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.

Random propagation in complex systems : nonlinear matrix recursions and epidemic spread

This dissertation studies long-term behavior of random Riccati recursions and mathematical epidemic model. Riccati recursions are derived from Kalman filtering. The error covariance matrix of Kalman filtering satisfies Riccati recursions. Convergence condition of time-invariant Riccati recursions are well-studied by researchers. We focus on time-varying case, and assume that regressor matrix is random and identical and independently distributed according to given distribution whose probability distribution function is continuous, supported on whole space, and decaying faster than any polynomial. We study the geometric convergence of the probability distribution. We also study the global dynamics of the epidemic spread over complex networks for various models. For instance, in the discrete-time Markov chain model, each node is either healthy or infected at any given time. In this setting, the number of the state increases exponentially as the size of the network increases. The Markov chain has a unique stationary distribution where all the nodes are healthy with probability 1. Since the probability distribution of Markov chain defined on finite state converges to the stationary distribution, this Markov chain model concludes that epidemic disease dies out after long enough time. To analyze the Markov chain model, we study nonlinear epidemic model whose state at any given time is the vector obtained from the marginal probability of infection of each node in the network at that time. Convergence to the origin in the epidemic map implies the extinction of epidemics. The nonlinear model is upper-bounded by linearizing the model at the origin. As a result, the origin is the globally stable unique fixed point of the nonlinear model if the linear upper bound is stable. The nonlinear model has a second fixed point when the linear upper bound is unstable. We work on stability analysis of the second fixed point for both discrete-time and continuous-time models. Returning back to the Markov chain model, we claim that the stability of linear upper bound for nonlinear model is strongly related with the extinction time of the Markov chain. We show that stable linear upper bound is sufficient condition of fast extinction and the probability of survival is bounded by nonlinear epidemic map.

Studies in nuclear reactor dynamics : I. The accuracy of point kinetics. II. The effect of delayed neutrons on the spectrum of the group-diffusion operator

This thesis is a theoretical work on the space-time dynamic behavior of a nuclear reactor without feedback. Diffusion theory with G-energy groups is used.

In the first part the accuracy of the point kinetics (lumped-parameter description) model is examined. The fundamental approximation of this model is the splitting of the neutron density into a product of a known function of space and an unknown function of time; then the properties of the system can be averaged in space through the use of appropriate weighting functions; as a result a set of ordinary differential equations is obtained for the description of time behavior. It is clear that changes of the shape of the neutron-density distribution due to space-dependent perturbations are neglected. This results to an error in the eigenvalues and it is to this error that bounds are derived. This is done by using the method of weighted residuals to reduce the original eigenvalue problem to that of a real asymmetric matrix. Then Gershgorin-type theorems .are used to find discs in the complex plane in which the eigenvalues are contained. The radii of the discs depend on the perturbation in a simple manner.

In the second part the effect of delayed neutrons on the eigenvalues of the group-diffusion operator is examined. The delayed neutrons cause a shifting of the prompt-neutron eigenvalue s and the appearance of the delayed eigenvalues. Using a simple perturbation method this shifting is calculated and the delayed eigenvalues are predicted with good accuracy.

Analyses of planetary atmospheres across the spectrum : from Titan to exoplanets

Planetary atmospheres exist in a seemingly endless variety of physical and chemical environments. There are an equally diverse number of methods by which we can study and characterize atmospheric composition. In order to better understand the fundamental chemistry and physical processes underlying all planetary atmospheres, my research of the past four years has focused on two distinct topics. First, I focused on the data analysis and spectral retrieval of observations obtained by the Ultraviolet Imaging Spectrograph (UVIS) instrument onboard the Cassini spacecraft while in orbit around Saturn. These observations consisted of stellar occultation measurements of Titan's upper atmosphere, probing the chemical composition in the region 300 to 1500 km above Titan's surface. I examined the relative abundances of Titan's two most prevalent chemical species, nitrogen and methane. I also focused on the aerosols that are formed through chemistry involving these two major species, and determined the vertical profiles of aerosol particles as a function of time and latitude. Moving beyond our own solar system, my second topic of investigation involved analysis of infra-red light curves from the Spitzer space telescope, obtained as it measured the light from stars hosting planets of their own. I focused on both transit and eclipse modeling during Spitzer data reduction and analysis. In my initial work, I utilized the data to search for transits of planets a few Earth masses in size. In more recent research, I analyzed secondary eclipses of three exoplanets and constrained the range of possible temperatures and compositions of their atmospheres.

