Part 1: Longitudinal static and dynamic effects in semiconductor lasers. Part II: Spectral characteristics of passively mode-locked quantum well lasers

In the first part of this thesis a study of the effect of the longitudinal distribution of optical intensity and electron density on the static and dynamic behavior of semiconductor lasers is performed. A static model for above threshold operation of a single mode laser, consisting of multiple active and passive sections, is developed by calculating the longitudinal optical intensity distribution and electron density distribution in a self-consistent manner. Feedback from an index and gain Bragg grating is included, as well as feedback from discrete reflections at interfaces and facets. Longitudinal spatial holeburning is analyzed by including the dependence of the gain and the refractive index on the electron density. The mechanisms of spatial holeburning in quarter wave shifted DFB lasers are analyzed. A new laser structure with a uniform optical intensity distribution is introduced and an implementation is simulated, resulting in a large reduction of the longitudinal spatial holeburning effect.

A dynamic small-signal model is then developed by including the optical intensity and electron density distribution, as well as the dependence of the grating coupling coefficients on the electron density. Expressions are derived for the intensity and frequency noise spectrum, the spontaneous emission rate into the lasing mode, the linewidth enhancement factor, and the AM and FM modulation response. Different chirp components are identified in the FM response, and a new adiabatic chirp component is discovered. This new adiabatic chirp component is caused by the nonuniform longitudinal distributions, and is found to dominate at low frequencies. Distributed feedback lasers with partial gain coupling are analyzed, and it is shown how the dependence of the grating coupling coefficients on the electron density can result in an enhancement of the differential gain with an associated enhancement in modulation bandwidth and a reduction in chirp.

In the second part, spectral characteristics of passively mode-locked two-section multiple quantum well laser coupled to an external cavity are studied. Broad-band wavelength tuning using an external grating is demonstrated for the first time in passively mode-locked semiconductor lasers. A record tuning range of 26 nm is measured, with pulse widths of typically a few picosecond and time-bandwidth products of more than 10 times the transform limit. It is then demonstrated that these large time-bandwidth products are due to a strong linear upchirp, by performing pulse compression by a factor of 15 to a record pulse widths as low 320 fs.

A model for pulse propagation through a saturable medium with self-phase-modulation, due to the a-parameter, is developed for quantum well material, including the frequency dependence of the gain medium. This model is used to simulate two-section devices coupled to an external cavity. When no self-phase-modulation is present, it is found that the pulses are asymmetric with a sharper rising edge, that the pulse tails have an exponential behavior, and that the transform limit is 0.3. Inclusion of self-phase-modulation results in a linear upchirp imprinted on the pulse after each round-trip. This linear upchirp is due to a combination of self-phase-modulation in a gain section and absorption of the leading edge of the pulse in the saturable absorber.

Dirac spectra, summation formulae, and the spectral action

Noncommutative geometry is a source of particle physics models with matter Lagrangians coupled to gravity. One may associate to any noncommutative space (A, H, D) its spectral action, which is defined in terms of the Dirac spectrum of its Dirac operator D. When viewing a spin manifold as a noncommutative space, D is the usual Dirac operator. In this paper, we give nonperturbative computations of the spectral action for quotients of SU(2), Bieberbach manifolds, and SU(3) equipped with a variety of geometries. Along the way we will compute several Dirac spectra and refer to applications of this computation.

Characterization of exoplanet atmospheres : spectral retrieval and chemistry

The study of exoplanets is rapidly evolving into an important and exciting field of its own. My investigations over the past half-decade have focused on understanding just a small sliver of what they are trying to tell us. That small sliver is their atmospheres. Atmospheres are the buffer between the bulk planet and the vacuum of space. The atmosphere is an important component of a planet as it is the most readily observable and contains the most information about the physical processes that can occur in a planet. I have focused on two aspects of exoplanetary atmospheres. First, I aimed to understand the chemical mechanisms that control the atmospheric abundances. Second, I focused on interpreting exoplanet atmospheric spectra and what they tell us about the temperatures and compositions through inverse modeling. Finally, I interpreted the retrieved temperature and abundances from inverse modeling in the context of chemical disequilibrium in the planetary atmospheres.

