A marriage of convenience: Hybridization of surface plasmon and dielectric waveguide modes

Plasmonics has attracted a lot of interest in the past few years because of its unique features, especially for its ability to confine light in extremely small volumes. However, application of plasmonics is restricted by the large propagation loss associated with plasmonic waveguides. On the other hand, dielectric waveguides enjoy low loss, although the mode confinement is relatively weaker. Hybrid plasmonic waveguides (HPWGs), which combine these two guiding mechanisms, allow one to utilize the benefits of both technologies. Over the past few years there have been intense research activities around the world on this new guiding scheme. In this work the operating principle of HPWGs, various HPWG structures proposed by different research groups, and their potentail applications are reviewed.     

Gravitational shock waves

This paper reports on and summarizes some recent progress on gravitational shocks, i.e., discontinuities in the Riemann curvature tensor. It is shown how the constraint equations play a crucial rôle in determining the nature and propagation of the shocks. Existence results are stated and are illustrated by some examples from numerical relativity.     

Highly regioselective palladium/copper-catalysed cross-coupling reactions of terminal alkynes and allenes

The Pd/Cu-catalysed cross-coupling reaction of heterocyclic terminal alkynes and allene/allenyl heterocycles affords novel trisubstituted en-ynes in good yield.     

The enclosed laser ablation of multiple stacks of laminated, metallised polymer

Enclosed laser ablation of single laminated, metallised polymer films (i.e. polymer, metal, adhesive, polymer layers respectively) has been studied in depth previously by the authors. It was found that most of the energy during this process was transmitted by the transparentised films. Therefore, it was proposed that multiple stacks of laminated metallised polymer samples could be transparentised with a single pass. In this paper, such experiments were carried out and stacks of 10 samples could be transparentised successfully with a single laser pass. The pulse energy incident upon each film was calculated from transmissivity measurements of each sample layer in a successfully demetallised stack, and the results were used to explain the behaviour observed from the experiments. Additional physical phenomena that were not present with single layer enclosed ablation have now been observed for the enclosed laser ablation of multiple layered stacks.     

Asymmetric Baeyer-Villiger oxidations of 4-mono- and 4,4-disubstituted cyclohexanones by whole cells of engineered Escherichia coli.

Whole cells of an Escherichia coli strain that overexpresses Acinetobacter sp. NCIB 9871 cyclohexanone monooxygenase have been used for the Baeyer-Villiger oxidations of a variety of 4-mono- and 4,4-disubstituted cyclohexanones. In cases where comparisons were possible, this new biocatalytic reagent provided lactones with chemical yields and optical purities that were comparable to those obtained from the purified enzyme or a strain of bakers' yeast that expresses the same enzyme. The efficient production of cyclohexanone monooxygenase in the E. coli expression system (ca. 30% of total soluble protein) allowed these oxidations to reach completion in approximately half the time required for the engineered bakers' yeast strain. Surprisingly, 4,4-disubstituted cyclohexanones were also accepted by the enzyme, and the enantioselectivities of these oxidations could be rationalized by considering the conformational energies of bound substrates along with the enzyme's intrinsic enantioselectivity. The enzyme expressed in E. coli cells also oxidized several 4-substituted cyclohexanones bearing polar substituents, often with high enantioselectivities. In the case of 4-iodocyclohexanone, the lactone was obtained in > 98% ee and its absolute configuration was assigned by X-ray crystallography. The crystal belongs to the monoclinic P2(1) space group with a = 5.7400(10), b = 6.1650(10), c = 11.377(2) A, b = 99.98(2) degrees, and Z = 2. Taken together, these results demonstrate the utility of an engineered bacterial strain in delivering useful chiral building blocks in an experimentally simple manner.     

On the weighting method for least squares problems with linear equality constraints

The weighting method for solving a least squares problem with linear equality constraints multiplies the constraints by a large number and appends them to the top of the least squares problem, which is then solved by standard techniques. In this paper we give a new analysis of the method, based on the QR decomposition, that exhibits many features of the algorithm. In particular it suggests a natural criterion for chosing the weighting factor. This work was supported in part by the National Science Foundation under grant CCR 95503126.