comets) that cannot afford the power and mass required for active cryogenic cooling. To date, the only option for such applications has been Schottky-diode mixers that work at ambient temperature, but at the cost of significantly lower sensitivity (T\textsubscript{SSB} $\sim 10,000 $ K above 1 THz) and a higher required LO power ($\sim$1 mW). The latter especially limits the use of Schottky mixers in heterodyne array applications, which is important for cost- and time-effective heterodyne observations in space.

In this work, we explore a new type of THz heterodyne detector based on intersubband transitions of high-mobility 2-dimensional electron gas (2DEG) confined in single GaAs/AlGaAs quantum wells. Named as Tunable Antenna-Coupled Intersubband Terahertz (TACIT) mixer, our device is predicted to be as sensitive as superconducting HEB mixers (with $T_{SSB} \sim 1,000$ K) at relatively high operating temperature (20--60 K), with a wide IF bandwidth ($\sim 10 $ GHz) and a small required LO power ($< 1 \mu$W). In addition, THz absorption frequency of TACIT mixers can be tuned with small ($<2$) DC voltage biases, offering wide in-situ tunability in the detection frequency (2--5 THz). The operating temperature of TACIT mixers can be accessible with passive cooling for deep-space missions or with compact, light-weight coolers for other applications, which, along with other useful mixer characteristics, makes TACIT mixers an attractive mixer technology for a low-noise, multi-pixel THz heterodyne receiver for applications in THz high-resolution spectroscopy in deep space and for other applications in which relaxed cryogenic and LO power requirements are advantageous.

Despite the impressive mixer characteristics of TACIT mixers, experimental realization and characterization of the TACIT mixers have been challenging due to difficulties in fabricating reliable dual-gate structures required for their operation. In this work, using an advanced flip-chip technique that we developed in-house, we successfully fabricate and demonstrate two versions of prototype TACIT mixers. In the first prototype TACIT mixer integrated with a single slot antenna, we demonstrate the tunability in the detection frequency (2.52--3.44 THz) with relatively small ($< 5$ V) DC bias voltages, as well as the heterodyne detection (mixing) capability at 60 K with a wide IF bandwidth ($\sim$ 6 GHz). The observed tunability in the direct detection responses is consistent with the model responses based on intersubband transitions. In the second prototype TACIT mixers integrated with a modified, broadband bow-tie antenna, we explore capacitive coupling for the read-out of the device IF response and investigate the capacitive IF read-out and other properties of the device using various characterization methods, including microwave measurements and noise power measurements. In addition, we demonstrate tunability in both the direct detection and heterodyne detection consistent with the results from the first prototype TACIT mixer and with our model responses. In both prototype devices, the mixer noise temperature, conversion loss, and required LO power were not measured due the unexpectedly large conversion losses. We attribute these large losses to poor radiation efficiency of the antenna structures caused by impedance mismatch and non-optimal radiation patterns, as well as to possible degradation in the IF response caused by diffusion and ballistic cooling of the high-mobility 2DEG at low temperatures. To address these issues, we briefly discuss our plans for designing more optimized antenna structures and employing a different read-out mechanism based on the thermoelectric effect of high-mobility 2DEGs for future iterations of TACIT mixers.

Driving semiconductor quantum wells with terahertz electric fields strong enough to overcome the Coulomb attraction between bound electron-hole pairs leads to high-order sideband generation (HSG). In HSG, excitons are optically-injected into quantum wells by a weak near-infrared (NIR) laser while simultaneously being illuminated with a terahertz field from the UCSB Free Electron Laser. The phenomenon can be described by the so-called "three step model" developed in high-field atomic physics: (1) the electron and hole tunnel-ionize in the strong field, (2) the now-free particles accelerate in the field, and (3) they recollide, emitting a photon. The two lasers are continuous, so the emitted photons are sidebands on the NIR laser. Because of the large gain of kinetic energy before recollision, an HSG spectrum has a broad bandwidth with many more sidebands above the NIR frequency than below. The largest spectra span over one hundred nanometers, with over 100th order sidebands above and 20th order below.

The electron and hole must remain coherent throughout their trajectories, which can last hundreds of femtoseconds and extend for more than fifty nanometers, if they are to recollide. Sidebands have been observed that result from recollisions with kinetic energies far above the threshold for optical phonon emission. These high orders persist up to room temperature. Not even quenched disorder in the quantum wells strongly attenuates the HSG signal.

Because of this coherence, the electron and hole are very sensitive to the complete band structure of the material. Excitation by linear NIR polarization creates both the electron and hole in a superposition of spin-up and spin-down states with complex coefficients given by the relative orientation of the NIR polarization and the THz polarization. Interference between these the spin-up and spin-down particles, particularly in the valence band and mediated by non-Abelian Berry curvature, has large effects on both the intensity and polarization state of the sidebands. The connection between HSG and complete band structure points to the possibility of directly measuring both the band dispersion relations as well as the non-Abelian Berry curvature of the host material.

