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

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

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

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

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 Cavities and Waveguides

Recently, it has also become possible to microfabricate high reflectivity mirrors by creating two- and three-dimensional periodic structures. These periodic "photonic crystals" can be designed to open up frequency bands within which the propagation of electromagnetic waves is forbidden irrespective of the propagation direction in space and define photonic bandgaps. 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. Here we show the use of these "artificially" microfabricated crystals in functional nonlinear optical devices, such as lasers, modulators, and waveguides

Convergence of a cancer invasion model to a logistic chemotaxis model

A characteristic feature of tumor invasion is the destruction of the healthy tissue surrounding it. Open space is generated, which invasive tumor cells can move into. One such mechanism is the urokinase plasminogen system (uPS), which is found in many processes of tissue reorganization. Lolas, Chaplain and collaborators have developed a series of mathematical models for the uPS and tumor invasion. These models are based upon degradation of the extracellular material through plasmid plus chemotaxis and haptotaxis. In this paper we consider the uPS invasion models in one-space dimension and we identify a condition under which this cancer invasion model converges to a chemotaxis model with logistic growth. This condition assumes that the density of the extracellular material is not too large. Our result shows that the complicated spatio-temporal patterns, which were observed by Lolas and Chaplain et al. are organized by the chaotic attractor of the logistic chemotaxis system. Our methods are based on energy estimates, where, for convergence, we needed to find lower estimates in Lγ for 0 < γ < 1. This is a new method for these types of PDE. © 2013 World Scientific Publishing Company

Global solvability and explicit bounds for non-local adhesion models

Adhesion between cells and other cells (cell-cell adhesion) or other tissue components (cell-matrix adhesion) is an intrinsically non-local phenomenon. Consequently, a number of recently developed mathematical models for cell adhesion have taken the form of non-local partial differential equations, where the non-local term arises inside a spatial derivative. The mathematical properties of such a non-local gradient term are not yet well understood. Here we use sophisticated estimation techniques to show local and global existence of classical solutions for such examples of adhesion-type models, and we provide a uniform upper bound for the solutions. Further, we discuss the significance of these results to applications in cell sorting and in cancer invasion and support the theoretical results through numerical simulations

The pursuit of happiness in ethical consumption; trade-offs, values and endless ends

Whilst the moral 'problem' could be considered to be increasing the chances of everyone to start life with an equal chance of achieving happiness (Rorty 1999), in a consumer culture in which ethical consumption is both a part and a consequence (Newholm and Shaw 2007), the potential for unhappiness is rife. Whilst consumers may be morally culpable for their actions (Schwartz 2010), they are faced with their consequences without the benefit of the guidance of 'grand narratives' (Cherrier 2007; Bauman 1993). Further, this may be characterised by uncertainty (Hassan et al. 2013), rationalisation, dependency and realism (Eckhardt, Belk and Devinney 2010), or recognition of the role of ethical consumption in relieving guilt from the middle classes and as a source of profit (Littler 2011). Others have suggested the ethical consumer is a 'myth' (Devinney, Auger and Eckhardt 2010), as consumer decision-making is entirely context-specific and based on complex individual trade-offs. Consequently ethical consumption is often framed in terms of its numerous failures (Littler 2011). Unhappy times indeed