A multi-scale approach to shaping carbon nanotube structures for hollow microneedles

The concept of a carbon nanotube microneedle array is explored in this thesis from multiple perspectives including microneedle fabrication, physical aspects of transdermal delivery, and in vivo transdermal drug delivery experiments. Starting with standard techniques in carbon nanotube (CNT) fabrication, including catalyst patterning and chemical vapor deposition, vertically-aligned carbon nanotubes are utilized as a scaffold to define the shape of the hollow microneedle. Passive, scalable techniques based on capillary action and unique photolithographic methods are utilized to produce a CNT-polymer composite microneedle. Specific examples of CNT-polyimide and CNT-epoxy microneedles are investigated. Further analysis of the transport properties of polymer resins reveals general requirements for applying arbitrary polymers to the fabrication process.

The bottom-up fabrication approach embodied by vertically-aligned carbon nanotubes allows for more direct construction of complex high-aspect ratio features than standard top-down fabrication approaches, making microneedles an ideal application for CNTs. However, current vertically-aligned CNT fabrication techniques only allow for the production of extruded geometries with a constant cross-sectional area, such as cylinders. To rectify this limitation, isotropic oxygen etching is introduced as a novel fabrication technique to create true 3D CNT geometry. Oxygen etching is utilized to create a conical geometry from a cylindrical CNT structure as well as create complex shape transformations in other CNT geometries.

CNT-polymer composite microneedles are anchored onto a common polymer base less than 50 µm thick, which allows for the microneedles to be incorporated into multiple drug delivery platforms, including modified hypodermic syringes and silicone skin patches. Cylindrical microneedles are fabricated with 100 µm outer diameter and height of 200-250 µm with a central cavity, or lumen, diameter of 30 µm to facilitate liquid drug flow. In vitro delivery experiments in swine skin demonstrate the ability of the microneedles to successfully penetrate the skin and deliver aqueous solutions.

An in vivo study was performed to assess the ability of the CNT-polymer microneedles to deliver drugs transdermally. CNT-polymer microneedles are attached to a hand actuated silicone skin patch that holds a liquid reservoir of drugs. Fentanyl, a potent analgesic, was administered to New Zealand White Rabbits through 3 routes of delivery: topical patch, CNT-polymer microneedles, and subcutaneous hypodermic injection. Results demonstrate that the CNT-polymer microneedles have a similar onset of action as the topical patch. CNT-polymer microneedles were also vetted as a painless delivery approach compared to hypodermic injection. Comparative analysis with contemporary microneedle designs demonstrates that the delivery achieved through CNT-polymer microneedles is akin to current hollow microneedle architectures. The inherent advantage of applying a bottom-up fabrication approach alongside similar delivery performance to contemporary microneedle designs demonstrates that the CNT-polymer composite microneedle is a viable architecture in the emerging field of painless transdermal delivery.

A variational framework for spectral discretization of the density matrix in Kohn Sham density functional theory