Studies of response to earthquake ground motion

A study is made of the accuracy of electronic digital computer calculations of ground displacement and response spectra from strong-motion earthquake accelerograms. This involves an investigation of methods of the preparatory reduction of accelerograms into a form useful for the digital computation and of the accuracy of subsequent digital calculations. Various checks are made for both the ground displacement and response spectra results, and it is concluded that the main errors are those involved in digitizing the original record. Differences resulting from various investigators digitizing the same experimental record may become as large as 100% of the maximum computed ground displacements. The spread of the results of ground displacement calculations is greater than that of the response spectra calculations. Standardized methods of adjustment and calculation are recommended, to minimize such errors.

Studies are made of the spread of response spectral values about their mean. The distribution is investigated experimentally by Monte Carlo techniques using an electric analog system with white noise excitation, and histograms are presented indicating the dependence of the distribution on the damping and period of the structure. Approximate distributions are obtained analytically by confirming and extending existing results with accurate digital computer calculations. A comparison of the experimental and analytical approaches indicates good agreement for low damping values where the approximations are valid. A family of distribution curves to be used in conjunction with existing average spectra is presented. The combination of analog and digital computations used with Monte Carlo techniques is a promising approach to the statistical problems of earthquake engineering.

Methods of analysis of very small earthquake ground motion records obtained simultaneously at different sites are discussed. The advantages of Fourier spectrum analysis for certain types of studies and methods of calculation of Fourier spectra are presented. The digitizing and analysis of several earthquake records is described and checks are made of the dependence of results on digitizing procedure, earthquake duration and integration step length. Possible dangers of a direct ratio comparison of Fourier spectra curves are pointed out and the necessity for some type of smoothing procedure before comparison is established. A standard method of analysis for the study of comparative ground motion at different sites is recommended.

Photonic and Device Design Principles for Ultrahigh-Efficiency (>50%), Spectrum-Splitting Photovoltaics

The sun has the potential to power the Earth's total energy needs, but electricity from solar power still constitutes an extremely small fraction of our power generation because of its high cost relative to traditional energy sources. Therefore, the cost of solar must be reduced to realize a more sustainable future. This can be achieved by significantly increasing the efficiency of modules that convert solar radiation to electricity. In this thesis, we consider several strategies to improve the device and photonic design of solar modules to achieve record, ultrahigh (> 50%) solar module efficiencies. First, we investigate the potential of a new passivation treatment, trioctylphosphine sulfide, to increase the performance of small GaAs solar cells for cheaper and more durable modules. We show that small cells (mm2), which currently have a significant efficiency decrease (~ 5%) compared to larger cells (cm2) because small cells have a higher fraction of recombination-active surface from the sidewalls, can achieve significantly higher efficiencies with effective passivation of the sidewalls. We experimentally validate the passivation qualities of treatment by trioctylphosphine sulfide (TOP:S) through four independent studies and show that this facile treatment can enable efficient small devices. Then, we discuss our efforts toward the design and prototyping of a spectrum-splitting module that employs optical elements to divide the incident spectrum into different color bands, which allows for higher efficiencies than traditional methods. We present a design, the polyhedral specular reflector, that has the potential for > 50% module efficiencies even with realistic losses from combined optics, cell, and electrical models. Prototyping efforts of one of these designs using glass concentrators yields an optical module whose combined spectrum-splitting and concentration should correspond to a record module efficiency of 42%. Finally, we consider how the manipulation of radiatively emitted photons from subcells in multijunction architectures can be used to achieve even higher efficiencies than previously thought, inspiring both optimization of incident and radiatively emitted photons for future high efficiency designs. In this thesis work, we explore novel device and photonic designs that represent a significant departure from current solar cell manufacturing techniques and ultimately show the potential for much higher solar cell efficiencies.