Fourier-Domain Electromagnetic Wave Theory for Layered Metamaterials of Finite Extent

The Floquet-Bloch theorem allows waves in infinite, lossless periodic media to be expressed as a sum of discrete Floquet-Bloch modes, but its validity is challenged under the realistic constraints of loss and finite extent. In this work, we mathematically reveal the existence of Floquet-Bloch modes in the electromagnetic fields sustained by lossy, finite periodic layered media using Maxwell's equations alone without invoking the Floquet-Bloch theorem. Starting with a transfer-matrix representation of the electromagnetic field in a generic layered medium, we apply Fourier transformation and a series of mathematical manipulations to isolate a term explicitly dependent on Floquet-Bloch modes. Fourier-domain representation of the electromagnetic field can be reduced into a product of the Floquet-Bloch term and two other matrix factors: one governed by reflections from the medium boundaries and another dependent on layer composition. Electromagnetic fields in any finite, lossy, layered structure can now be interpreted in the Fourier-domain by separable factors dependent on distinct physical features of the structure. The developed theory enables new methods for analyzing and communicating the electromagnetic properties of layered metamaterials.Comment: 10 pages, 3 figure

Producing a Past: Cyrus Mccormick\u27s Reaper from Heritage to History

Producing a Past explores how the false fact of Cyrus McCormick\u27s 1831 invention of the reaper came to be incorporated into the American historical cannon. From 1884 to 1932, the McCormick Harvester family and their various affiliated businesses created a useable past about their departed patriarch, Cyrus McCormick, and his role in producing civilization through advertising and the emerging historical profession. The McCormick narrative of the past which was peddled in advertising and supported in scholarship justified the family\u27s elite position in American society and its monopolistic control of the harvester industry in the face of political and popular antagonism. As a parallel story to the McCormick\u27s hegemonic use of history, this dissertation also focuses on the professionalizing historical discipline during the Progressive Era. These early historians were anxious to demonstrate their concrete value in the corporate economy as objective guardians of the past. While ethics might have prevented them from being historians for hire, their own positions as middle-class workers pre-disposed them to be receptive to both the McCormick\u27s financial influence and their historical messages

Observation of local temporal correlations in trapped quantum gases

We measure the temporal pair correlation function $g^{(2)}(\tau)$ of a trapped gas of bosons above and below the critical temperature for Bose-Einstein condensation. The measurement is performed {\it in situ} using a local, time-resolved single-atom sensitive probing technique. Third and fourth order correlation functions are also extracted. We develop a theoretical model and compare it with our experimental data, finding good quantitative agreement and highlighting the role of interactions. Our results promote temporal correlations as new observables to study the dynamics of ultracold quantum gases

Wellington : a novel method for the accurate identification of digital genomic footprints from DNase-seq data

The expression of eukaryotic genes is regulated by cis-regulatory elements such as promoters and enhancers, which bind sequence-specific DNA-binding proteins. One of the great challenges in the gene regulation field is to characterise these elements. This involves the identification of transcription factor (TF) binding sites within regulatory elements that are occupied in a defined regulatory context. Digestion with DNase and the subsequent analysis of regions protected from cleavage (DNase footprinting) has for many years been used to identify specific binding sites occupied by TFs at individual cis-elements with high resolution. This methodology has recently been adapted for high-throughput sequencing (DNase-seq). In this study, we describe an imbalance in the DNA strand-specific alignment information of DNase-seq data surrounding protein–DNA interactions that allows accurate prediction of occupied TF binding sites. Our study introduces a novel algorithm, Wellington, which considers the imbalance in this strand-specific information to efficiently identify DNA footprints. This algorithm significantly enhances specificity by reducing the proportion of false positives and requires significantly fewer predictions than previously reported methods to recapitulate an equal amount of ChIP-seq data. We also provide an open-source software package, pyDNase, which implements the Wellington algorithm to interface with DNase-seq data and expedite analyses

Millimeter-long Fiber Fabry-Perot cavities

We demonstrate fiber Fabry-Perot (FFP) cavities with concave mirrors that can be operated at cavity lengths as large as 1.5mm without significant deterioration of the finesse. This is achieved by using a laser dot machining technique to shape spherical mirrors with ultralow roughness and employing single-mode fibers with large mode area for good mode matching to the cavity. Additionally, in contrast to previous FFPs, these cavities can be used over an octave-spanning frequency range with adequate coatings. We also show directly that shape deviations caused by the fiber's index profile lead to a finesse decrease as observed in earlier attempts to build long FFP cavities, and show a way to overcome this problem