Browsing by Author "Bradley, Mark, committee member"

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Open Access
Advancements in the optical damage resistance of ion beam sputter deposited interference coatings for high energy lasers
(Colorado State University. Libraries, 2015) Schiltz, Drew, author; Menoni, Carmen, advisor; Marconi, Mario, committee member; Bradley, Mark, committee member
The work presented in this thesis is dedicated toward investigating, and ultimately improving the laser damage resistance of ion beam sputtered interference coatings. Not only are interference coatings a key component of the modern day laser, but they also limit energy output due to their susceptibility to laser induced damage. Thus, advancements in the fluence handling capabilities of interference coatings will enable increased energy output of high energy laser systems. Design strategies aimed at improving the laser damage resistance of Ta2O5/SiO2 high reflectors for operation at one micron wavelengths and pulse durations of several nanoseconds to a fraction of a nanosecond are presented. These modified designs are formulated to reduce effects from the standing wave electric field distribution in the coating. Design modifications from a standard quarter wave stack structure include increasing the thickness of SiO2 top layers and reducing the Ta2O5 thickness in favor of SiO2 in the top four bi-layers. The coating structures were deposited with ion beam sputtering. The modified designs exhibit improved performance when irradiated with 4 ns duration pulses, but little effect at 0.19 ns. Scaling between the results from testing at these two pulse durations shows deviation from τ1/2 scaling, where τ is the pulse duration. This suggests possible differences in the initial damage mechanism. Also presented are results for at-wavelength optical absorption losses measured with photothermal common-path interferometry and surface roughness measurements with atomic force microscopy. Further studies on the damage thresholds of interference coatings operating at 1.6 micron wavelength and 2 picosecond pulse durations are presented. High reflection and anti-reflection coating structures were fabricated with varied high index materials: HfO2, Y2O3 and Ta2O5. For damage testing, an optical parametric chirped pulse amplifier was fabricated and implemented. This source is capable of producing ~5 millijoule pulses with a tunable wavelength between 1.5 and 2 micron. When investigated at 1.6 micron wavelength, the interference coatings exhibit ultra-low absorption losses and damage thresholds at ~7.0 J/cm2 and 3.5 TW/cm2 peak intensities, near that of the infrared grade fused silica substrates they are deposited on. Furthermore, interference effects and lower band gap materials do not impair the damage threshold. This behavior is significantly different than what has previously been observed at similar pulse durations and more common laser wavelengths around 0.8 to 1 micron. I show that conventional rate equation modeling proves inadequate at describing the obtained results.
Open Access
An investigation of the Novikov-Veselov equation: new solutions, stability and implications for the inverse scattering transform
(Colorado State University. Libraries, 2012) Croke, Ryan P., author; Mueller, Jennifer, advisor; Bradley, Mark, committee member; Shipman, Patrick, committee member; Zhou, Yongcheng, committee member
Integrable systems in two spatial dimensions have received far less attention by scholars than their one--dimensional counterparts. In this dissertation the Novikov--Veselov (NV) equation, a (2+1)--dimensional integrable system that is a generalization of the famous Korteweg de--Vreis (KdV) equation is investigated. New traveling wave solutions to the NV equation are presented along with an analysis of the stability of certain types of soliton solutions to transverse perturbations. To facilitate the investigation of the qualitative nature of various types of solutions, including solitons and their stability under transverse perturbations, a version of a pseudo-spectral numerical method introduced by Feng [J. Comput. Phys., 153(2), 1999] is developed. With this fast numerical solver some conjectures related to the inverse scattering method for the NV equation are also examined. The scattering transform for the NV equation is the same as the scattering transform used to solve the inverse conductivity problem, a problem useful in medical applications and seismic imaging. However, recent developments have shed light on the nature of the long-term behavior of certain types of solutions to the NV equation that cannot be investigated using the inverse scattering method. The numerical method developed here is used to research these exciting new developments.
