Designing coupled-resonator optical waveguide delay lines

We address the trade-offs among delay, loss, and bandwidth in the design of coupled-resonator optical waveguide (CROW) delay lines. We begin by showing the convergence of the transfer matrix, tight-binding, and time domain formalisms in the theoretical analysis of CROWs. From the analytical formalisms we obtain simple, analytical expressions for the achievable delay, loss, bandwidth, and a figure of merit to be used to compare delay line performance. We compare CROW delay lines composed of ring resonators, toroid resonators, Fabry-Perot resonators, and photonic crystal defect cavities based on recent experimental results reported in the literature

Coupled Resonator Optical Waveguides: Toward the Slowing and Storage of Light

The development of a simple, solid-state-based technology to slow the propagation of light could prove an important step in the realization of the high-bit-rate communication systems of the future. The use of coupled resonator optical waveguides (CROWs) as practical elements to slow and store light pulses is one possibility

Microring coupled-resonator optical waveguides

We use transfer matrices to obtain the dispersion relations of microring coupled-resonator optical waveguides (CROWs). We also analyze pulse propagation through finite and semi-infinite microring CROWs. The results agree well with FDTD simulations

Interactions of a Light Hypersonic Jet with a Non-Uniform Interstellar Medium

We present three dimensional simulations of the interaction of a light hypersonic jet with an inhomogeneous thermal and turbulently supported disk in an elliptical galaxy. We model the jet as a light, supersonic non-relativistic flow with parameters selected to be consistent with a relativistic jet with kinetic power just above the FR1/FR2 break. We identify four generic phases in the evolution of such a jet with the inhomogeneous interstellar medium: 1) an initial ``flood and channel'' phase, where progress is characterized by high pressure gas finding changing weak points in the ISM, flowing through channels that form and re-form over time, 2) a spherical, energy-driven bubble phase, were the bubble is larger than the disk scale, but the jet remains fully disrupted close to the nucleus, 3) a rapid, jet break--out phase the where jet breaks free of the last dense clouds, becomes collimated and pierces the spherical bubble, and 4) a classical phase, the jet propagates in a momentum-dominated fashion leading to the classical jet + cocoon + bow-shock structure. Mass transport in the simulations is investigated, and we propose a model for the morphology and component proper motions in the well-studied Compact Symmetric Object 4C31.04.Comment: 66 pages, 22 figures, PDFLaTeX, aastex macros, graphicx and amssymb packages, Accepted, to be published 2007 ApJ

Heating the bubbly gas of galaxy clusters with weak shocks and sound waves

Using hydrodynamic simulations and a technique to extract the rotational component of the velocity field, we show how bubbles of relativistic gas inflated by AGN jets in galaxy clusters act as a catalyst, transforming the energy carried by sound and shock waves to heat. The energy is stored in a vortex field around the bubbles which can subsequently be dissipated. The efficiency of this process is set mainly by the fraction of the cluster volume filled by (sub-)kpc scale filaments and bubbles of relativistic plasma.Comment: Accepted for publication in ApJ Letters after minor wording changes, 4 figures, 4 page

The importance of radio sources in accounting for the highest mass black holes

The most massive black holes lie in the most massive elliptical galaxies, and at low-z all radio-loud AGNs lie in giant ellipticals. This strongly suggests a link between radio-loudness and black hole mass. We argue that the increase in the radio-loud fraction with AGN luminosity in optically-selected quasar samples is consistent with this picture. We also use the ratio of black holes today to quasars at z~2 to conclude that the most bolometrically-luminous AGN, either radio-loud or radio quiet, are constrained to have lifetimes <~10^8 yr. If radio sources are associated with black holes of >~10^9 M_sun at all redshifts, then the same lifetime constraint applies to all radio sources with luminosities above L_5GHz ~ 10^24 W/Hz/sr.Comment: 6 pages, 2 figures. To appear in "Lifecycles of Radio Galaxies", ed J. Biretta et al., New Astronomy Review

Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature

We prove convergence results for expanding curvature flows in the Euclidean and hyperbolic space. The flow speeds have the form $F^{-p}$, where $p>1$ and $F$ is a positive, strictly monotone and 1-homogeneous curvature function. In particular this class includes the mean curvature $F=H$. We prove that a certain initial pinching condition is preserved and the properly rescaled hypersurfaces converge smoothly to the unit sphere. We show that an example due to Andrews-McCoy-Zheng can be used to construct strictly convex initial hypersurfaces, for which the inverse mean curvature flow to the power $p>1$ loses convexity, justifying the necessity to impose a certain pinching condition on the initial hypersurface.Comment: 18 pages. We included an example for the loss of convexity and pinching. In the third version we dropped the concavity assumption on F. Comments are welcom

A General Formulation of the Source Confusion Statistics and Application to Infrared Galaxy Surveys

Source confusion has been a long-standing problem in the astronomical history. In the previous formulation, sources are assumed to be distributed homogeneously on the sky. This fundamental assumption is not realistic in many applications. In this work, by making use of the point field theory, we derive general analytic formulae for the confusion problems with arbitrary distribution and correlation functions. As a typical example, we apply these new formulae to the source confusion of infrared galaxies. We first calculate the confusion statistics for power-law galaxy number counts as a test case. When the slope of differential number counts, \gamma, is steep, the confusion limits becomes much brighter and the probability distribution function (PDF) of the fluctuation field is strongly distorted. Then we estimate the PDF and confusion limits based on the realistic number count model for infrared galaxies. The gradual flattening of the slope of the source counts makes the clustering effect rather mild. Clustering effects result in an increase of the limiting flux density with \sim 10%. In this case, the peak probability of the PDF decreases up to \sim 15% and its tail becomes heavier.Comment: ApJ in press, 21 pages, 9 figures, using aastex.cls, emulateapj5.sty. Abstract abridge

Jet propagation and the asymmetries of CSS radio sources

As Compact Steep Spectrum radio sources have been shown to be more asymmetrical than larger sources of similar powers, there is a high probability that they interact with an asymmetric medium in the central regions of the host elliptical galaxy. We consider a simple analytical model of the propagation of radio jets through a reasonable asymmetric environment and show that they can yield the range of arm-length and luminosity asymmetries that have been observed. We then generalize this to allow for the effects of orientation, and quantify the substantial enhancements of the asymmetries that can be produced in this fashion. We present two-dimensional and three-dimensional simulations of jets propagating through multi-phase media and note that the results from the simulations are also broadly consistent with the observations.Comment: 11 pages, 6 figures, 1 table, accepted for publication in A&