Kohn-Sham density functional theory (KSDFT) is currently the main work-horse of quantum mechanical calculations in physics, chemistry, and materials science. From a mechanical engineering perspective, we are interested in studying the role of defects in the mechanical properties in materials. In real materials, defects are typically found at very small concentrations e.g., vacancies occur at parts per million, dislocation density in metals ranges from $10^{10} m^{-2}$ to $10^{15} m^{-2}$, and grain sizes vary from nanometers to micrometers in polycrystalline materials, etc. In order to model materials at realistic defect concentrations using DFT, we would need to work with system sizes beyond millions of atoms. Due to the cubic-scaling computational cost with respect to the number of atoms in conventional DFT implementations, such system sizes are unreachable. Since the early 1990s, there has been a huge interest in developing DFT implementations that have linear-scaling computational cost. A promising approach to achieving linear-scaling cost is to approximate the density matrix in KSDFT. The focus of this thesis is to provide a firm mathematical framework to study the convergence of these approximations. We reformulate the Kohn-Sham density functional theory as a nested variational problem in the density matrix, the electrostatic potential, and a field dual to the electron density. The corresponding functional is linear in the density matrix and thus amenable to spectral representation. Based on this reformulation, we introduce a new approximation scheme, called spectral binning, which does not require smoothing of the occupancy function and thus applies at arbitrarily low temperatures. We proof convergence of the approximate solutions with respect to spectral binning and with respect to an additional spatial discretization of the domain. For a standard one-dimensional benchmark problem, we present numerical experiments for which spectral binning exhibits excellent convergence characteristics and outperforms other linear-scaling methods.

Quantifying Earthquake Collapse Risk of Tall Steel Braced Frame Buildings Using Rupture-to-Rafters Simulations

This thesis examines collapse risk of tall steel braced frame buildings using rupture-to-rafters simulations due to suite of San Andreas earthquakes. Two key advancements in this work are the development of (i) a rational methodology for assigning scenario earthquake probabilities and (ii) an artificial correction-free approach to broadband ground motion simulation. The work can be divided into the following sections: earthquake source modeling, earthquake probability calculations, ground motion simulations, building response, and performance analysis.

As a first step the kinematic source inversions of past earthquakes in the magnitude range of 6-8 are used to simulate 60 scenario earthquakes on the San Andreas fault. For each scenario earthquake a 30-year occurrence probability is calculated and we present a rational method to redistribute the forecast earthquake probabilities from UCERF to the simulated scenario earthquake. We illustrate the inner workings of the method through an example involving earthquakes on the San Andreas fault in southern California.

Next, three-component broadband ground motion histories are computed at 636 sites in the greater Los Angeles metropolitan area by superposing short-period (0.2~s-2.0~s) empirical Green's function synthetics on top of long-period ($>$ 2.0~s) spectral element synthetics. We superimpose these seismograms on low-frequency seismograms, computed from kinematic source models using the spectral element method, to produce broadband seismograms.

Using the ground motions at 636 sites for the 60 scenario earthquakes, 3-D nonlinear analysis of several variants of an 18-story steel braced frame building, designed for three soil types using the 1994 and 1997 Uniform Building Code provisions and subjected to these ground motions, are conducted. Model performance is classified into one of five performance levels: Immediate Occupancy, Life Safety, Collapse Prevention, Red-Tagged, and Model Collapse. The results are combined with the 30-year probability of occurrence of the San Andreas scenario earthquakes using the PEER performance based earthquake engineering framework to determine the probability of exceedance of these limit states over the next 30 years.

Gauge Invariant Spectral Cauchy Characteristic Extraction of Gravitational Waves in Computational General Relativity

We present a complete system for Spectral Cauchy characteristic extraction (Spectral CCE). Implemented in C++ within the Spectral Einstein Code (SpEC), the method employs numerous innovative algorithms to efficiently calculate the Bondi strain, news, and flux.

Spectral CCE was envisioned to ensure physically accurate gravitational wave-forms computed for the Laser Interferometer Gravitational wave Observatory (LIGO) and similar experiments, while working toward a template bank with more than a thousand waveforms to span the binary black hole (BBH) problem’s seven-dimensional parameter space.

The Bondi strain, news, and flux are physical quantities central to efforts to understand and detect astrophysical gravitational wave sources within the Simulations of eXtreme Spacetime (SXS) collaboration, with the ultimate aim of providing the first strong field probe of the Einstein field equation.

In a series of included papers, we demonstrate stability, convergence, and gauge invariance. We also demonstrate agreement between Spectral CCE and the legacy Pitt null code, while achieving a factor of 200 improvement in computational efficiency.

