Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics

The ability to achieve near lossless coupling between a waveguide and a resonator is fundamental to many quantum-optical studies as well as to practical applications of such structures. The nature of loss at the junction is described by a figure of merit called ideality. It is shown here that under appropriate conditions ideality in excess of 99.97% is possible using fiber-taper coupling to high-Q silica microspheres. To verify this level of coupling, a technique is introduced that can both measure ideality over a range of coupling strengths and provide a practical diagnostic of parasitic coupling within the fiber-taper-waveguide junction

Photonic Crystal Nanocavities and Waveguides

Fabrication of optical structures has evolved to a precision which allows us to control light within etched nanostructures. Nano-optic cavities can be used for efficient and flexible concentration of light in small volumes, and control over both emission wavelength and frequency. Conversely, if a periodic pattern is defined in the top semitransparent metal layer by lithography, it is possible to efficiently couple out the light out of a semiconductor and to simultaneously enhance the spontaneous emission rate. Here we demonstrate the use of photonic crystals for efficient light localization and light extraction

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

Photonic Crystals and their Applications to Efficient Light Emitters

When combined with high index contrast slabs in which light can be efficiently guided, microfabricated two-dimensional photonic bandgap mirrors provide us with the geometries needed to confine and concentrate light into extremely small volumes and to obtain very high field intensities. Fabrication of optical structures has now evolved to a precision which allows us to control light within such etched nanostructures. Sub-wavelength nano-optic cavities can be used for efficient and flexible control over both emission wavelength and frequency, and nanofabricated optical waveguides can be used for efficient coupling of light between devices. The reduction of the size of optical components leads to their integration in large numbers and the possibility to combine different functionalities on a single chip. We show uses of such crystals in functional nonlinear optical devices, such as lasers, modulators, add/drop filters, polarizers and detectors

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

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

A user's guide to PDE models for chemotaxis

Mathematical modelling of chemotaxis (the movement of biological cells or organisms in response to chemical gradients) has developed into a large and diverse discipline, whose aspects include its mechanistic basis, the modelling of specific systems and the mathematical behaviour of the underlying equations. The Keller-Segel model of chemotaxis (Keller and Segel in J Theor Biol 26:399-415, 1970; 30:225- 234, 1971) has provided a cornerstone for much of this work, its success being a consequence of its intuitive simplicity, analytical tractability and capacity to replicate key behaviour of chemotactic populations. One such property, the ability to display "auto-aggregation", has led to its prominence as a mechanism for self-organisation of biological systems. This phenomenon has been shown to lead to finite-time blow-up under certain formulations of the model, and a large body of work has been devoted to determining when blow-up occurs or whether globally existing solutions exist. In this paper, we explore in detail a number of variations of the original Keller-Segel model. We review their formulation from a biological perspective, contrast their patterning properties, summarise key results on their analytical properties and classify their solution form. We conclude with a brief discussion and expand on some of the outstanding issues revealed as a result of this work. © Springer-Verlag 2008

Transport and anisotropic diffusion models for movement in oriented habitats

A common feature of many living organisms is the ability to move and navigate in heterogeneous environments. While models for spatial spread of populations are often based on the diffusion equation, here we aim to advertise the use of transport models; in particular in cases where data from individual tracking are available. Rather than developing a full general theory of transport models, we focus on the specific case of animal movement in oriented habitats. The orientations can be given by magnetic cues, elevation profiles, food sources, or disturbances such as seismic lines or roads. In this case we are able to present and contrast the three most common scaling limits, (i) the parabolic scaling, (ii) the hyperbolic scaling, and (iii) the moment closure method. We clearly state the underlying assumptions and guide the reader to an understanding of which scaling method is used in what kind of situations. One interesting result is that the macroscopic drift velocity is given by the mean direction of the underlying linear features, and the diffusion is given by the variance-covariance matrix of the underlying oriented habitat. We illustrate our findings with specific applications to wolf movement in habitats with seismic lines. © 2013 Springer-Verlag Berlin Heidelberg

Mathematical modelling of glioma growth: The use of Diffusion Tensor Imaging (DTI) data to predict the anisotropic pathways of cancer invasion

The nonuniform growth of certain forms of cancer can present significant complications for their treatment, a particularly acute problem in gliomas. A number of experimental results have suggested that invasion is facilitated by the directed movement of cells along the aligned neural fibre tracts that form a large component of the white matter. Diffusion tensor imaging (DTI) provides a window for visualising this anisotropy and gaining insight on the potential invasive pathways. In this paper we develop a mesoscopic model for glioma invasion based on the individual migration pathways of invading cells along the fibre tracts. Via scaling we obtain a macroscopic model that allows us to explore the overall growth of a tumour. To connect DTI data to parameters in the macroscopic model we assume that directional guidance along fibre tracts is described by a bimodal von Mises-Fisher distribution (a normal distribution on a unit sphere) and parametrised according to the directionality and degree of anisotropy in the diffusion tensors. We demonstrate the results in a simple model for glioma growth, exploiting both synthetic and genuine DTI datasets to reveal the potentially crucial role of anisotropic structure on invasion. © 2013 Elsevier Ltd