Near-infrared optical properties and proposed phase-change usefulness of transition metal disulfides

The development of photonic integrated circuits would benefit from a wider selection of materials that can strongly-control near-infrared (NIR) light. Transition metal dichalcogenides (TMDs) have been explored extensively for visible spectrum opto-electronics, but the NIR properties of these layered materials have been less-studied. The measurement of optical constants is the foremost step to qualify TMDs for use in NIR photonics. Here we measure the complex optical constants for select sulfide TMDs (bulk crystals of MoS2, TiS2 and ZrS2) via spectroscopic ellipsometry in the visible-to-NIR range. Through Mueller matrix measurements and generalized ellipsometry, we explicitly measure the direction of the ordinary optical axis. We support our measurements with density functional theory (DFT) calculations, which agree with our measurements and predict giant birefringence. We further propose that TMDs could find use as photonic phase-change materials, by designing alloys that are thermodynamically adjacent to phase boundaries between competing crystal structures, to realize martensitic (i.e. displacive, order-order) switching.Comment: supplementary at end of document. 6 main figure

Defect Perturbations in Landau-Ginzburg Models

Perturbations of B-type defects in Landau-Ginzburg models are considered. In particular, the effect of perturbations of defects on their fusion is analyzed in the framework of matrix factorizations. As an application, it is discussed how fusion with perturbed defects induces perturbations on boundary conditions. It is shown that in some classes of models all boundary perturbations can be obtained in this way. Moreover, a universal class of perturbed defects is constructed, whose fusion under certain conditions obey braid relations. The functors obtained by fusing these defects with boundary conditions are twist functors as introduced in the work of Seidel and Thomas.Comment: 46 page

Homotopy Theory of Labelled Symmetric Precubical Sets

This paper is the third paper of a series devoted to higher dimensional transition systems. The preceding paper proved the existence of a left determined model structure on the category of cubical transition systems. In this sequel, it is proved that there exists a model category of labelled symmetric precubical sets which is Quillen equivalent to the Bousfield localization of this left determined model category by the cubification functor. The realization functor from labelled symmetric precubical sets to cubical transition systems which was introduced in the first paper of this series is used to establish this Quillen equivalence. However, it is not a left Quillen functor. It is only a left adjoint. It is proved that the two model categories are related to each other by a zig-zag of Quillen equivalences of length two. The middle model category is still the model category of cubical transition systems, but with an additional family of generating cofibrations. The weak equivalences are closely related to bisimulation. Similar results are obtained by restricting the constructions to the labelled symmetric precubical sets satisfying the HDA paradigm.Comment: 31 pages ; final versio

Multi-Dimensional Astrophysical Structural and Dynamical Analysis I. Development of a Nonlinear Finite Element Approach

A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional spacetimes, etc.). The technique employed is the Finite Element Method (FEM), commonly used to solve engineering structural problems. The approach developed herein has the following key features: 1. The computational mesh can extend into the time dimension, as well as space, perhaps only a few cells, or throughout spacetime. 2. Virtually all equations describing the astrophysics of continuous media, including the field equations, can be written in a compact form similar to that routinely solved by most engineering finite element codes. 3. The transformations that occur naturally in the four-dimensional FEM possess both coordinate and boost features, such that (a) although the computational mesh may have a complex, non-analytic, curvilinear structure, the physical equations still can be written in a simple coordinate system independent of the mesh geometry. (b) if the mesh has a complex flow velocity with respect to coordinate space, the transformations will form the proper arbitrary Lagrangian- Eulerian advective derivatives automatically. 4. The complex difference equations on the arbitrary curvilinear grid are generated automatically from encoded differential equations. This first paper concentrates on developing a robust and widely-applicable set of techniques using the nonlinear FEM and presents some examples.Comment: 28 pages, 9 figures; added integral boundary conditions, allowing very rapidly-rotating stars; accepted for publication in Ap.

Birefringence Measurements on Crystalline Silicon

Crystalline silicon has been proposed as a new test mass material in third generation gravitational wave detectors such as the Einstein Telescope (ET). Birefringence can reduce the interferometric contrast and can produce dynamical disturbances in interferometers. In this work we use the method of polarisation-dependent resonance frequency analysis of Fabry-Perot-cavities containing silicon as a birefringent medium. Our measurements show a birefringence of silicon along the (111) axis of the order of $\Delta\, n \approx 10^{-7}$ at a laser wavelength of 1550nm and room temperature. A model is presented that explains the results of different settings of our measurements as a superposition of elastic strains caused by external stresses in the sample and plastic strains possibly generated during the production process. An application of our theory on the proposed ET test mass geometry suggests no critical effect on birefringence due to elastic strains.Comment: 19 pages, 6 figures, 2 table

Effects of Nanoparticle Geometry and Size Distribution on Diffusion Impedance of Battery Electrodes

The short diffusion lengths in insertion battery nanoparticles render the capacitive behavior of bounded diffusion, which is rarely observable with conventional larger particles, now accessible to impedance measurements. Coupled with improved geometrical characterization, this presents an opportunity to measure solid diffusion more accurately than the traditional approach of fitting Warburg circuit elements, by properly taking into account the particle geometry and size distribution. We revisit bounded diffusion impedance models and incorporate them into an overall impedance model for different electrode configurations. The theoretical models are then applied to experimental data of a silicon nanowire electrode to show the effects of including the actual nanowire geometry and radius distribution in interpreting the impedance data. From these results, we show that it is essential to account for the particle shape and size distribution to correctly interpret impedance data for battery electrodes. Conversely, it is also possible to solve the inverse problem and use the theoretical "impedance image" to infer the nanoparticle shape and/or size distribution, in some cases, more accurately than by direct image analysis. This capability could be useful, for example, in detecting battery degradation in situ by simple electrical measurements, without the need for any imaging.Comment: 30 page