Spectral CCE represents a significant computational advance. It is the foundation upon which further capability will be built, specifically enabling the complete calculation of junk-free, gauge-free, and physically valid waveform data on the fly within SpEC.

On Ultrafast Time-Domain TeraHertz Spectroscopy in the Condensed Phase: Linear Spectroscopic Measurements of Hydrogen-Bond Dynamics of Astrochemical Ice Analogs and Nonlinear TeraHertz Kerr Effect Measurements of Vibrational Quantum Beats

Much of the chemistry that affects life on planet Earth occurs in the condensed phase. The TeraHertz (THz) or far-infrared (far-IR) region of the electromagnetic spectrum (from 0.1 THz to 10 THz, 3 cm^-1 to 300 cm^-1, or 3000 μm to 30 μm) has been shown to provide unique possibilities in the study of condensed-phase processes. The goal of this work is to expand the possibilities available in the THz region and undertake new investigations of fundamental interest to chemistry. Since we are fundamentally interested in condensed-phase processes, this thesis focuses on two areas where THz spectroscopy can provide new understanding: astrochemistry and solvation science. To advance these fields, we had to develop new instrumentation that would enable the experiments necessary to answer new questions in either astrochemistry or solvation science. We first developed a new experimental setup capable of studying astrochemical ice analogs in both the TeraHertz (THz), or far-Infrared (far-IR), region (0.3 - 7.5 THz; 10 - 250 cm^-1) and the mid-IR (400 - 4000 cm^-1). The importance of astrochemical ices lies in their key role in the formation of complex organic molecules, such as amino acids and sugars in space. Thus, the instruments are capable of performing variety of spectroscopic studies that can provide especially relevant laboratory data to support astronomical observations from telescopes such as the Herschel Space Telescope, the Stratospheric Observatory for Infrared Astronomy (SOFIA), and the Atacama Large Millimeter Array (ALMA). The experimental apparatus uses a THz time-domain spectrometer, with a 1750/875 nm plasma source and a GaP detector crystal, to cover the bandwidth mentioned above with ~10 GHz (~0.3 cm^-1) resolution.

Using the above instrumentation, experimental spectra of astrochemical ice analogs of water and carbon dioxide in pure, mixed, and layered ices were collected at different temperatures under high vacuum conditions with the goal of investigating the structure of the ice. We tentatively observe a new feature in both amorphous solid water and crystalline water at 33 cm^-1 (1 THz). In addition, our studies of mixed and layered ices show how it is possible to identify the location of carbon dioxide as it segregates within the ice by observing its effect on the THz spectrum of water ice. The THz spectra of mixed and layered ices are further analyzed by fitting their spectra features to those of pure amorphous solid water and crystalline water ice to quantify the effects of temperature changes on structure. From the results of this work, it appears that THz spectroscopy is potentially well suited to study thermal transformations within the ice.

To advance the study of liquids with THz spectroscopy, we developed a new ultrafast nonlinear THz spectroscopic technique: heterodyne-detected, ultrafast THz Kerr effect (TKE) spectroscopy. We implemented a heterodyne-detection scheme into a TKE spectrometer that uses a stilbazoiumbased THz emitter, 4-N,N-dimethylamino-4-N-methyl-stilbazolium 2,4,6-trimethylbenzenesulfonate (DSTMS), and high numerical aperture optics which generates THz electric field in excess of 300 kV/cm, in the sample. This allows us to report the first measurement of quantum beats at terahertz (THz) frequencies that result from vibrational coherences initiated by the nonlinear, dipolar interaction of a broadband, high-energy, (sub)picosecond THz pulse with the sample. Our instrument improves on both the frequency coverage, and sensitivity previously reported; it also ensures a backgroundless measurement of the THz Kerr effect in pure liquids. For liquid diiodomethane, we observe a quantum beat at 3.66 THz (122 cm^-1), in exact agreement with the fundamental transition frequency of the υ4 vibration of the molecule. This result provides new insight into dipolar vs. Raman selection rules at terahertz frequencies.

