Nonlinear optics in planar silica-on-silicon disk resonators

Optical frequency combs (OFCs) provide direct phase-coherent link between optical and RF frequencies, and enable precision measurement of optical frequencies. In recent years, a new class of frequency combs (microcombs) have emerged based on parametric frequency conversions in dielectric microresonators. Micocombs have large line spacing from 10's to 100's GHz, allowing easy access to individual comb lines for arbitrary waveform synthesis. They also provide broadband parametric gain bandwidth, not limited by specific atomic or molecular transitions in conventional OFCs. The emerging applications of microcombs include low noise microwave generation, astronomical spectrograph calibration, direct comb spectroscopy, and high capacity telecommunications.

In this thesis, research is presented starting with the introduction of a new type of chemically etched, planar silica-on-silicon disk resonator. A record Q factor of 875 million is achieved for on-chip devices. A simple and accurate approach to characterize the FSR and dispersion of microcavities is demonstrated. Microresonator-based frequency combs (microcombs) are demonstrated with microwave repetition rate less than 80 GHz on a chip for the first time. Overall low threshold power (as low as 1 mW) of microcombs across a wide range of resonator FSRs from 2.6 to 220 GHz in surface-loss-limited disk resonators is demonstrated. The rich and complex dynamics of microcomb RF noise are studied. High-coherence, RF phase-locking of microcombs is demonstrated where injection locking of the subcomb offset frequencies are observed by pump-detuning-alignment. Moreover, temporal mode locking, featuring subpicosecond pulses from a parametric 22 GHz microcomb, is observed. We further demonstrated a shot-noise-limited white phase noise of microcomb for the first time. Finally, stabilization of the microcomb repetition rate is realized by phase lock loop control.

For another major nonlinear optical application of disk resonators, highly coherent, simulated Brillouin lasers (SBL) on silicon are also demonstrated, with record low Schawlow-Townes noise less than 0.1 Hz^2/Hz for any chip-based lasers and low technical noise comparable to commercial narrow-linewidth fiber lasers. The SBL devices are efficient, featuring more than 90% quantum efficiency and threshold as low as 60 microwatts. Moreover, novel properties of the SBL are studied, including cascaded operation, threshold tuning, and mode-pulling phenomena. Furthermore, high performance microwave generation using on-chip cascaded Brillouin oscillation is demonstrated. It is also robust enough to enable incorporation as the optical voltage-controlled-oscillator in the first demonstration of a photonic-based, microwave frequency synthesizer. Finally, applications of microresonators as frequency reference cavities and low-phase-noise optomechanical oscillators are presented.

Grain growth in protoplanetary disks

The majority of young, low-mass stars are surrounded by optically thick accretion disks. These circumstellar disks provide large reservoirs of gas and dust that will eventually be transformed into planetary systems. Theory and observations suggest that the earliest stage toward planet formation in a protoplanetary disk is the growth of particles, from sub-micron-sized grains to centimeter- sized pebbles. Theory indicates that small interstellar grains are well coupled into the gas and are incorporated to the disk during the proto-stellar collapse. These dust particles settle toward the disk mid-plane and simultaneously grow through collisional coagulation in a very short timescale. Observationally, grain growth can be inferred by measuring the spectral energy distribution at long wavelengths, which traces the continuum dust emission spectrum and hence the dust opacity. Several observational studies have indicated that the dust component in protoplanetary disks has evolved as compared to interstellar medium dust particles, suggesting at least 4 orders of magnitude in particle- size growth. However, the limited angular resolution and poor sensitivity of previous observations has not allowed for further exploration of this astrophysical process.

As part of my thesis, I embarked in an observational program to search for evidence of radial variations in the dust properties across a protoplanetary disk, which may be indicative of grain growth. By making use of high angular resolution observations obtained with CARMA, VLA, and SMA, I searched for radial variations in the dust opacity inside protoplanetary disks. These observations span more than an order of magnitude in wavelength (from sub-millimeter to centimeter wavelengths) and attain spatial resolutions down to 20 AU. I characterized the radial distribution of the circumstellar material and constrained radial variations of the dust opacity spectral index, which may originate from particle growth in these circumstellar disks. Furthermore, I compared these observational constraints with simple physical models of grain evolution that include collisional coagulation, fragmentation, and the interaction of these grains with the gaseous disk (the radial drift problem). For the parameters explored, these observational constraints are in agreement with a population of grains limited in size by radial drift. Finally, I also discuss future endeavors with forthcoming ALMA observations.