Open Access
Discrete-time topological dynamics, complex Hadamard matrices, and oblique-incidence ion bombardment
(Colorado State University. Libraries, 2014) Motta, Francis Charles, author; Shipman, Patrick D., advisor; Dangelmayr, Gerhard, committee member; Peterson, Chris, committee member; Bradley, Mark, committee member
The topics covered in this dissertation are not unified under a single mathematical discipline. However, the questions posed and the partial solutions to problems of interest were heavily influenced by ideas from dynamical systems, mathematical experimentation, and simulation. Thus, the chapters in this document are unified by a common flavor which bridges several mathematical and scientific disciplines. The first chapter introduces a new notion of orbit density applicable to discrete-time dynamical systems on a topological phase space, called the linear limit density of an orbit. For a fixed discrete-time dynamical system, Φ(χ) : M → M defined on a bounded metric space, we introduce a function E : {γχ : χ ∈ Mg} → R∪{∞} on the orbits of Φ, γχ ≐ {Φt(χ) : t ∈ N}, and interpret E(γχ) as a measure of the orbit's approach to density; the so-called linear limit density (LLD) of an orbit. We first study the family of dynamical systems Rθ : [0; 1) → [0; 1)(θ ∈ (0; 1)) defined by Rθ(χ) = (χ + θ) mod 1. Utilizing a formula derived from the Three-Distance theorem, we compute the exact value of E({RtΦ(χ) : t ∈ N}, χ ∈ [0; 1)), where Φ = √5 – 1) /2. We further compute E({Rtθ(χ) : t ∈ N}; χ ∈ [0, 1)) for a class of irrational rotation angles θ = [j, j,…] with period-1 continued fraction expansions and discuss how this measure distinguishes the topologically transitive behavior of different choices of θ. We then expand our focus to a much broader class of orientation-preserving homeomorphisms of the circle and extend a result of R. Graham and J.H. van Lint about optimal irrational rotations. Finally, we consider the LLD of orbits of the Bernoulli shift map acting on sequences defined over a finite alphabet and prove bounds for a class of sequences built by recursive extension of de Bruijn sequences. To compute approximations of E(γχ) for orbits of the Bernoulli shift map, we develop an efficient algorithm which determines a point in the set of all words of a fixed length over a finite alphabet whose distance to a distinguished subset is maximal. Chapter two represents a departure from a dynamical systems problem by instead exploring the structure of the space of complex Hadamard matrices and mutually unbiased bases (MUBs) of complex Hilbert space. Although the problem is not intrinsically dynamical, our mechanisms for experimentation and exploration include an algorithm which can be viewed as a discrete-time dynamical system as well as a gradient system of ordinary differential equations (ODEs) whose fixed points are dephased complex Hadamards. We use our discrete system to produce numerical evidence which supports existing conjectures regarding complex Hadamards and mutually unbiased bases, including that the maximal size of a set of 6 x 6 MUBs is four. By applying center-manifold theory to our gradient system, we introduce a novel method to analyze the structure of Hadamards near a fixed matrix. In addition to formalizing this technique, we apply it to prove that a particular 9 x 9 Hadamard does not belong to a continuous family of inequivalent matrices, despite having a positive defect. This is the first known example of this type. The third chapter explores the phenomenon of pattern formation in dynamical systems by considering a model of off-normal incidence ion bombardment (OIIB) of a binary material. We extend the Bradley-Shipman theory of normal-incidence ion bombardment of a binary material by analyzing a system of partial differential equations that models the off-normal incidence ion bombardment of a binary material by coupling surface topography and composition. In this chapter we perform linear and non-linear analysis of the equations modeling the interaction between surface height and composition and derive a system of ODEs which govern the time-evolution of the unstable modes, allowing us to identify parameter ranges which lead to patterns of interest. In particular, we demonstrate that an unusual "dots-on-ripples" topography can emerge for nonzero angles of ion incidence θ. In such a pattern, nanodots arranged in a hexagonal array sit atop a ripple topography. We find that if dots-on-ripples are supplanted by surface ripples as θ or the ion energy are varied, the transition is continuous.