To conclude we discuss future directions for the nonlinear THz spectroscopy in the Blake lab. We report the first results from an experiment using a plasma-based THz source for nonlinear spectroscopy that has the potential to enable nonlinear THz spectra with a sub-100 fs temporal resolution, and how the optics involved in the plasma mechanism can enable THz pulse shaping. Finally, we discuss how a single-shot THz detection scheme could improve the acquisition of THz data and how such a scheme could be implemented in the Blake lab. The instruments developed herein will hopefully remain a part of the groups core competencies and serve as building blocks for the next generation of THz instrumentation that pushes the frontiers of both chemistry and the scientific enterprise as a whole.

Infared observations of H II regions

Spectral data are presented, giving intensities of the Brackett ɤ (B₇) line at six positions in M 42 and of the Brackett ten through fourteen (B₁₀-B₁₄) lines plus the He 4d³D-3p³p⁰ line at three positions in M 42. Observations of the Brackett ɤ line are also given for the planetary nebulae NGC 7027 and IC 418. Brackett gamma is shown to exhibit an anomalous satellite line in NGC 7027. Broadband data are presented, giving intensities at effective wavelengths of 1.25 μ, 1.65 μ, 2.2 μ, 3.5 μ and 4.8 μ for three positions in M 42.

Comparisons with visual and radio data as well as 12 micron and 20 micron data are used to derive reddening, electron temperatures, and electron densities for M 42 and the two planetaries, as well as a helium abundance for M 42. A representative electron temperature of 8400°K ± 1000°K, an electron density of 1.5 ±0.1 x 10³ cm^-3 and a He/H number density ratio of 0.10 +0.10/-0.05 are derived for the central region of M 42. The electron temperature is found to increase slightly with distance from the Trapezium.

M 42 is shown to emit in excess of the predicted recombination radiation throughout the entire infrared spectrum. The variations in the excess with wavelength and with position are analyzed to determine which of several physical processes may be operating. The longer wavelength infrared excess is shown to be dominated by dust emission, while the shorter wavelength infrared excess is caused by dust scattering. The dust is shown to be larger than the average interstellar particle. A new feature of the Orion red star ORS-1 is found in that it appears to have a reflection nebula around it.

Fast numerical methods for mixed, singular Helmholtz boundary value problems and Laplace eigenvalue problems - with applications to antenna design, sloshing, electromagnetic scattering and spectral geometry

This thesis presents a novel class of algorithms for the solution of scattering and eigenvalue problems on general two-dimensional domains under a variety of boundary conditions, including non-smooth domains and certain "Zaremba" boundary conditions - for which Dirichlet and Neumann conditions are specified on various portions of the domain boundary. The theoretical basis of the methods for the Zaremba problems on smooth domains concern detailed information, which is put forth for the first time in this thesis, about the singularity structure of solutions of the Laplace operator under boundary conditions of Zaremba type. The new methods, which are based on use of Green functions and integral equations, incorporate a number of algorithmic innovations, including a fast and robust eigenvalue-search algorithm, use of the Fourier Continuation method for regularization of all smooth-domain Zaremba singularities, and newly derived quadrature rules which give rise to high-order convergence even around singular points for the Zaremba problem. The resulting algorithms enjoy high-order convergence, and they can tackle a variety of elliptic problems under general boundary conditions, including, for example, eigenvalue problems, scattering problems, and, in particular, eigenfunction expansion for time-domain problems in non-separable physical domains with mixed boundary conditions.

