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Quadratic spatial soliton interactions were investigated in this Dissertation. The first part deals with characterizing the principal features of multi-soliton generation and soliton self-reflection. The second deals with two beam processes leading to soliton interactions and collisions. These subjects were investigated both theoretically and experimentally. The experiments were performed by using potassium niobate (KNBO3) and periodically poled potassium titanyl phosphate (KTP) crystals. These particular crystals were desirable for these experiments because of their large nonlinear coefficients and, more importantly, because the experiments could be performed under non-critical-phase-matching (NCPM) conditions. The single soliton generation measurements, performed on KNBO3 by launching the fundamental component only, showed a broad angular acceptance bandwidth which was important for the soliton collisions performed later. Furthermore, at high input intensities multi-soliton generation was observed for the first time. The influence on the multi-soliton patterns generated of the input intensity and beam symmetry was investigated. The combined experimental and theoretical efforts indicated that spatial and temporal noise on the input laser beam induced multi-soliton patterns. Another research direction pursued was intensity dependent soliton routing by using of a specially engineered quadratically nonlinear interface within a periodically poled KTP sample. This was the first time demonstration of the self-reflection phenomenon in a system with a quadratic nonlinearity. The feature investigated is believed to have a great potential for soliton routing and manipulation by engineered structures. A detailed investigation was conducted on two soliton interaction and collision processes. Birth of an additional soliton resulting from a two soliton collision was observed and characterized for the special case of a non-planar geometry. A small amount of spiraling, up to 30 degrees rotation, was measured in the experiments performed. The parameters relevant for characterizing soliton collision processes were also studied in detail. Measurements were performed for various collision angles (from 0.2 to 4 degrees), phase mismatch, relative phase between the solitons and the distance to the collision point within the sample (which affects soliton formation). Both the individual and combined effects of these collision variables were investigated. Based on the research conducted, several all-optical switching scenarios were proposed.

Attosecond pulses have been developed as a means for investigating phenomena that proceed on the order of the atomic unit of time (24 as). Unfortunately, these extreme ultraviolet (XUV) pulses by themselves contain too few photons to initiate nonlinear dynamics or dress states in an attosecond pump--attosecond probe scheme. As a result, most attosecond experiments thus far have featured complementary near infrared (NIR) femtosecond lasers for instigating electron dynamics. In order to access the benefits of all-attosecond measurements and open attosecond physics to new fields of exploration, the photon flux of these pulses must be increased. One way to boost the attosecond pulse energy is to scale up the energy of the NIR pulse responsible for driving high-harmonic generation (HHG). With generalized double optical gating (GDOG), isolated attosecond pulses can be generated with multi-cycle laser systems, wherein the pulse energy can be boosted more easily than in the few-cycle laser systems required by other gating methods. At the Institute for the Frontier of Attosecond Science and Technology (IFAST), this scalability was demonstrated using a 350 mJ, 15 fs (10 TW) Ti:sapphire laser, which was used to generate a 100 nJ XUV continuum. This represented an order-of-magnitude improvement over typical attosecond pulse energies achievable by millijoule-level few-cycle lasers. To obtain the microjoule-level attosecond pulse energy required for performing all-attosecond experiments, the attosecond flux generated by the IFAST 10 TW system was still deficient by an order of magnitude. To this end, the laser system was upgraded to provide joule-level output energies while maintaining pulse compression to 15 fs, with a targeted peak power of 200 TW. This was accomplished by adding an additional Ti:sapphire amplifier to the existing 10 TW system and implementing a new pulse compression system to accommodate the higher pulse energy. Because this system operated at a 10 Hz repetition rate, stabilization of the carrier-envelope phase (CEP) -- important for controlling attosecond pulse production -- could not be achieved using traditional methods. Therefore, a new scheme was developed, demonstrating the first-ever control of CEP in a chirped-pulse amplifier (CPA) at low repetition rates. Finally, a new variation of optical gating was proposed as a way to improve the efficiency of the attosecond pulse generation process. This method was also predicted to allow for the generation of isolated attosecond pulses with longer driving laser pulses, as well as the extension of the high-energy photon cut-off of the XUV continuum.

