Improved photonic crystal directional coupler with short length

We investigate a photonic crystal (PC) waveguide coupler which is formed by two closely spaced linear waveguides in a two-dimensional triangular lattice of air holes. Our study shows that shifting one row of the air holes between the waveguides affects the dispersion curves of the guided modes and if the triangular lattice of air holes between the waveguides is replaced by a rectangular lattice, this modification results in an ultra-short coupling structure with coupling length less than 3a, where a is the lattice constant. Also, we investigate the effect of changing the radii of air holes that are adjacent to or between the waveguides on the coupling length and show that increasing the radius of air holes between the waveguides decreases the coupling length. We analyze the output spectrum of an ultra-short channel drop filter designed based on this structure.     

A recyclable chiral Ru catalyst for enantioselective olefin metathesis. Efficient catalytic asymmetric ring-opening/cross metathesis in air

The synthesis and structure of a new chiral bidentate imidazolinylidene ligand and a derived chiral Ru-based carbene are disclosed. The Ru complex is stereogenic at the metal center; it can be prepared in >98% diastereoselectivity and purified by silica gel chromatography with undistilled solvents. The air-stable Ru complex efficiently catalyzes ring-closing and ring-opening metathesis and is recyclable. The chiral complex is highly effective (0.5-10 mol % loading) in promoting enantioselective ring-opening/cross metathesis reactions (up to >98% ee). These enantioselective transformations can be effected in air, with unpurified solvent and with substrates that would only polymerize with Mo-based catalysts.     

On parallel asynchronous high-order solutions of parabolic PDEs

In achieving significant speed-up on parallel machines, a major obstacle is the overhead associated with synchronizing the concurrent processes. This paper presents high-orderparallel asynchronous schemes, which are schemes that are specifically designed to minimize the associated synchronization overhead of a parallel machine in solving parabolic PDEs. They are asynchronous in the sense that each processor is allowed to advance at its own speed. Thus, these schemes are suitable for single (or multi) user shared memory or (message passing) MIMD multiprocessors. Our approach is demonstrated for the solution of the multidimensional heat equation, of which we present a spatial second-order Parametric Asynchronous Finite-Difference (PAFD) scheme. The well-known synchronous schemes are obtained as its special cases. This is a generalization and expansion of the results in [5] and [7]. The consistency, stability and convergence of this scheme are investigated in detail. Numerical tests show that although PAFD provides the desired order of accuracy, its efficiency is inadequate when performed on each grid point.In an alternative approach that uses domain decomposition, the problem domain is divided among the processors. Each processor computes its subdomain mostly independently, while the PAFD scheme provides the solutions at the subdomains' boundaries. We use high-order finite-difference implicit scheme within each subdomain and determine the values at subdomains' boundaries by the PAFD scheme. Moreover, in order to allow larger time-step, we use remote neighbors' values rather than those of the immediate neighbors. Numerical tests show that this approach provides high efficiency and in the case which uses remote neighbors' values an almost linear speedup is achieved. Schemes similar to the PAFD can be developed for other types of equations [3].This research was supported by the fund for promotion of research at the Technion.     

Critical behavior of light in mode-locked lasers

Light is shown to exhibit critical and tricritical behavior in passively mode-locked lasers with externally injected pulses. It is a first and unique example of critical phenomena in a one-dimensional many-body light-mode system. The phase diagrams consist of regimes with continuous wave, driven parapulses, spontaneous pulses via mode condensation, and heterogeneous pulses, separated by phase transition lines that terminate with critical or tricritical points. Enhanced non-Gaussian fluctuations and collective dynamics are present at the critical and tricritical points, showing a mode system analog of the critical opalescence phenomenon. The critical exponents are calculated and shown to comply with the mean field theory, which is rigorous in the light system.     

Faraday rotation in a two-dimensional photonic crystal with a magneto-optic defect

We study the magneto-optic (MO) Faraday rotation in a two-dimensional square-lattice photonic crystal with a central MO defect layer in the optical wavelength range. We show that when a TM plane wave is incident upon a photonic crystal, an enhancement of Faraday rotation takes place in a region where a resonance peak appears in the photonic bandgap. In this region the mode conversion is high.     

Cu-catalyzed asymmetric allylic alkylations of aromatic and aliphatic phosphates with alkylzinc reagents. An effective method for enantioselective synthesis of tertiary and quaternary carbons

Efficient enantioselective Cu-catalyzed allylic alkylations of aromatic and aliphatic allylic phosphates bearing di- and trisubstituted olefins are disclosed. Enantioselective C-C bond forming reactions are promoted in the presence of 10 mol % readily available chiral amino acid-based ligand (5 steps, 40% overall yield synthesis) and 5 mol % (CuOTf)2 x C6H6. Reactions deliver tertiary and quaternary stereogenic carbon centers regioselectively and in 78-96% ee. Data regarding the effect of variations in ligand structure on the efficiency and enantioselectivity of the alkylation process, as well as a mechanistic working model, are presented. The suggested model involves a dual role for the chiral Cu complex: association of the Cu(I) center to the olefin is facilitated by a two-point binding between the carbonyl of the ligand's amide terminus and the P=O of the substrate.     

Real-time 2D NMR identification of analytes undergoing continuous chromatographic separation

We have recently proposed and demonstrated an approach that enables the acquisition of multidimensional nuclear magnetic resonance (NMR) spectra within a single scan. A promising application opened up by this new accelerated form of data acquisition concerns the possibility of monitoring in real time the chemical nature of analytes subject to a continuous flow. The present paper illustrates such potential, with the real-time acquisition of a series of 2D 1H NMR spectra arising from a mixture of compounds subject to a continuous liquid chromatography (LC) separation. This real-time 2D NMR identification of chemicals eluted minutes apart under usual LC-NMR conditions differs from the way in which LC-2D NMR has hitherto been carried out, which relies on stopped-flow modes of operations whereby fractions are first collected and then subject to individual, aliquot-by-aliquot analyses. The real-time LC-2D NMR experiment hereby introduced can be implemented in a straightforward manner using modern commercial LC-NMR hardware, thus opening up immediate possibilities in high-throughput characterizations of complex molecules.