A Multiwavelength Study of the Intracluster Medium and the Characterization of the Multiwavelength Sub/millimeter Inductance Camera

The first part of this thesis combines Bolocam observations of the thermal Sunyaev-Zel’dovich (SZ) effect at 140 GHz with X-ray observations from Chandra, strong lensing data from the Hubble Space Telescope (HST), and weak lensing data from HST and Subaru to constrain parametric models for the distribution of dark and baryonic matter in a sample of six massive, dynamically relaxed galaxy clusters. For five of the six clusters, the full multiwavelength dataset is well described by a relatively simple model that assumes spherical symmetry, hydrostatic equilibrium, and entirely thermal pressure support. The multiwavelength analysis yields considerably better constraints on the total mass and concentration compared to analysis of any one dataset individually. The subsample of five galaxy clusters is used to place an upper limit on the fraction of pressure support in the intracluster medium (ICM) due to nonthermal processes, such as turbulent and bulk flow of the gas. We constrain the nonthermal pressure fraction at r500c to be less than 0.11 at 95% confidence, where r500c refers to radius at which the average enclosed density is 500 times the critical density of the Universe. This is in tension with state-of-the-art hydrodynamical simulations, which predict a nonthermal pressure fraction of approximately 0.25 at r500c for the clusters in this sample.

The second part of this thesis focuses on the characterization of the Multiwavelength Sub/millimeter Inductance Camera (MUSIC), a photometric imaging camera that was commissioned at the Caltech Submillimeter Observatory (CSO) in 2012. MUSIC is designed to have a 14 arcminute, diffraction-limited field of view populated with 576 spatial pixels that are simultaneously sensitive to four bands at 150, 220, 290, and 350 GHz. It is well-suited for studies of dusty star forming galaxies, galaxy clusters via the SZ Effect, and galactic star formation. MUSIC employs a number of novel detector technologies: broadband phased-arrays of slot dipole antennas for beam formation, on-chip lumped element filters for band definition, and Microwave Kinetic Inductance Detectors (MKIDs) for transduction of incoming light to electric signal. MKIDs are superconducting micro-resonators coupled to a feedline. Incoming light breaks apart Cooper pairs in the superconductor, causing a change in the quality factor and frequency of the resonator. This is read out as amplitude and phase modulation of a microwave probe signal centered on the resonant frequency. By tuning each resonator to a slightly different frequency and sending out a superposition of probe signals, hundreds of detectors can be read out on a single feedline. This natural capability for large scale, frequency domain multiplexing combined with relatively simple fabrication makes MKIDs a promising low temperature detector for future kilopixel sub/millimeter instruments. There is also considerable interest in using MKIDs for optical through near-infrared spectrophotometry due to their fast microsecond response time and modest energy resolution. In order to optimize the MKID design to obtain suitable performance for any particular application, it is critical to have a well-understood physical model for the detectors and the sources of noise to which they are susceptible. MUSIC has collected many hours of on-sky data with over 1000 MKIDs. This work studies the performance of the detectors in the context of one such physical model. Chapter 2 describes the theoretical model for the responsivity and noise of MKIDs. Chapter 3 outlines the set of measurements used to calibrate this model for the MUSIC detectors. Chapter 4 presents the resulting estimates of the spectral response, optical efficiency, and on-sky loading. The measured detector response to Uranus is compared to the calibrated model prediction in order to determine how well the model describes the propagation of signal through the full instrument. Chapter 5 examines the noise present in the detector timestreams during recent science observations. Noise due to fluctuations in atmospheric emission dominate at long timescales (less than 0.5 Hz). Fluctuations in the amplitude and phase of the microwave probe signal due to the readout electronics contribute significant 1/f and drift-type noise at shorter timescales. The atmospheric noise is removed by creating a template for the fluctuations in atmospheric emission from weighted averages of the detector timestreams. The electronics noise is removed by using probe signals centered off-resonance to construct templates for the amplitude and phase fluctuations. The algorithms that perform the atmospheric and electronic noise removal are described. After removal, we find good agreement between the observed residual noise and our expectation for intrinsic detector noise over a significant fraction of the signal bandwidth.