The structure and payload of a CubeSat flight experiment that investigates the performance of particle dampers in a micro-gravity environment was designed, built, and tested, and will provide on orbit data for model validation and improved performance predictions for space applications of particle damping. A 3-D solid model of the integrated CubeSat structure and payload was created satisfying all constraints from CubeSat and the System Dynamics Department at Northrop Grumman Aerospace Systems. The model was verified using commercially available Finite Element Analysis software (FEA), and a prototype structure part was fabricated. The prototype was tested and verified the FEA. A complete subassembly ready for flight was manufactured as an engineering unit and tested to space qualification loads of both launch vibration and thermal vacuum. Two additional units were contracted out for manufactured to serve as the flight unit and backup, and are currently ready for launch.

This dissertation proposes a model of word stress in a derivational version of Optimality Theory (OT) called Harmonic Serialism (HS; Prince and Smolensky 1993/2004, McCarthy 2000, 2006, 2010a). In this model, the metrical structure of a word is derived through a series of optimizations in which the 'best' metrical foot is chosen according to a ranking of violable constraints. Like OT, HS models cross-linguistic typology under the assumption that every constraint ranking should correspond to an attested language. Chapter 2 provides an argument for modeling stress typology in HS by showing that the serial model correctly rules out stress patterns that display non-local interactions, while a parallel OT model with the same constraints and representations fails to make such a distinction. Chapter 3 discusses two types of primary stress---autonomous and parasitic---and argues that limited parallelism in the assignment of primary stress is warranted by a consideration of attested typology. Stress systems in which the primary stress appears to behave autonomously from secondary stresses require that primary stress assignment be simultaneous with a foot's construction. As a result, a provision to allow primary stress to be reassigned during a derivation is necessary to account for a class of stress systems in which primary stress is parasitic on secondary stresses. Chapter 4 takes up two issues in the definition of constraints on primary stress, including a discussion of how primary stress alignment should be formulated and the identification of vacuous satisfaction as a cause of problematic typological predictions. It is proposed that all primary stress constraints be redefined according to non-vacuous schemata, which eliminate the problematic predictions when implemented within HS. Finally, chapter 5 considers the role of representational assumptions in typological predictions with comparisons between HS and parallel OT. The primary conclusion of this chapter is that constituent representations (i.e., feet) are necessary in HS to account for rhythmic stress patterns in a typologically restrictive way.

In this thesis, I develop a novel time-domain approach for nonlinear scattering theory (NLST), a previously frequency domain method for estimating the nonlinear generation from a nanostructure. Due to a gap in literature, I then perform a full comparison of this novel time domain approach to the existing one in the frequency domain. Using the example scenario of third harmonic generation from various media in 1D and 3D, I compare - quantitatively - the NLST estimated nonlinear spectra to two types of direct nonlinear simulations: one using an experimental value for the nonlinear optical susceptibility, and, for plasmonic systems, another using a hydrodynamics model for the nonlinear plasmonic response. Through testing differing NLST approaches on these systems, I demonstrate the effectiveness of the novel time-domain NLST and assess the use cases for this method as well as the pre-existing ones. Lastly, I discuss the applicability of NLST in future works involving the inverse design process, and high-order harmonic generation.

The Fundamental Theorem of Algebra is a useful tool in determining the number of zeros of complex-valued polynomials and rational functions. It does not, however, apply to complex-valued harmonic polynomials and rational functions generally. In this thesis, we determine behaviors of the family of complex-valued harmonic functions $f_{c}(z) = z^{n} + \frac{c}{\overline{z}^{k}} - 1$ that defy intuition for analytic polynomials. We first determine the sum of the orders of zeros by using the harmonic analogue of Rouch\'e's Theorem. We then determine useful geometry of the critical curve and its image in order to count winding numbers by applying the harmonic analogue of the Argument Principle. Combining these results, we fully determine the number of zeros of $f_{c}$ for $c > 0$.

