Abstract:We use the coupling matrix formalism to investigate continuouswave and pulse propagation through microring coupled-resonator optical waveguides (CROWs). The dispersion relation agrees with that derived using the tight-binding model in the limit of weak inter-resonator coupling. We obtain an analytical expression for pulse propagation through a semi-infinite CROW in the case of weak coupling which fully accounts for the nonlinear dispersive characteristics. We also show that intensity of a pulse in a CROW is enhanced by a factor inversely proportional to the inter-resonator coupling. In finite CROWs, anomalous dispersions allows for a pulse to propagate with a negative group velocity such that the output pulse appears to emerge before the input as in "superluminal" propagation. The matrix formalism is a powerful approach for microring CROWs since it can be applied to structures and geometries for which analyses with the commonly used tight-binding approach are not applicable.

The mixture of EDTA-soluble proteins found in abalone nacre are known to cause the nucleation and growth of aragonite on calcite seed crystals in supersaturated solutions of calcium carbonate. Past atomic force microscope studies of the interaction of these proteins with calcite crystals did not observe this transition because no information about the crystal polymorph on the surface was obtained. Here we have used the atomic force microscope to directly observe changes in the atomic lattice on a calcite seed crystal after the introduction of abalone shell proteins. The observed changes are consistent with a transition to (001) aragonite growth on a (1014) calcite surface.

Small cantilevers allow for faster imaging and faster force spectroscopy of single biopolymers than previously possible because they have higher resonant frequencies and lower coefficients of viscous damping. We have used a new prototype atomic force microscope with small cantilevers to produce stable tapping-mode images ͑1 mϫ1 m͒ in liquid of DNA adsorbed onto mica in as little as 1.7 s per image. We have also used these cantilevers to observe the forced unfolding of individual titin molecules on a time scale an order of magnitude faster than previously reported. These experiments demonstrate that a new generation of atomic force microscopes using small cantilevers will enable us to study biological processes with greater time resolution. Furthermore, these instruments allow us to narrow the gap in time between results from force spectroscopy experiments and molecular dynamics calculations.

A family of soluble proteins from the shell of Haliotis rufescens was introduced over a growing calcite crystal being scanned in situ by an atomic force microscope (AFM). Atomic step edges on the crystal surface were altered in shape and speed of growth by the proteins. Proteins attached nonuniformly to the surface, indicating different interactions with crystallographically different step edges. The observed changes were consistent with the habit modification induced by this family of proteins, as previously observed by optical microscopy. To facilitate further studies in this area, AFM techniques and certain AFM imaging artifacts are discussed in detail.

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