Segmented waveguides in thin silicon-on-insulator

We have developed new silicon-on-insulator waveguide designs for simultaneously achieving both low-loss optical confinement and electrical contacts, and we present a design methodology based on calculating the Bloch modes of such segmented waveguides. With this formalism, waveguides are designed in a single thin layer of silicon-on-insulator to achieve both optical confinement and minimal insertion loss. Waveguides were also fabricated and tested, and the measured data were found to closely agree with theoretical predictions, demonstrating input insertion loss and propagation loss better than 0.1 dB and -16 dB/cm, respectively

On a class of stable, traversable Lorentzian wormholes in classical general relativity

It is known that Lorentzian wormholes must be threaded by matter that violates the null energy condition. We phenomenologically characterize such exotic matter by a general class of microscopic scalar field Lagrangians and formulate the necessary conditions that the existence of Lorentzian wormholes imposes on them. Under rather general assumptions, these conditions turn out to be strongly restrictive. The most simple Lagrangian that satisfies all of them describes a minimally coupled massless scalar field with a reversed sign kinetic term. Exact, non-singular, spherically symmetric solutions of Einstein's equations sourced by such a field indeed describe traversable wormhole geometries. These wormholes are characterized by two parameters: their mass and charge. Among them, the zero mass ones are particularly simple, allowing us to analytically prove their stability under arbitrary space-time dependent perturbations. We extend our arguments to non-zero mass solutions and conclude that at least a non-zero measure set of these solutions is stable.Comment: 23 pages, 4 figures, uses RevTeX4. v2: Changes to accommodate added references. Statement about masses of the wormhole correcte

Galilean invariance and homogeneous anisotropic randomly stirred flows

The Ward-Takahashi (WT) identities for incompressible flow implied by Galilean invariance are derived for the randomly forced Navier-Stokes equation (NSE), in which both the mean and fluctuating velocity components are explicitly present. The consequences of Galilean invariance for the vertex renormalization are drawn from this identity.Comment: REVTeX 4, 4 pages, no figures. To appear as a Brief Report in the Physical Review

Method and apparatus for white-light dispersed-fringe interferometric measurement of corneal topography

An novel interferometric apparatus and method for measuring the topography of aspheric surfaces, without requiring any form of scanning or phase shifting. The apparatus and method of the present invention utilize a white-light interferometer, such as a white-light Twyman-Green interferometer, combined with a means for dispersing a polychromatic interference pattern, using a fiber-optic bundle and a disperser such as a prism for determining the monochromatic spectral intensities of the polychromatic interference pattern which intensities uniquely define the optical path differences or OPD between the surface under test and a reference surface such as a reference sphere. Consequently, the present invention comprises a snapshot approach to measuring aspheric surface topographies such as the human cornea, thereby obviating vibration sensitive scanning which would otherwise reduce the accuracy of the measurement. The invention utilizes a polychromatic interference pattern in the pupil image plane, which is dispersed on a point-wise basis, by using a special area-to-line fiber-optic manifold, onto a CCD or other type detector comprising a plurality of columns of pixels. Each such column is dedicated to a single point of the fringe pattern for enabling determination of the spectral content of the pattern. The auto-correlation of the dispersed spectrum of the fringe pattern is uniquely characteristic of a particular optical path difference between the surface under test and a reference surface

Tolman wormholes violate the strong energy condition

For an arbitrary Tolman wormhole, unconstrained by symmetry, we shall define the bounce in terms of a three-dimensional edgeless achronal spacelike hypersurface of minimal volume. (Zero trace for the extrinsic curvature plus a "flare-out" condition.) This enables us to severely constrain the geometry of spacetime at and near the bounce and to derive general theorems regarding violations of the energy conditions--theorems that do not involve geodesic averaging but nevertheless apply to situations much more general than the highly symmetric FRW-based subclass of Tolman wormholes. [For example: even under the mildest of hypotheses, the strong energy condition (SEC) must be violated.] Alternatively, one can dispense with the minimal volume condition and define a generic bounce entirely in terms of the motion of test particles (future-pointing timelike geodesics), by looking at the expansion of their timelike geodesic congruences. One re-confirms that the SEC must be violated at or near the bounce. In contrast, it is easy to arrange for all the other standard energy conditions to be satisfied.Comment: 8 pages, ReV-TeX 3.

Vacuum polarization of a scalar field in wormhole spacetimes

An analitical approximation of $$ for a scalar field in a static spherically symmetric wormhole spacetime is obtained. The scalar field is assumed to be both massive and massless, with an arbitrary coupling $\xi$ to the scalar curvature, and in a zero temperature vacuum state.Comment: 10 pages, RevTeX, two eps figure

Dilatonic wormholes: construction, operation, maintenance and collapse to black holes

The CGHS two-dimensional dilaton gravity model is generalized to include a ghost Klein-Gordon field, i.e. with negative gravitational coupling. This exotic radiation supports the existence of static traversible wormhole solutions, analogous to Morris-Thorne wormholes. Since the field equations are explicitly integrable, concrete examples can be given of various dynamic wormhole processes, as follows. (i) Static wormholes are constructed by irradiating an initially static black hole with the ghost field. (ii) The operation of a wormhole to transport matter or radiation between the two universes is described, including the back-reaction on the wormhole, which is found to exhibit a type of neutral stability. (iii) It is shown how to maintain an operating wormhole in a static state, or return it to its original state, by turning up the ghost field. (iv) If the ghost field is turned off, either instantaneously or gradually, the wormhole collapses into a black hole.Comment: 9 pages, 7 figure

Renormalization Group Analysis of a Quivering String Model of Posture Control

Scaling concepts and renormalization group (RG) methods are applied to a simple linear model of human posture control consisting of a trembling or quivering string subject to damping and restoring forces. The string is driven by uncorrelated white Gaussian noise intended to model the corrections of the physiological control system. We find that adding a weak quadratic nonlinearity to the posture control model opens up a rich and complicated phase space (representing the dynamics) with various non-trivial fixed points and basins of attraction. The transition from diffusive to saturated regimes of the linear model is understood as a crossover phenomenon, and the robustness of the linear model with respect to weak non-linearities is confirmed. Correlations in posture fluctuations are obtained in both the time and space domain. There is an attractive fixed point identified with falling. The scaling of the correlations in the front-back displacement, which can be measured in the laboratory, is predicted for both the large-separation (along the string) and long-time regimes of posture control.Comment: 20 pages, 13 figures, RevTeX, accepted for publication in PR