Open Access
Exotic phenomena in rare-earth based geometrically frustrated magnets
(Colorado State University. Libraries, 2022) Yahne, Danielle Rose, author; Ross, Kate A., advisor; Bradley, Mark, committee member; Buchanan, Kristen, committee member; Zadrozny, Joe, committee member
Rare-earth (RE) based frustrated magnets are ideal systems to explore quantum effects in materials, which are paramount for the development of quantum computers, MRAM, and other next-generation technology. RE based materials are of specific interest due to the strong spin-orbit coupling and crystal electric field effects, which split the degenerate 4f angular momentum states, often leading to an effective spin-1/2 doublet with anisotropic effective exchange models. For this reason, RE materials are paramount to investigating the effects of anisotropic exchange on exotic ground states or quantum phases. Exchange frustration refers to when a system cannot simultaneously satisfy competing interactions, which can lead to a macroscopic degeneracy in the ground state of the system. Materials with geometric frustration, where competing interactions occur due to the crystal geometry alone, have been shown to host a wealth of exotic phenomena, including spin ice phases, quasi-particle excitations, order-by-disorder, and the highly entangled quantum spin liquid (QSL) state, to name a few. In this thesis, we will discuss three RE systems that exhibit geometric frustration in addition to exchange frustration: two RE pyrochlore oxides (RE2TM2O7) and a 2D isosceles triangular lattice material K3Er(VO4)2. Spin-1/2 antiferromagnetic (AFM) 2D triangular lattice magnets are an archetype of geometric frustration. While these materials are theorized to host a variety of different ground states and exotic phases depending on the anisotropies of the system, only a handful of RE material examples have been explored. We report the first deep dive into one such system, K3Er(VO4)2. We have determined the ordered magnetic structure of K3Er(VO4)2, finding an unusual structure with alternating layers comprised of AFM aligned and zero moment. We theorize this unique structure is due to the strong XY single-ion anisotropy, suggested from magnetometry measurements, which acts to suppress (to the point of vanishing completely) the out-of-plane pseudo-spin-1/2 magnetic moments. Next, we explored the effects of phase competition in a well-studied effective spin-1/2 RE pyrochlore oxide, Er2Sn2O7. Previous polycrystalline work has found Er2Sn2O7 to possess a suppressed critical temperature and an AFM Palmer-Chalker ground state. The determined exchange and single-ion anisotropy of Er2Sn2O7 find the ground state lies in close proximity to a competing AFM phase. Through extensive single crystal heat capacity measurements, we discovered a reentrant field vs. temperature phase diagram, where a system that has developed order returns to the original, less ordered (paramagnetic) state as some external parameter (field) is tuned continuously. We investigated the underlying mechanisms behind the reentrance by utilizing Monte Carlo simulations, mean field theory, and classical linear spin-wave calculations. This theory suggests that reentrance is linked to soft modes arising from phase competition, either from enhanced competition of the proximal AFM phase or from competing T=0 field-evolved ground states, depending on the specific applied field direction. In both cases, the soft modes enhance thermal fluctuations which cause the specific ordered phase to be entropically stabilized, thus forming a reentrant phase diagram. Finally, we report recent elastic neutron diffraction results on a RE pyrochlore oxide and candidate octupolar spin-ice, Ce2Sn2O7. The pseudo-spin-1/2 moments in Ce2Sn2O7 are known to possess dipolar-octupolar character and a large parameter space within the phase diagram is theorized to host novel QSL states. Previous powder neutron diffraction found diffuse scattering at high scattering vectors associated with magnetic octupoles. However, our undertaking of a similar measurement on nominally the same sample, found strikingly different results. Our neutron diffraction resulted in a broad, diffuse signal at low scattering vectors, reminiscent of a dipolar spin-ice. Neutron diffraction and atomic PDF measurements have not turned up obvious sample deformities or evidence of oxidation that could explain the differences in the diffuse signals. Further atomic studies and significant theory work is necessary to fully understand the results of this measurements, but the similarities to sister compound Ce2Zr2O7 suggest that Ce2Sn2O7 could lie on a phase boundary that is sensitive to minor distortions.
Open Access
Expected distances on homogeneous manifolds and notes on pattern formation
(Colorado State University. Libraries, 2023) Balch, Brenden, author; Shipman, Patrick, advisor; Bradley, Mark, committee member; Shonkwiler, Clay, committee member; Peterson, Chris, committee member; Chen, Hua, committee member
Flag manifolds are generalizations of projective spaces and other Grassmannians: they parametrize flags, which are nested sequences of subspaces in a given vector space. These are important objects in algebraic and differential geometry, but are also increasingly being used in data science, where many types of data are properly understood as subspaces rather than vectors. In Chapter 1 of this dissertation, we discuss partially oriented flag manifolds, which parametrize flags in which some of the subspaces may be endowed with an orientation. We compute the expected distance between random points on some low-dimensional examples, which we view as a statistical baseline against which to compare the distances between particular partially oriented flags coming from geometry or data. Lens spaces are a family of manifolds that have been a source of many interesting phenomena in topology and differential geometry. Their concrete construction, as quotients of odd-dimensional spheres by a free linear action of a finite cyclic group, allows a deeper analysis of their structure. In Chapter 2, we consider the problem of moments for the distance function between randomly selected pairs of points on homogeneous three-dimensional lens spaces. We give a derivation of a recursion relation for the moments, a formula for the kth moment, and a formula for the moment generating function, as well as an explicit formula for the volume of balls of all radii in these lens spaces. Motivated by previous results showing that the addition of a linear dispersive term to the two-dimensional Kuramoto-Sivashinsky equation has a dramatic effect on the pattern formation, we study the Swift-Hohenberg equation with an added linear dispersive term, the dispersive Swift-Hohenberg equation (DSHE) in Chapter 3. The DSHE produces stripe patterns with spatially extended defects that we call seams. A seam is defined to be a dislocation that is smeared out along a line segment that is obliquely oriented relative to an axis of reflectional symmetry. In contrast to the dispersive Kuramoto-Sivashinsky equation, the DSHE has a narrow band of unstable wavelengths close to an instability threshold. This allows for analytical progress to be made. We show that the amplitude equation for the DSHE close to threshold is a special case of the anisotropic complex Ginzburg-Landau equation (ACGLE) and that seams in the DSHE correspond to spiral waves in the ACGLE. Seam defects and the corresponding spiral waves tend to organize themselves into chains, and we obtain formulas for the velocity of the spiral wave cores and for the spacing between them. In the limit of strong dispersion, a perturbative analysis yields a relationship between the amplitude and wavelength of a stripe pattern and its propagation velocity. Numerical integrations of the ACGLE and the DSHE confirm these analytical results. Chapter 4 explores the measurement and characterization of order in non-equilibrium pattern forming systems. The study focuses on the use of topological measures of order, via persistent homology and the Wasserstein metric. We investigate the quantification of order with respect to ideal lattice patterns and demonstrate the effectiveness of the introduced measures of order in analyzing imperfect three-dimensional patterns and their time evolution. The paper provides valuable insights into the complex pattern formation and contributes to the understanding of order in three dimensions.
