Optical Resonator Analog of a Two-Dimensional Topological Insulator

A lattice of optical ring resonators can exhibit a topological insulator phase, with the role of spin played by the direction of propagation of light within each ring. Unlike the system studied by Hafezi et al., topological protection is achieved without fine-tuning the inter-resonator couplings, which are given the same periodicity as the underlying lattice. The topological insulator phase occurs for strong couplings, when the tight-binding method is inapplicable. Using the transfer matrix method, we derive the bandstructure and phase diagram, and demonstrate the existence of robust edge states. When gain and loss are introduced, the system functions as a diode for coupled resonator modes.Comment: 10 pages, 9 figure

NeIII/OII as an oxygen abundance indicator in the HII regions and HII galaxies

To calibrate the relationship between Ne3O2 (Ne3O2 = log(\neiii$\lambda3869$/\oii$\lambda3727$)) and oxygen abundances, we present a sample of $\sim$3000 \hii galaxies from the Sloan Digital Sky Survey (SDSS) data release four. They are associated with a sample from the literature intended to enlarge the oxygen abundance region. We calculated the electron temperatures ($T_e$) of 210 galaxies in the SDSS sample with the direct method, and $T_e$ of the other 2960 galaxies in SDSS sample calculated with an empirical method. Then, we use a linear least-square fitting to calibrate the Ne3O2 oxygen abundance indicator. It is found that the Ne3O2 estimator follows a linear relation with \zoh\ that holds for the whole abundance range covered by the sample, from approximately 7.0 to 9.0. The best linear relationship between the Ne3O2 and the oxygen abundance is calibrated. The dispersion between oxygen abundance and Ne3O2 index in the metal rich galaxies may come partly from the moderate depletion of oxygen onto grains. The $Ne3O2$ method has the virtue of being single-valued and not affected by internal reddening. As a result, the $Ne3O2$ method can be a good metallicity indicator in the \hii regions and \hii galaxies, especially in high-redshift galaxies.Comment: 7 pages, 6 figures. A&A accepte

Quantisation of 2D-gravity with Weyl and area-preserving diffeomorphism invariances

The constraint structure of 2D-gravity with the Weyl and area-preserving diffeomorphism invariances is analysed in the ADM formulation. It is found that when the area-preserving diffeomorphism constraints are kept, the usual conformal gauge does not exist, whereas there is the possibility to choose the so-called ``quasi-light-cone'' gauge, in which besides the area-preserving diffeomorphism invariance, the reduced Lagrangian also possesses the SL(2,R) residual symmetry. The string-like approach is applied to quantise this model, but a fictitious non-zero central charge in the Virasoro algebra appears. When a set of gauge-independent SL(2,R) current-like fields is introduced instead of the string-like variables, a consistent quantum theory is obtained.Comment: 14 pages, Latex fil