Resonant couplers acting as add-drop filters made withsilica-on-silicon waveguide technology

Add-drop filters are demonstrated using silica-on-silicon optical waveguide technology. This device consists of a full directional coupler subdivided by Mach-Zehnder sections. Tapering of the coupling coefficients is experimentally shown to dramatically reduce the filters' sidelobes. Only one photolithographic step is required using the silica planar waveguide technology, yielding accurate wavelength control of the filters. Excellent agreement between measurement and design was achieved     

Approximating the Pathway Axis and the Persistence Diagrams for a Collection of Balls in 3-Space

Given a collection ℬ of balls in a three-dimensional space, we wish to explore the cavities, voids, and tunnels in the complement space of ∪ℬ. We introduce the pathway axis of ℬ as a useful subset of the medial axis of the complement of ∪ℬ and prove that it satisfies several desirable geometric properties. We present an algorithm that constructs the pathway graph of ∪ℬ, a piecewise-linear approximation of the pathway axis. At the heart of our approach is an approximation scheme that constructs a collection K{\mathcal{K}} of same-size balls that approximate ℬ so that the Hausdorff distance between ∪ℬ and èK\bigcup{\mathcal{K}} is bounded by a prescribed parameter. We prove a bound on the ratio between the number of balls in K{\mathcal{K}} and the number of balls in ℬ. We employ this bound and the approximation scheme to show how to approximate the persistence diagrams for ∪ℬ, which can be used to extract major topological features such as the large voids and tunnels in the complement of ∪ℬ. We show that our approach is superior in terms of complexity to the standard point-sample approaches for the two problems that we address in this paper: approximating the pathway axis of ℬ and approximating the persistence diagrams for ∪ℬ. In a companion paper we introduce MolAxis, a tool for the identification of channels in macromolecules that demonstrates how the pathway graph and the persistence diagrams are used to identify plausible pathways in the complement of molecules.     

A study of the reactions π−p → K1X, K1Σ and K1Y11(1385) at 3.93 GeV/c

We have investigated the final states K¹⁰(890)Σ, $\text{K}{}^{10}\text{(890)Σ}{}^0$ and K¹⁰(890) Y₁¹⁰(1385) produced in π^?p interactions at 3.93 GeV/c. We present the differential cross sections and spin density matrix elements for the resonances as functions of momentum transfer, as well as the gL and Σ⁰ polarizations. The Σ⁰ polarization is found to be positive and maximal. An amplitude analysis is performed for the K¹ Λ and $\text{K}{}^1\text{Σ}{}^0$ reactions, and it is found that one natural parity transversity amplitude is dominant for the latter.     

Almost isometric embeddings into configuration-compacta

We show that a Polish metric space X which has ‘compact configuration spaces’ is free of almost isometric embeddings, i.e. given such an embedding into X one gets an isometric embedding. By assuming a continuous version of ℵ₀-homogeneity we get the converse statement, and also prove almost isometry uniqueness.     

Nonlinear effects in coherent multichannel transmission throughoptical fibers

Various nonlinear optical interactions in single-mode fibers that are used in coherent FDM (frequency division multiplexed) transmission systems are examined. It is these nonlinearities that lead to crosstalk between channels, power losses, and deleterious fluctuations, which in turn limit the power of the transmitted light and the number of allowed channels, and dictate the channel allocations. It is shown that, for long-haul transmission systems with fiber lengths exceeding 100 km, typical channel separation of 10 GHz, and few channels, the maximum allowed input power per channel, P_max, is limited by SBS (stimulated Brillouin scattering) to about 5 dBm. As the number of channels increases, FWM (four wave mixing) becomes the limiting process with P_max of about -5 dBm, whereas above several hundred channels SRS (stimulated Raman scattering) becomes dominant with P_max of about -5 dBm. For local area networks with shorter lengths, the results are similar, except that the values of P_max are uniformly higher by about 5 dB