Open Access
High-power deep-UV laser for improved and novel experiments on hydrogen
(Colorado State University. Libraries, 2019) Burkley, Zakary Neumann, author; Yost, Dylan, advisor; Roberts, Jacob, committee member; Bradley, Mark, committee member; Menoni, Carmen, committee member
This dissertation details the design, performance, and cavity enhancement of a novel, high-power coherent 243.1 nm laser system, and through simulations, its ability to trap hydrogen in a magic wavelength optical trap. This wavelength of light is necessary to address the 1S–2S two-photon transition in hydrogen, and the primary motivation behind development of this laser system is obtaining high enough 243.1 nm powers for two-photon cooling of hydrogen. Due to the light mass of hydrogen, high precision spectroscopy of hydrogen is limited by unwanted motional effects, which could be mitigated with laser cooling and confinement in an optical trap. Besides laser cooling, a high power deep-UV laser system at this wavelength has great utility for improving spectroscopy of hydrogen and other exotic simple systems. High-power fiber lasers from 1-1.2 µm have flourished as a result of advances in ytterbium(Yb)-doped fiber amplifiers. In addition, high-power Yb-fiber lasers between 975-980 nm have also been developed—a notable accomplishment due to gain competition in the > 1 µm spectral region. These systems initially lacked sufficiently narrow spectral bandwidth for efficient harmonic generation, motivating further development since there is significant interest in frequency doubling and quadrupling these sources to produce coherent blue radiation and deep-UV radiation. Here, we generate coherent, high-power deep-UV radiation through frequency quadrupling of a high-power, highly coherent Yb-fiber amplifier at 972.5 nm. The Yb-fiber amplifier system consists of a frequency stabilized master oscillator power amplifier (MOPA) that can be referenced to a coherent frequency comb. This MOPA can be amplified to > 10 W of narrow linewidth power at 972.5 nm in the Yb-fiber amplifier. This is a technically challenging and notable result for this wavelength as gain is much more readily obtained in Yb-doped fibers at the absorption/emission cross-section peak near 975 nm and in the > 1 µm spectral region where the emission cross-section is much larger than the absorption cross-section. This system successfully combated unwanted gain at these wavelengths by using a relatively short (≈ 10 cm), angle-polished Yb-fiber with a large core-cladding ratio, along with aggressive spectral filtering and large amounts of seed power at 972.5 nm. With this narrow linewidth Yb-fiber amplifier, efficient frequency conversion of high power 972-976 nm radiation to 243-244 nm radiation is possible through intracavity doubling. Through successive resonant doubling stages, this system demonstrates > 1 W of highly stable, continuous-wave (CW) 243.1 nm power. To the author's knowledge, this is a record amount of CW deep-UV power below 266 nm, and is made possible thanks to advances in the production of a relatively new non-linear crystal for robust deep-UV generation, cesium lithium borate (CLBO). The precise frequency control of this radiation is established via excitation of the 1S–2S transition in hydrogen, and the viability for two-photon laser cooling on this transition is shown through enhancement of this power to > 30 W of intracavity power in a deep-UV enhancement cavity. At these powers, UV-induced mirror degradation was observed and mitigated by flushing the enhancement cavity mirrors with ultra-pure oxygen. With these powers, rapid two-photon laser cooling of a hydrogen atomic beam approaches reality. The 243.1 nm powers offered by this laser system also offer unique methods for capturing hydrogen in an optical trap. Explored via simulations, single optical scatter capture of hydrogen in a magic wavelength dipole trap is demonstrated, promising exciting new avenues for high precision spectroscopy of hydrogen.
