Travelling waves in hyperbolic chemotaxis equations

Mathematical models of bacterial populations are often written as systems of partial differential equations for the densities of bacteria and concentrations of extracellular (signal) chemicals. This approach has been employed since the seminal work of Keller and Segel in the 1970s [Keller and Segel, J. Theor. Biol., 1971]. The system has been shown to permit travelling wave solutions which correspond to travelling band formation in bacterial colonies, yet only under specific criteria, such as a singularity in the chemotactic sensitivity function as the signal approaches zero. Such a singularity generates infinite macroscopic velocities which are biologically unrealistic. In this paper, we formulate a model that takes into consideration relevant details of the intracellular processes while avoiding the singularity in the chemotactic sensitivity. We prove the global existence of solutions and then show the existence of travelling wave solutions both numerically and analytically

An optical fiber-taper probe for wafer-scale microphotonic device characterization

A small depression is created in a straight optical fiber taper to form a local probe suitable for studying closely spaced, planar microphotonic devices. The tension of the "dimpled" taper controls the probe-sample interaction length and the level of noise present during coupling measurements. Practical demonstrations with high-Q silicon microcavities include testing a dense array of undercut microdisks (maximum Q = 3.3x10^6) and a planar microring (Q = 4.8x10^6).Comment: 8 pages, 5 figures, for high-res version see http://copilot.caltech.edu/publications/index.ht

Adiabatic self-tuning in a silicon microdisk optical resonator

We demonstrate a method for adiabatically self-tuning a silicon microdisk resonator. This mechanism is not only able to sensitively probe the fast nonlinear cavity dynamics, but also provides various optical functionalities like pulse compression, shaping, and tunable time delay

Lasers incorporating 2D photonic bandgap mirrors

Semiconductor lasers incorporating a 2D photonic lattice as a one end mirror in a Fabry-Perot cavity are demonstrated. The photonic lattice is a 2D hexagonal close-packed array with a lattice constant of 220 nm. Pulsed threshold currents of 110 mA were observed from a 180 μm laser

Two-dimensional photonic band-gap mirrors at 850 and 980 nm

Summary form only given. Photonic band-gap (PBG) crystals can be fabricated in semiconductor devices through the etching of patterns of holes in the device, resulting in a periodic dielectric structure. One of the more practical uses of photonic crystals in optoelectronic devices is for thin, high-reflectivity mirrors. The use of hexagonal arrays of etched circular holes results in a 2-D photonic band-gap mirror that can be tuned to a specific wavelength by varying the hole radius and the lattice spacing. 2-D mirror characterization is performed by evaluating the light emission from an active waveguide

Single quantum dot spectroscopy using a fiber taper waveguide near-field optic

Photoluminescence spectroscopy of single InAs quantum dots at cryogenic temperatures (~14 K) is performed using a micron-scale optical fiber taper waveguide as a near-field optic. The measured collection efficiency of quantum dot spontaneous emission into the fundamental guided mode of the fiber taper is estimated at 0.1%, and spatially-resolved measurements with ~600 nm resolution are obtained by varying the taper position with respect to the sample and using the fiber taper for both the pump and collection channels.Comment: 4 pages, 3 figure

A proposal for highly tunable optical parametric oscillation in silicon micro-resonators

We propose a novel scheme for continuous-wave pumped optical parametric oscillation (OPO) inside silicon micro-resonators. The proposed scheme not only requires a relative low lasing threshold, but also exhibits extremely broad tunability extending from the telecom band to mid infrared

Surface Encapsulation for Low-Loss Silicon Photonics

Encapsulation layers are explored for passivating the surfaces of silicon to reduce optical absorption in the 1500-nm wavelength band. Surface-sensitive test structures consisting of microdisk resonators are fabricated for this purpose. Based on previous work in silicon photovoltaics, coatings of SiNx and SiO2 are applied under varying deposition and annealing conditions. A short dry thermal oxidation followed by a long high-temperature N2 anneal is found to be most effective at long-term encapsulation and reduction of interface absorption. Minimization of the optical loss is attributed to simultaneous reduction in sub-bandgap silicon surface states and hydrogen in the capping material.Comment: 4 pages, 3 figure

On the dynamic tensile strength of Zirconium

Despite its fundamental nature, the process of dynamic tensile failure (spall) is poorly understood. Spall initiation via cracks, voids, etc, before subsequent coalesce, is known to be highly microstructure-dependant. In particular, the availability of slip planes and other methods of plastic deformation controls the onset (or lack thereof) of spall. While studies have been undertaken into the spall response of BCC and FCC materials, less attention has paid to the spall response of highly anisotropic HCP materials. Here the dynamic behaviour of zirconium is investigated via plate-impact experiments, with the aim of building on an ongoing in-house body of work investigating these highly complex materials. In particular, in this paper the effect of impact stress on spall in a commercially sourced Zr rod is considered, with apparent strain-rate softening highlighted

Superradiance for atoms trapped along a photonic crystal waveguide

We report observations of superradiance for atoms trapped in the near field of a photonic crystal waveguide (PCW). By fabricating the PCW with a band edge near the D$_1$ transition of atomic cesium, strong interaction is achieved between trapped atoms and guided-mode photons. Following short-pulse excitation, we record the decay of guided-mode emission and find a superradiant emission rate scaling as $\bar{\Gamma}_{\rm SR}\propto\bar{N}\cdot\Gamma_{\rm 1D}$ for average atom number $0.19 \lesssim \bar{N} \lesssim 2.6$ atoms, where $\Gamma_{\rm 1D}/\Gamma_0 =1.1\pm0.1$ is the peak single-atom radiative decay rate into the PCW guided mode and $\Gamma_{0}$ is the Einstein-$A$ coefficient for free space. These advances provide new tools for investigations of photon-mediated atom-atom interactions in the many-body regime.Comment: 11 pages, 10 figure