Retrieval of interatomic separations of molecules from laser-induced high-order harmonic spectra

We illustrate an iterative method for retrieving the internuclear separations of N$_2$, O$_2$ and CO$_2$ molecules using the high-order harmonics generated from these molecules by intense infrared laser pulses. We show that accurate results can be retrieved with a small set of harmonics and with one or few alignment angles of the molecules. For linear molecules the internuclear separations can also be retrieved from harmonics generated using isotropically distributed molecules. By extracting the transition dipole moment from the high-order harmonic spectra, we further demonstrated that it is preferable to retrieve the interatomic separation iteratively by fitting the extracted dipole moment. Our results show that time-resolved chemical imaging of molecules using infrared laser pulses with femtosecond temporal resolutions is possible.Comment: 14 pages, 9 figure

Methodology for testing high-performance data converters using low-accuracy instruments

There has been explosive growth in the consumer electronics market during the last decade. As the IC industry is shifting from PC-centric to consumer electronics-centric, digital technologies are no longer solving all the problems. Electronic devices integrating mixed-signal, RF and other non-purely digital functions are becoming new challenges to the industry. When digital testing has been studied for long time, testing of analog and mixed-signal circuits is still in its development stage. Existing solutions have two major problems. First, high-performance mixed-signal test equipments are expensive and it is difficult to integrate their functions on chip. Second, it is challenging to improve the test capability of existing methods to keep up with the fast-evolving performance of mixed-signal products demanded on the market. The International Technology Roadmap for Semiconductors identified mixed-signal testing as one of the most daunting system-on-a-chip challenges;My works have been focused on developing new strategies for testing the analog-to-digital converter (ADC) and digital-to-analog converter (DAC). Different from conventional methods that require test instruments to have better performance than the device under test, our algorithms allow the use of medium and low-accuracy instruments in testing. Therefore, we can provide practical and accurate test solutions for high-performance data converters. Meanwhile, the test cost is dramatically reduced because of the low price of such test instruments. These algorithms have the potential for built-in self-test and can be generalized to other mixed-signal circuitries. When incorporated with self-calibration, these algorithms can enable new design techniques for mixed-signal integrated circuits. Following contents are covered in the dissertation:;(1) A general stimulus error identification and removal (SEIR) algorithm that can test high-resolution ADCs using two low-linearity signals with a constant offset in between; (2) A center-symmetric interleaving (CSI) strategy for generating test signals to be used with the SEIR algorithm; (3) An architecture-based test algorithm for high-performance pipelined or cyclic ADCs using a single nonlinear stimulus; (4) Using Kalman Filter to improve the efficiency of ADC testing; and (5) A testing algorithm for high-speed high-resolution DACs using low-resolution ADCs with dithering

Auto-Encoding Sequential Monte Carlo

We build on auto-encoding sequential Monte Carlo (AESMC): a method for model and proposal learning based on maximizing the lower bound to the log marginal likelihood in a broad family of structured probabilistic models. Our approach relies on the efficiency of sequential Monte Carlo (SMC) for performing inference in structured probabilistic models and the flexibility of deep neural networks to model complex conditional probability distributions. We develop additional theoretical insights and introduce a new training procedure which improves both model and proposal learning. We demonstrate that our approach provides a fast, easy-to-implement and scalable means for simultaneous model learning and proposal adaptation in deep generative models

Generation of isolated attosecond pulses in the far field by spatial filtering with an intense few-cycle mid-infrared laser

We report theoretical calculations of high-order harmonic generation (HHG) of Xe with the inclusion of multi-electron effects and macroscopic propagation of the fundamental and harmonic fields in an ionizing medium. By using the time-frequency analysis we show that the reshaping of the fundamental laser field is responsible for the continuum structure in the HHG spectra. We further suggest a method for obtaining an isolated attosecond pulse (IAP) by using a filter centered on axis to select the harmonics in the far field with different divergence. We also discuss the carrier-envelope-phase dependence of an IAP and the possibility to optimize the yield of the IAP. With the intense few-cycle mid-infrared lasers, this offers a possible method for generating isolated attosecond pulses.Comment: 8 figure

Hybridizing two-step growth mixture model and exploratory factor analysis to examine heterogeneity in nonlinear trajectories

Empirical researchers are usually interested in investigating the impacts of baseline covariates have when uncovering sample heterogeneity and separating samples into more homogeneous groups. However, a considerable number of studies in the structural equation modeling (SEM) framework usually start with vague hypotheses in terms of heterogeneity and possible reasons. It suggests that (1) the determination and specification of a proper model with covariates is not straightforward, and (2) the exploration process may be computational intensive given that a model in the SEM framework is usually complicated and the pool of candidate covariates is usually huge in the psychological and educational domain where the SEM framework is widely employed. Following \citet{Bakk2017two}, this article presents a two-step growth mixture model (GMM) that examines the relationship between latent classes of nonlinear trajectories and baseline characteristics. Our simulation studies demonstrate that the proposed model is capable of clustering the nonlinear change patterns, and estimating the parameters of interest unbiasedly, precisely, as well as exhibiting appropriate confidence interval coverage. Considering the pool of candidate covariates is usually huge and highly correlated, this study also proposes implementing exploratory factor analysis (EFA) to reduce the dimension of covariate space. We illustrate how to use the hybrid method, the two-step GMM and EFA, to efficiently explore the heterogeneity of nonlinear trajectories of longitudinal mathematics achievement data.Comment: Draft version 1.6, 08/08/2020. This paper has not been peer reviewed. Please do not copy or cite without author's permissio