Demographic studies of extrasolar planets

Uncovering the demographics of extrasolar planets is crucial to understanding the processes of their formation and evolution. In this thesis, we present four studies that contribute to this end, three of which relate to NASA's Kepler mission, which has revolutionized the field of exoplanets in the last few years.

In the pre-Kepler study, we investigate a sample of exoplanet spin-orbit measurements---measurements of the inclination of a planet's orbit relative to the spin axis of its host star---to determine whether a dominant planet migration channel can be identified, and at what confidence. Applying methods of Bayesian model comparison to distinguish between the predictions of several different migration models, we find that the data strongly favor a two-mode migration scenario combining planet-planet scattering and disk migration over a single-mode Kozai migration scenario. While we test only the predictions of particular Kozai and scattering migration models in this work, these methods may be used to test the predictions of any other spin-orbit misaligning mechanism.

We then present two studies addressing astrophysical false positives in Kepler data. The Kepler mission has identified thousands of transiting planet candidates, and only relatively few have yet been dynamically confirmed as bona fide planets, with only a handful more even conceivably amenable to future dynamical confirmation. As a result, the ability to draw detailed conclusions about the diversity of exoplanet systems from Kepler detections relies critically on understanding the probability that any individual candidate might be a false positive. We show that a typical a priori false positive probability for a well-vetted Kepler candidate is only about 5-10%, enabling confidence in demographic studies that treat candidates as true planets. We also present a detailed procedure that can be used to securely and efficiently validate any individual transit candidate using detailed information of the signal's shape as well as follow-up observations, if available.

Finally, we calculate an empirical, non-parametric estimate of the shape of the radius distribution of small planets with periods less than 90 days orbiting cool (less than 4000K) dwarf stars in the Kepler catalog. This effort reveals several notable features of the distribution, in particular a maximum in the radius function around 1-1.25 Earth radii and a steep drop-off in the distribution larger than 2 Earth radii. Even more importantly, the methods presented in this work can be applied to a broader subsample of Kepler targets to understand how the radius function of planets changes across different types of host stars.

Developing and characterizing bulk metallic glasses for extreme applications

Metallic glasses have typically been treated as a “one size fits all” type of material. Every alloy is considered to have high strength, high hardness, large elastic limits, corrosion resistance, etc. However, similar to traditional crystalline materials, properties are strongly dependent upon the constituent elements, how it was processed, and the conditions under which it will be used. An important distinction which can be made is between metallic glasses and their composites. Charpy impact toughness measurements are performed to determine the effect processing and microstructure have on bulk metallic glass matrix composites (BMGMCs). Samples are suction cast, machined from commercial plates, and semi-solidly forged (SSF). The SSF specimens have been found to have the highest impact toughness due to the coarsening of the dendrites, which occurs during the semi-solid processing stages. Ductile to brittle transition (DTBT) temperatures are measured for a BMGMC. While at room temperature the BMGMC is highly toughened compared to a fully glassy alloy, it undergoes a DTBT by 250 K. At this point, its impact toughness mirrors that of the constituent glassy matrix. In the following chapter, BMGMCs are shown to have the capability of being capacitively welded to form single, monolithic structures. Shear measurements are performed across welded samples, and, at sufficient weld energies, are found to retain the strength of the parent alloy. Cross-sections are inspected via SEM and no visible crystallization of the matrix occurs.

Next, metallic glasses and BMGMCs are formed into sheets and eggbox structures are tested in hypervelocity impacts. Metallic glasses are ideal candidates for protection against micrometeorite orbital debris due to their high hardness and relatively low density. A flat single layer, flat BMG is compared to a BMGMC eggbox and the latter creates a more diffuse projectile cloud after penetration. A three tiered eggbox structure is also tested by firing a 3.17 mm aluminum sphere at 2.7 km/s at it. The projectile penetrates the first two layers, but is successfully contained by the third.