Quantum mechanics views particles as matter waves rippling through space, and when there are many of these waves present in the same system, they can interfere with one another. While quantum mechanics make the direct measurement of a particular wave function’s phase impossible, clever experiments can probe the interference of wave functions with different phases. High Order Sideband Generation (HSG) is an optical method which uses two frequencies of light to both excite quasiparticle-antiquasiparticle pairs and accelerate them through the Brillouin Zone. In the experiments detailed in this thesis, a near infrared (NIR) laser creates electron-hole (e-h) pairs in bulk Gallium Arsenide (GaAs). A strong Terahertz (THz) electric field ionizes the e-h pair, accelerates the pair to a higher energy, and slams the pair back together to have the e-h pair annihilate and emit a photon. Because the pair will gain energy from the THz acceleration process, the photon emitted by their annihilation will be offset in energy from the initial NIR excitation energy; a high order sideband. While the THz is accelerating the e-h pairs, the holes can be in one of four angular momentum eigenstates which exists in the valence band of bulk GaAs. The distribution of e-h pairs in the four states is determined by the Bloch wave functions and effective Hamiltonian of the valence band, called the Luttinger Hamiltonian. By the conservation of angular momentum, a given hole will produce a sideband with a specific polarization, and the total polarization of sideband photons at a given energy can be related to the Bloch wave functions. The reconstruction of Bloch wave functions in bulk GaAs is detailed in this thesis. The change in polarization as a function of sideband energy is presented as an interferogram. Analogous to a Michelson interferometer for Bloch waves, signal is connected to the difference in dynamical phase accrued by different quasiparticles being accelerated by the THz field. A classical model of the quasiparticle trajectories leads to an analytical theoretical calculation of the sideband polarization, which is in good quantitative agreement with experiment. The sideband polarization dependence on the initial energy of the NIR excitation photons is probed, and preliminary analysis of the dynamical gap of the driven quasiparticles yields a value of Eg = 1.511 eV. In addition, the sideband polarization can be related to the effective Hamiltonian and the dispersion relation of the quasiparticles in bulk GaAs. Beyond the experiments detailed in this thesis, HSG offers the opportunity to characterize the Bloch wave functions, effective Hamiltonians, and dynamical phases of more exotic quasiparticles and more exotic materials. With this thesis acting as a proof-of-concept for the HSG polarimetery methodology, the ambition is to extend this method to highly correlated systems or semiconductors with large spin-orbit coupling, or to measure geometric phases, indicative of non-trivial topologies.

Herein, we describe a momentum-resolved optical reflectometry technique for precisely quantifying absorption anisotropies, with a particular interest in its ability to estimate distinct out-of-plane dipole strengths in solution-processable semiconductors. We demonstrate major advantages over conventional techniques, e.g., variable-angle spectroscopic ellipsometry, and subsequently show how to merge the strengths of the two techniques. We interrogate two distinct material systems: organic semiconductor thin films and two-dimensional (2D) hybrid organic-inorganic perovskites (HOIPs). In organic thin films, we resolve molecular reorientations due to processing conditions. In 2D HOIPs, we adopt a layered effective medium model to show that strong optical anisotropies arise predominantly from classical electromagnetics effects (i.e., dielectric inhomogeneity) rather than anisotropies in the quantum-mechanical matrix elements. Finally, we demonstrate unexpected multipolar light-matter interactions in 2D HOIPs, revealed by a highly polarized and oblique emission sideband. Electromagnetic and quantum-mechanical analyses indicate that this emission originates from an out-of-plane magnetic dipole transition arising from the 2D character of electronic states. The techniques described herein are materials agnostic and may provide insight into fundamental optoelectronic processes and processing-dependent structure-function relationships in a wide variety of interrogated materials.

Electron paramagnetic resonance (EPR) in combination with site-directed spin labeling (SDSL) is a powerful tool for elucidating the structure, organization, and dynamics of biomolecules in native-like environments. With EPR and SDSL, we can site-specically label pairs of sites in a biomolecule and accurately measure the distance, or distribution of distances, between them on length scales ranging from Angstroms to several nanometers. Of particular interest are membrane proteins and higher-order membrane protein complexes, which have historically resisted traditional biophysical characterization techniques. EPR as a means to measure protein structure becomes even more powerful at high fields and using Gd(III) spin labels, which together provide much improved sensitivity. This work expands on the capabilities of high-field continuous-wave (CW) EPR for distance measurement with spin labels based on Gd(III) complexes. First, we investigate a model system of and show that CW EPR with Gd(III) labels allows for distance measurements in the range of at least 1.2 - 3.4 nm at cryogenic temperatures. We additionally show that distance measurements are possible up to room temperature. Next, we investigate the zero-field splitting - a property of great importance for determining the EPR lineshape of high-spin systems - for a variety of different Gd(III) complexes. Combining EPR spectra measured at 35 GHz, 95 GHz, and 240 GHz, we compare literature models for the broadly distributed second-order ZFS parameters D and E. We test these results against a superposition model for predicting the magnitude of the ZFS based on knowledge of the structure of a Gd(III) complex, which can potentially be useful for designing new Gd(III) complexes tailored for use as spin labels with high-field EPR. Finally, we apply high-field CW EPR with Gd(III) spin labels to the study of proteorhodopsin (PR), a transmembrane protein that functions as a light-driven proton pump for marine bacteria. Inter-PR CW EPR distance measurements in the range of ~1.5 - 3 nm are used to elucidate the functionally relevant oligomeric structure of PR, demonstrating the usefulness of this technique in targeting complex oligomeric systems. Finally, we present the development of methods which will allow CW EPR with Gd(III) to be used as a probe of protein dynamics, by measuring at a distance change induced by motions of the E-F loop region of PR upon light activation.