<p> A high-resolution, low-noise far-infrared Fourier transform spectrometer system has been developed and utilized to study optical absorption in the III-V compound semiconductor InSb.</p> <p> Its electron effective mass was investigated, using cyclotron resonance absorption, as a function of magnetic field and compared with a theory originated by Kane (1957). The agreement was good and accurate values of the band edge effective mass and effective g factors were determined. Resonant electron-LO phonon coupling between the n = 2 and n = 0 + wLO Landau levels was observed and the polaron effective mass enhancement measured as a function of magnetic field. Comparison with Larsen's theory (1966), permitted an accurate value of the coupling constant to be derived. The temperature dependence of the electron effective mass was shown to be primarily due to dilation of the crystal lattice in confirmation of other workers' suggestions. However, some discrepancy, whose origin is unknown, was found to exist between experiment and theory.</p> <p> Single phonon absorption by the longitudinal optic phonon mode at the zone center was observed on the side of the main Reststrahl band in a thin sample. The shapes, frequencies and intensities of far-infrared absorptions attributable to two-phonon processes were found to compare favourably with a theoretical two-phonon density of states curve calculated by G. Dolling (1972). The parameters used in the theory were derived from inelastic neutron scattering experiments. Two phonon combinations and their locations in the Brillouin zone which give rise to strong features in the two-phonon density of states were identified by comparing theory and experiment. Important critical points were discovered to be located on or near the zone boundary and not only at the symmetry points X and L as previously suggested. The frequency shifts of some two-phonon features were measured as a function of temperature and analyzed in terms of a quasi-harmonic lattice dilation component and an anharmonic component. The two terms were found to be mirror images as a function of temperature.</p> / Thesis / Doctor of Philosophy (PhD)

The semiconductor Bloch equations (SBEs) are an insightful and well-established formalism for studying light-matter interactions in solids. When Coulomb interactions between electrons are omitted, the SBEs are simplified to a single particle model. The SBEs in this single electron approximation have been used extensively to model strong-field interactions in condensed matter. The SBEs in the length gauge provide an intuitive and numerically efficient model of high harmonic generation (HHG) in solids. In this approach, the SBEs involve Berry connections and transition dipole moments, which are gauge dependent structural quantities. This thesis studies the role of gauge symmetry in the SBEs, and how it can be exploited to facilitate efficient numerical analysis of HHG in solids. In the length gauge, the macroscopic current describing HHG can be decomposed into physically intuitive contributions. In particular, this leads to a contribution known as the "mixture" current, which has been overlooked by the HHG community until recently. We study the influence of this contribution using the analytic tight-binding model for gapped graphene. We derive an analytic gauge transformation that removes singular behaviour from the gapped graphene model, thus enabling efficient numerical integration of the SBEs. We also present an alternative approach for simulating dynamics in tight-binding models. Instead of simulating the SBEs in the usual basis of Bloch functions, we transform to the basis in which the tight-binding Hamiltonian is represented. The dipole matrix elements necessarily vanish in this basis, and the SBEs can be integrated using only the Hamiltonian matrix elements. We first generalize the SBEs to accomodate a non-diagonal Hamiltonian matrix, and we demonstrate this formalism numerically using two different tight-binding models. Finally, we derive a novel formulation of the SBEs which involve only gauge invariant matrix elements. Specifically, the Berry connections and transition dipole phases are replaced by a gauge invariant quantity known as the shift vector. This yields a fully gauge invariant description of HHG in solids, and the shift vector provides intuitive insight for HHG in systems with broken inversion symmetry. Further, the ability to describe HHG solely in terms of gauge invariant quantities raises new possibilities for tomographic reconstruction of crystal band structure, and this idea is discussed as a possible direction of future work.

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