A large series of metallic glass alloys are created and their wear loss is measured in a pin on disk test. Wear is found to vary dramatically among different metallic glasses, with some considerably outperforming the current state-of-the-art crystalline material (most notably Cu₄₃Zr₄₃Al₇Be₇). Others, on the other hand, suffered extensive wear loss. Commercially available Vitreloy 1 lost nearly three times as much mass in wear as alloy prepared in a laboratory setting. No conclusive correlations can be found between any set of mechanical properties (hardness, density, elastic, bulk, or shear modulus, Poisson’s ratio, frictional force, and run in time) and wear loss. Heat treatments are performed on Vitreloy 1 and Cu₄₃Zr₄₃Al₇Be₇. Anneals near the glass transition temperature are found to increase hardness slightly, but decrease wear loss significantly. Crystallization of both alloys leads to dramatic increases in wear resistance. Finally, wear tests under vacuum are performed on the two alloys above. Vitreloy 1 experiences a dramatic decrease in wear loss, while Cu₄₃Zr₄₃Al₇Be₇ has a moderate increase. Meanwhile, gears are fabricated through three techniques: electrical discharge machining of 1 cm by 3 mm cylinders, semisolid forging, and copper mold suction casting. Initial testing finds the pin on disk test to be an accurate predictor of wear performance in gears.

The final chapter explores an exciting technique in the field of additive manufacturing. Laser engineered net shaping (LENS) is a method whereby small amounts of metallic powders are melted by a laser such that shapes and designs can be built layer by layer into a final part. The technique is extended to mixing different powders during melting, so that compositional gradients can be created across a manufactured part. Two compositional gradients are fabricated and characterized. Ti 6Al¬ 4V to pure vanadium was chosen for its combination of high strength and light weight on one end, and high melting point on the other. It was inspected by cross-sectional x-ray diffraction, and only the anticipated phases were present. 304L stainless steel to Invar 36 was created in both pillar and as a radial gradient. It combines strength and weldability along with a zero coefficient of thermal expansion material. Only the austenite phase is found to be present via x-ray diffraction. Coefficient of thermal expansion is measured for four compositions, and it is found to be tunable depending on composition.

Understanding planet formation through high precision photometry and spectroscopy

From studies of protoplanetary disks to extrasolar planets and planetary debris, we aim to understand the full evolution of a planetary system. Observational constraints from ground- and space-based instrumentation allows us to measure the properties of objects near and far and are central to developing this understanding. We present here three observational campaigns that, when combined with theoretical models, reveal characteristics of different stages and remnants of planet formation. The Kuiper Belt provides evidence of chemical and dynamical activity that reveals clues to its primordial environment and subsequent evolution. Large samples of this population can only be assembled at optical wavelengths, with thermal measurements at infrared and sub-mm wavelengths currently available for only the largest and closest bodies. We measure the size and shape of one particular object precisely here, in hopes of better understanding its unique dynamical history and layered composition.

Molecular organic chemistry is one of the most fundamental and widespread facets of the universe, and plays a key role in planet formation. A host of carbon-containing molecules vibrationally emit in the near-infrared when excited by warm gas, T~1000 K. The NIRSPEC instrument at the W.M. Keck Observatory is uniquely configured to study large ranges of this wavelength region at high spectral resolution. Using this facility we present studies of warm CO gas in protoplanetary disks, with a new code for precise excitation modeling. A parameterized suite of models demonstrates the abilities of the code and matches observational constraints such as line strength and shape. We use the models to probe various disk parameters as well, which are easily extensible to others with known disk emission spectra such as water, carbon dioxide, acetylene, and hydrogen cyanide.