Open Access
Near-resonant and resonant light in ultracold gases
(Colorado State University. Libraries, 2020) Gilbert, Jonathan, author; Roberts, Jacob, advisor; Yost, Dylan, committee member; Bradley, Mark, committee member; Marconi, Mario, committee member
This dissertation describes experiments and calculations involving light manipulation of atoms and light propagation in ultracold gases. There are three major sections to this dissertation. Each section presents a research topic connected to the main subject of near-resonant and resonant light in ultracold gases. First, this dissertation details the theoretical description and experimental implementation of a novel cooling technique for ultracold atoms trapped in a confining potential. Manipulating the internal states of atoms by applying near-resonant laser pulses at specified times leads to high energy atoms being preferentially selected and then slowed to achieve cooling. We call the technique "spatially truncated optical pumping (STOP) cooling." Advantages of the technique include its straightforward adaptability into experiments already using a magneto-optical trap; its applicability to any species that can be laser cooled and trapped in a confining potential; it does not depend on highly specific transitions for cooling; it does not depend on number loss for cooling. We present experimental results from applying the technique to an ultracold gas of 87Rb. We also present theoretical predictions of expected cooling rates, along with possible improvements to our apparatus that could lead to further cooling. Next, this dissertation details numerical calculations of near-resonant light propagation through a highly absorptive elongated ultracold gas. The confined gas modeled by these calculations are representative of gases commonly found in ultracold atom experiments. The spatial density distribution and spatial extent of these gases leads to a substantial gradient in the index of refraction. In addition, these gases can have a smaller spatial extent than that of the cross section of a laser beam that illuminates them. We present calculations that show the index variation in these systems can lead to frequency-dependent focusing or defocusing of incident near-resonant light. In some cases, focusing results in light intensities inside of the gas that are over an order of magnitude higher than the incident value. Additionally, we show that refraction and diffraction of the light results in non-intuitive patterns forming in the directions perpendicular to the light propagation. Lastly, this dissertation details the theoretical treatment and experimental measurements of the time-dependent absorption and phase response of an ultracold gas that is suddenly illuminated by near-resonant light. These studies focus on dynamics occurring over timescales on the order of an atomic excited state lifetime. Because the atoms cannot respond instantaneously to the applied light, both the absorption response and phase response require time to develop, with the phase response being slower than the absorption response. Related polarization effects such as Faraday rotation are due to phase shifts imparted by the gas, and therefore these effects also require time to develop. We detail our experimental measurements of the time-dependent development of Faraday rotation in an ultracold gas of 85Rb and compare the results to predictions using a theoretical approach based on solving optical Bloch equations. We identify how parameters such as the applied magnetic field strength and optical thickness of the gas influence the response timescales of the gas.
Open Access
Stability of thin-film CdTe solar cells with various back contacts
(Colorado State University. Libraries, 2021) Hill, Taylor D., author; Sites, James, advisor; Sampath, Walajabad, advisor; Bradley, Mark, committee member
With an increasing reliance on photovoltaic energy comes an ever-increasing demand to understand the mechanisms of failure which lead one to having an under-performing solar module. Recent technological advances have proven CdTe solar cells to be competitive with traditional Si, taking up 5% of the world solar market and reaching efficiency upwards of 22.1% for small area scale and 18.6% for module scale. This thesis explores various back-contact configurations to reduce the contact barrier height as well as how they hold up under accelerated lifetime testing. Various degradation mechanisms, such as diffusion of species, drift within the built-in fields, and formations of various impurities/complexes on the surface and within the bulk were explored. The results of accelerated-lifetime experiments revealed the instability of devices with large amounts of Cu and those containing the colloidal Ni based paint solution as a metallic back contact. Sputtered films of nickel doped with vanadium (Ni:V) and chromium (Cr) demonstrated the capability to produce cells with efficiencies between 12-13% with fill factors up to 75%. Metallic bilayers containing a metallic cap of aluminum (Al) were then evaluated, demonstrating an increase in efficiency up to 15.1%. Buffer layers of NiO revealed the presence of a large back-contact barrier via the rollover effect in forward bias, leading to devices with efficiency of only 3%, but subsequent work revealed that by applying the NiO buffer prior to CdCl2 passivation reduces the back barrier and produces cells with peak efficiency of 14.8%.