Spectral density of first order Piecewise linear systems excited by white noise

The Fokker-Planck (FP) equation is used to develop a general method for finding the spectral density for a class of randomly excited first order systems. This class consists of systems satisfying stochastic differential equations of form ẋ + f(x) = m/Ʃ/j = 1 h_j(x)n_j(t) where f and the h_j are piecewise linear functions (not necessarily continuous), and the n_j are stationary Gaussian white noise. For such systems, it is shown how the Laplace-transformed FP equation can be solved for the transformed transition probability density. By manipulation of the FP equation and its adjoint, a formula is derived for the transformed autocorrelation function in terms of the transformed transition density. From this, the spectral density is readily obtained. The method generalizes that of Caughey and Dienes, J. Appl. Phys., 32.11.

This method is applied to 4 subclasses: (1) m = 1, h₁ = const. (forcing function excitation); (2) m = 1, h₁ = f (parametric excitation); (3) m = 2, h₁ = const., h₂ = f, n₁ and n₂ correlated; (4) the same, uncorrelated. Many special cases, especially in subclass (1), are worked through to obtain explicit formulas for the spectral density, most of which have not been obtained before. Some results are graphed.

Dealing with parametrically excited first order systems leads to two complications. There is some controversy concerning the form of the FP equation involved (see Gray and Caughey, J. Math. Phys., 44.3); and the conditions which apply at irregular points, where the second order coefficient of the FP equation vanishes, are not obvious but require use of the mathematical theory of diffusion processes developed by Feller and others. These points are discussed in the first chapter, relevant results from various sources being summarized and applied. Also discussed is the steady-state density (the limit of the transition density as t → ∞).

A mathematical and experimental investigation of microcycle spectral estimates of semiconductor flicker noise

The experimental portion of this thesis tries to estimate the density of the power spectrum of very low frequency semiconductor noise, from 10^-6.3 cps to 1. cps with a greater accuracy than that achieved in previous similar attempts: it is concluded that the spectrum is 1/f^α with α approximately 1.3 over most of the frequency range, but appearing to have a value of about 1 in the lowest decade. The noise sources are, among others, the first stage circuits of a grounded input silicon epitaxial operational amplifier. This thesis also investigates a peculiar form of stationarity which seems to distinguish flicker noise from other semiconductor noise.

In order to decrease by an order of magnitude the pernicious effects of temperature drifts, semiconductor "aging", and possible mechanical failures associated with prolonged periods of data taking, 10 independent noise sources were time-multiplexed and their spectral estimates were subsequently averaged. If the sources have similar spectra, it is demonstrated that this reduces the necessary data-taking time by a factor of 10 for a given accuracy.

In view of the measured high temperature sensitivity of the noise sources, it was necessary to combine the passive attenuation of a special-material container with active control. The noise sources were placed in a copper-epoxy container of high heat capacity and medium heat conductivity, and that container was immersed in a temperature controlled circulating ethylene-glycol bath.

Other spectra of interest, estimated from data taken concurrently with the semiconductor noise data were the spectra of the bath's controlled temperature, the semiconductor surface temperature, and the power supply voltage amplitude fluctuations. A brief description of the equipment constructed to obtain the aforementioned data is included.

The analytical portion of this work is concerned with the following questions: what is the best final spectral density estimate given 10 statistically independent ones of varying quality and magnitude? How can the Blackman and Tukey algorithm which is used for spectral estimation in this work be improved upon? How can non-equidistant sampling reduce data processing cost? Should one try to remove common trands shared by supposedly statistically independent noise sources and, if so, what are the mathematical difficulties involved? What is a physically plausible mathematical model that can account for flicker noise and what are the mathematical implications on its statistical properties? Finally, the variance of the spectral estimate obtained through the Blackman/Tukey algorithm is analyzed in greater detail; the variance is shown to diverge for α ≥ 1 in an assumed power spectrum of k/|f|^α, unless the assumed spectrum is "truncated".