Lastly, the existence of molecules in extrasolar planets can also be studied with NIRSPEC and reveals a great deal about the evolution of the protoplanetary gas. The species we observe in protoplanetary disks are also often present in exoplanet atmospheres, and are abundant in Earth's atmosphere as well. Thus, a sophisticated telluric removal code is necessary to analyze these high dynamic range, high-resolution spectra. We present observations of a hot Jupiter, revealing water in its atmosphere and demonstrating a new technique for exoplanet mass determination and atmospheric characterization. We will also be applying this atmospheric removal code to the aforementioned disk observations, to improve our data analysis and probe less abundant species. Guiding models using observations is the only way to develop an accurate understanding of the timescales and processes involved. The futures of the modeling and of the observations are bright, and the end goal of realizing a unified model of planet formation will require both theory and data, from a diverse collection of sources.

Hall coefficient and resistivity of an amorphous palladium-silicon alloy

The Hall coefficient and resistance in several specimens of an amorphous metallic alloy containing 80 at.% palladium and 20 at.% silicon have been investigated at temperatures between 4.2°K and room temperature. An ideal limiting behavior of these transport coefficients was analyzed on the basis of the nearly free electron model to yield a carrier density of 9 x 10²² cm.^-3, or about 1.7 electrons per palladium atom, and a mean free path of about 9Å which is almost constant with temperature. The deviations of the individual specimens from this ideal behavior, which were small but noticeable in the relative resistivity and much greater in the Hall coefficient, can be explained by invoking disk-shaped crystalline regions with low resistivity and a positive Hall coefficient. A detailed calculation shows how a volume fraction of such crystalline material too small to be noticed in X-ray diffraction could have a significant effect on the resistivity and a much greater effect on the Hall coefficient.

New Insights from Aperiodic Variability of Young Stars

Nearly all young stars are variable, with the variability traditionally divided into two classes: periodic variables and aperiodic or "irregular" variables. Periodic variables have been studied extensively, typically using periodograms, while aperiodic variables have received much less attention due to a lack of standard statistical tools. However, aperiodic variability can serve as a powerful probe of young star accretion physics and inner circumstellar disk structure. For my dissertation, I analyzed data from a large-scale, long-term survey of the nearby North America Nebula complex, using Palomar Transient Factory photometric time series collected on a nightly or every few night cadence over several years. This survey is the most thorough exploration of variability in a sample of thousands of young stars over time baselines of days to years, revealing a rich array of lightcurve shapes, amplitudes, and timescales.

I have constrained the timescale distribution of all young variables, periodic and aperiodic, on timescales from less than a day to ~100 days. I have shown that the distribution of timescales for aperiodic variables peaks at a few days, with relatively few (~15%) sources dominated by variability on tens of days or longer. My constraints on aperiodic timescale distributions are based on two new tools, magnitude- vs. time-difference (Δm-Δt) plots and peak-finding plots, for describing aperiodic lightcurves; this thesis provides simulations of their performance and presents recommendations on how to apply them to aperiodic signals in other time series data sets. In addition, I have measured the error introduced into colors or SEDs from combining photometry of variable sources taken at different epochs. These are the first quantitative results to be presented on the distributions in amplitude and time scale for young aperiodic variables, particularly those varying on timescales of weeks to months.

A Cerenkov-ΔΕ-Cerenkov detector for high energy cosmic ray isotopes and an accelerator study of ^(40)Ar & ^(56)Fe fragmentation

This thesis has two major parts. The first part of the thesis will describe a high energy cosmic ray detector -- the High Energy Isotope Spectrometer Telescope (HEIST). HEIST is a large area (0.25 m²sr) balloon-borne isotope spectrometer designed to make high-resolution measurements of isotopes in the element range from neon to nickel (10 ≤ Z ≤ 28) at energies of about 2 GeV/nucleon. The instrument consists of a stack of 12 NaI(Tl) scintilla tors, two Cerenkov counters, and two plastic scintillators. Each of the 2-cm thick NaI disks is viewed by six 1.5-inch photomultipliers whose combined outputs measure the energy deposition in that layer. In addition, the six outputs from each disk are compared to determine the position at which incident nuclei traverse each layer to an accuracy of ~2 mm. The Cerenkov counters, which measure particle velocity, are each viewed by twelve 5-inch photomultipliers using light integration boxes.

