Oscillatory crossover from two-dimensional to three-dimensional topological insulators

In the development of topological photonics, achieving three-dimensional topological insulators is of notable interest since it enables the exploration of new topological physics with photons and promises novel photonic devices that are robust against disorders in three dimensions. Previous theoretical proposals toward three-dimensional topological insulators use complex geometries that are challenging to implement. On the basis of the concept of synthetic dimension, we show that a two-dimensional array of ring resonators, which was previously demonstrated to exhibit a two-dimensional topological insulator phase, automatically becomes a three-dimensional topological insulator when the frequency dimension is taken into account. Moreover, by modulating a few of the resonators, a screw dislocation along the frequency axis can be created, which provides robust one-way transport of photons along the frequency axis. Demonstrating the physics of screw dislocation in a topological system has been a substantial challenge in solid-state systems. Our work indicates that the physics of three-dimensional topological insulators can be explored in standard integrated photonic platforms, leading to opportunities for novel devices that control the frequency of light.

Download Full-text

High Resolution Microscopy of Multi-Layered Biological Crystals

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010005319x ◽

1982 ◽

Vol 40 ◽

pp. 80-83

Author(s):

H.A. Cohen ◽

T.W. Jeng ◽

W. Chiu

Keyword(s):

High Resolution ◽

Low Dose ◽

Three Dimensional ◽

Data Interpretation ◽

Two Dimensional ◽

Biological Objects ◽

Density Maps ◽

Density Map ◽

Complex Crystal ◽

High Resolution Microscopy

This tutorial will discuss the methodology of low dose electron diffraction and imaging of crystalline biological objects, the problems of data interpretation for two-dimensional projected density maps of glucose embedded protein crystals, the factors to be considered in combining tilt data from three-dimensional crystals, and finally, the prospects of achieving a high resolution three-dimensional density map of a biological crystal. This methodology will be illustrated using two proteins under investigation in our laboratory, the T4 DNA helix destabilizing protein gp32*I and the crotoxin complex crystal.

Download Full-text

Instrumentation For Quantitative Microscopy

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100078584 ◽

1977 ◽

Vol 35 ◽

pp. 206-209

Author(s):

B. Ralph ◽

A.R. Jones

Keyword(s):

Volume Fraction ◽

Three Dimensional ◽

Two Dimensional ◽

Automatic Data ◽

Phase Volume Fraction ◽

Statistical Confidence ◽

Resultant Data ◽

Automatic Data Collection ◽

Third Dimension ◽

Evolution Of Microstructure

In all fields of microscopy there is an increasing interest in the quantification of microstructure. This interest may stem from a desire to establish quality control parameters or may have a more fundamental requirement involving the derivation of parameters which partially or completely define the three dimensional nature of the microstructure. This latter categorey of study may arise from an interest in the evolution of microstructure or from a desire to generate detailed property/microstructure relationships. In the more fundamental studies some convolution of two-dimensional data into the third dimension (stereological analysis) will be necessary.In some cases the two-dimensional data may be acquired relatively easily without recourse to automatic data collection and further, it may prove possible to perform the data reduction and analysis relatively easily. In such cases the only recourse to machines may well be in establishing the statistical confidence of the resultant data. Such relatively straightforward studies tend to result from acquiring data on the whole assemblage of features making up the microstructure. In this field data mode, when parameters such as phase volume fraction, mean size etc. are sought, the main case for resorting to automation is in order to perform repetitive analyses since each analysis is relatively easily performed.

Download Full-text

A linearity test for thick specimens imaged by HVEM over a 180° angular range

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100087070 ◽

1991 ◽

Vol 49 ◽

pp. 552-553

Author(s):

Yu Liu

Keyword(s):

Phase Contrast ◽

Three Dimensional ◽

Angular Range ◽

Two Dimensional ◽

Back Projection ◽

Line Integral ◽

Exponential Law ◽

Transmission Electron ◽

Absorption Law ◽

Linearity Test

The image obtained in a transmission electron microscope is the two-dimensional projection of a three-dimensional (3D) object. The 3D reconstruction of the object can be calculated from a series of projections by back-projection, but this algorithm assumes that the image is linearly related to a line integral of the object function. However, there are two kinds of contrast in electron microscopy, scattering and phase contrast, of which only the latter is linear with the optical density (OD) in the micrograph. Therefore the OD can be used as a measure of the projection only for thin specimens where phase contrast dominates the image. For thick specimens, where scattering contrast predominates, an exponential absorption law holds, and a logarithm of OD must be used. However, for large thicknesses, the simple exponential law might break down due to multiple and inelastic scattering.

Download Full-text