Topological nature of bound states in the radiation continuum

Bound states in the continuum (BICs) are unusual solutions of wave equations describing light or matter: they are discrete and spatially bounded, but exist at the same energy as a continuum of states which propagate to infinity. Until recently, BICs were constructed through fine-tuning parameters in the wave equation or exploiting the separability of the wave equation due to symmetry. More recently, BICs that that are both robust and not symmetry-protected (accidental) have been predicted and experimentally realized in periodic structures; the simplest such system is a periodic dielectric slab, which also has symmetry-protected BICs. Here we show that both types of BICs in such systems are vortex centers in the polarization direction of far-field radiation. The robustness of these BICs is due to the existence of conserved and quantized topological charges, defined by the number of times the polarization vectors wind around the vortex centers. Such charges can only be generated or annihilated by making large changes in the system parameters, and then only according to strict rules, which we derive and test numerically. Our results imply that laser emission based on such states will generate vector beams

Formation Mechanism of Guided Resonances and Bound States in the Continuum in Photonic Crystal Slabs

We develop a formalism, based on the mode expansion method, to describe the guided resonances and bound states in the continuum (BICs) in photonic crystal slabs with one-dimensional periodicity. This approach provides analytic insights to the formation mechanisms of these states: the guided resonances arise from the transverse Fabry-P\'erot condition, and the divergence of the resonance lifetimes at the BICs is explained by a destructive interference of radiation from different propagating components inside the slab. We show BICs at the center and on the edge of the Brillouin zone protected by symmetry, as well as BICs at generic wave vectors not protected by symmetry.Comment: 12 pages, 3 figure

Imaging of Iso-frequency Contours via Resonance-Enhanced Scattering in Near-Pristine Photonic Crystals

The iso-frequency contours of a photonic crystal are important for predicting and understanding exotic optical phenomena that are not apparent from high-symmetry band structure visualizations. Here, we demonstrate a method to directly visualize the iso-frequency contours of high-quality photonic crystal slabs that shows quantitatively good agreement with numerical results throughout the visible spectrum. Our technique relies on resonance-enhanced photon scattering from generic fabrication disorder and surface roughness, so it can be applied to general photonic and plasmonic crystals, or even quasi-crystals. We also present an analytical model of the scattering process, which explains the observation of iso-frequency contours in our technique. Furthermore, the iso-frequency contours provide information about the characteristics of the disorder and therefore serve as a feedback tool to improve fabrication processes.Comment: 8 pages, 5 figure

Language Modeling for limited-data domains

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 99-109).With the increasing focus of speech recognition and natural language processing applications on domains with limited amount of in-domain training data, enhanced system performance often relies on approaches involving model adaptation and combination. In such domains, language models are often constructed by interpolating component models trained from partially matched corpora. Instead of simple linear interpolation, we introduce a generalized linear interpolation technique that computes context-dependent mixture weights from features that correlate with the component confidence and relevance for each n-gram context. Since the n-grams from partially matched corpora may not be of equal relevance to the target domain, we propose an n-gram weighting scheme to adjust the component n-gram probabilities based on features derived from readily available corpus segmentation and metadata to de-emphasize out-of-domain n-grams. In scenarios without any matched data for a development set, we examine unsupervised and active learning techniques for tuning the interpolation and weighting parameters. Results on a lecture transcription task using the proposed generalized linear interpolation and n-gram weighting techniques yield up to a 1.4% absolute word error rate reduction over a linearly interpolated baseline language model. As more sophisticated models are only as useful as they are practical, we developed the MIT Language Modeling (MITLM) toolkit, designed for efficient iterative parameter optimization, and released it to the research community.(cont.) With a compact vector-based n-gram data structure and optimized algorithm implementations, the toolkit not only improves the running time of common tasks by up to 40x, but also enables the efficient parameter tuning for language modeling techniques that were previously deemed impractical.by Bo-June (Paul) Hsu.Ph.D