HEIST-2 determines the mass of individual nuclei by measuring both the change in the Lorentz factor (Δγ) that results from traversing the NaI stack, and the energy loss (ΔΕ) in the stack. Since the total energy of an isotope is given by Ε = γM, the mass M can be determined by M = ΔΕ/Δγ. The instrument is designed to achieve a typical mass resolution of 0.2 amu.

The second part of this thesis presents an experimental measurement of the isotopic composition of the fragments from the breakup of high energy ⁴⁰Ar and ⁵⁶Fe nuclei. Cosmic ray composition studies rely heavily on semi-empirical estimates of the cross-sections for the nuclear fragmentation reactions which alter the composition during propagation through the interstellar medium. Experimentally measured yields of isotopes from the fragmentation of ⁴⁰Ar and ⁵⁶Fe are compared with calculated yields based on semi-empirical cross-section formulae. There are two sets of measurements. The first set of measurements, made at the Lawrence Berkeley Laboratory Bevalac using a beam of 287 MeV/nucleon ⁴⁰Ar incident on a CH₂ target, achieves excellent mass resolution (σ_m ≤ 0.2 amu) for isotopes of Mg through K using a Si(Li) detector telescope. The second set of measurements, also made at the Lawrence Berkeley Laboratory Bevalac, using a beam of 583 MeV/nucleon ⁵⁶FeFe incident on a CH₂ target, resolved Cr, Mn, and Fe fragments with a typical mass resolution of ~ 0.25 amu, through the use of the Heavy Isotope Spectrometer Telescope (HIST) which was later carried into space on ISEE-3 in 1978. The general agreement between calculation and experiment is good, but some significant differences are reported here.

Multipole moments in general relativity and dynamical perturbations of black-hole magnetospheres

This thesis consists of two parts. In Part I, we develop a multipole moment formalism in general relativity and use it to analyze the motion and precession of compact bodies. More specifically, the generic, vacuum, dynamical gravitational field of the exterior universe in the vicinity of a freely moving body is expanded in positive powers of the distance r away from the body's spatial origin (i.e., in the distance r from its timelike-geodesic world line). The expansion coefficients, called "external multipole moments,'' are defined covariantly in terms of the Riemann curvature tensor and its spatial derivatives evaluated on the body's central world line. In a carefully chosen class of de Donder coordinates, the expansion of the external field involves only integral powers of r ; no logarithmic terms occur. The expansion is used to derive higher-order corrections to previously known laws of motion and precession for black holes and other bodies. The resulting laws of motion and precession are expressed in terms of couplings of the time derivatives of the body's quadrupole and octopole moments to the external moments, i.e., to the external curvature and its gradient.

In part II, we study the interaction of magnetohydrodynamic (MHD) waves in a black-hole magnetosphere with the "dragging of inertial frames" effect of the hole's rotation - i.e., with the hole's "gravitomagnetic field." More specifically: we first rewrite the laws of perfect general relativistic magnetohydrodynamics (GRMHD) in 3+1 language in a general spacetime, in terms of quantities (magnetic field, flow velocity, ...) that would be measured by the ''fiducial observers” whose world lines are orthogonal to (arbitrarily chosen) hypersurfaces of constant time. We then specialize to a stationary spacetime and MHD flow with one arbitrary spatial symmetry (e.g., the stationary magnetosphere of a Kerr black hole); and for this spacetime we reduce the GRMHD equations to a set of algebraic equations. The general features of the resulting stationary, symmetric GRMHD magnetospheric solutions are discussed, including the Blandford-Znajek effect in which the gravitomagnetic field interacts with the magnetosphere to produce an outflowing jet. Then in a specific model spacetime with two spatial symmetries, which captures the key features of the Kerr geometry, we derive the GRMHD equations which govern weak, linealized perturbations of a stationary magnetosphere with outflowing jet. These perturbation equations are then Fourier analyzed in time t and in the symmetry coordinate x, and subsequently solved numerically. The numerical solutions describe the interaction of MHD waves with the gravitomagnetic field. It is found that, among other features, when an oscillatory external force is applied to the region of the magnetosphere where plasma (e⁺e^-) is being created, the magnetosphere responds especially strongly at a particular, resonant, driving frequency. The resonant frequency is that for which the perturbations appear to be stationary (time independent) in the common rest frame of the freshly created plasma and the rotating magnetic field lines. The magnetosphere of a rotating black hole, when buffeted by nonaxisymmetric magnetic fields anchored in a surrounding accretion disk, might exhibit an analogous resonance. If so then the hole's outflowing jet might be modulated at resonant frequencies ω=(m/2) Ω_H where m is an integer and Ω_H is the hole's angular velocity.

Volatiles in Protoplanetary Disks

Planets are assembled from the gas, dust, and ice in the accretion disks that encircle young stars. Ices of chemical compounds with low condensation temperatures (<200 K), the so-called volatiles, dominate the solid mass reservoir from which planetesimals are formed and are thus available to build the protoplanetary cores of gas/ice giant planets. It has long been thought that the regions near the condensation fronts of volatiles are preferential birth sites of planets. Moreover, the main volatiles in disks are also the main C-and O-containing species in (exo)planetary atmospheres. Understanding the distribution of volatiles in disks and their role in planet-formation processes is therefore of great interest.

This thesis addresses two fundamental questions concerning the nature of volatiles in planet-forming disks: (1) how are volatiles distributed throughout a disk, and (2) how can we use volatiles to probe planet-forming processes in disks? We tackle the first question in two complementary ways. We have developed a novel super-resolution method to constrain the radial distribution of volatiles throughout a disk by combining multi-wavelength spectra. Thanks to the ordered velocity and temperature profiles in disks, we find that detailed constraints can be derived even with spatially and spectrally unresolved data -- provided a wide range of energy levels are sampled. We also employ high-spatial resolution interferometric images at (sub)mm frequencies using the Atacama Large Millimeter Array (ALMA) to directly measure the radial distribution of volatiles.

For the second question, we combine volatile gas emission measurements with those of the dust continuum emission or extinction to understand dust growth mechanisms in disks and disk instabilities at planet-forming distances from the central star. Our observations and models support the idea that the water vapor can be concentrated in regions near its condensation front at certain evolutionary stages in the lifetime of protoplanetary disks, and that fast pebble growth is likely to occur near the condensation fronts of various volatile species.

Electrocatalytic reduction of dioxygen at chemically modified electrodes

The kinetics of the reduction of O₂ by Ru(NH₃)₆⁺² as catalyzed by cobalt(II) tetrakis(4-N-methylpyridyl)porphyrin are described both in homogeneous solution and when the reactants are confined to Nafion coatings on graphite electrodes. The catalytic mechanism is determined and the factors that can control the total reduction currents at Nafion-coated electrodes are specified. A kinetic zone diagram for analyzing the behavior of catalyst-mediator-substrate systems at polymer coated electrodes is presented and utilized in identifying the current-limiting processes. Good agreement is demonstrated between calculated and measured reduction currents at rotating disk electrodes. The experimental conditions that will yield the optimum performance of coated electrodes are discussed, and a relationship is derived for the optimal coating thickness.

The relation between the reduction potentials of adsorbed and unadsorbed cobalt(III) tetrakis(4-N-methylpyridyl)porphyrin and those where it catalyzes the electroreduction of dioxygen is described. There is an unusually large change in the formal potential of the Co(III) couple upon the adsorption of the porphyrin on the graphite electrode surface. The mechanism in which the (inevitably) adsorbed porphyrin catalyzes the reduction of O₂ is in accord with a general mechanistic scheme proposed for most monomeric cobalt porphyrins.

Four new dimeric metalloporphyrins (prepared in the laboratory of Professor C. K. Chang) have the two porphyrin rings linked by an anthracene bridge attached to meso positions. The electrocatalytic behavior of the diporphyrins towards the reduction of O₂ at graphite electrodes has been examined for the following combination of metal centers: Co-Cu, Co-Fe, Fe-Fe, Fe-H₂. The Co-Cu diporphyrin catalyzes the reduction of O₂ to H₂O₂ but no further. The other three catalysts all exhibit mixed reduction pathways leading to both H₂O₂ and H₂O. However, the pathways that lead to H₂O do not involve H₂O₂ as an intermediate. A possible mechanistic scheme is offered to account for the observed behavior.