Combinatorial Frequency Generation in Quasi-Periodic Stacks of Nonlinear Dielectric Layers

Three-wave mixing in quasi-periodic structures (QPSs) composed of nonlinear anisotropic dielectric layers, stacked in Fibonacci and Thue-Morse sequences, has been explored at illumination by a pair of pump waves with dissimilar frequencies and incidence angles. A new formulation of the nonlinear scattering problem has enabled the QPS analysis as a perturbed periodic structure with defects. The obtained solutions have revealed the effects of stack composition and constituent layer parameters, including losses, on the properties of combinatorial frequency generation (CFG). The CFG features illustrated by the simulation results are discussed. It is demonstrated that quasi-periodic stacks can achieve a higher efficiency of CFG than regular periodic multilayers.

On the derived category of a regular toric scheme

Let X be a quasi-compact scheme, equipped with an open covering by affine schemes U s = Spec A s . A quasi-coherent sheaf on X gives rise, by taking sections over the U s , to a diagram of modules over the coordinate rings A s , indexed by the intersection poset S of the covering. If X is a regular toric scheme over an arbitrary commutative ring, we prove that the unbounded derived category of quasi-coherent sheaves on X can be obtained from a category of Sop-diagrams of chain complexes of modules by inverting maps which induce homology isomorphisms on hyper-derived inverse limits. Moreover, we show that there is a finite set of weak generators, one for each cone in the fan S. The approach taken uses the machinery of Bousfield–Hirschhorn colocalisation of model categories. The first step is to characterise colocal objects; these turn out to be homotopy sheaves in the sense that chain complexes over different open sets U s agree on intersections up to quasi-isomorphism. In a second step it is shown that the homotopy category of homotopy sheaves is equivalent to the derived category of X.

Three different types of quasi-model networks: synthesis by group transfer polymerization and characterization

Group transfer polymerization (GTP) chemistry was employed for the preparation of polymethacrylate networks of controlled structure (quasi-model networks) of three different types: (a) regular quasi-model networks, in which all polymer chains were linked at their ends, leaving, in principle, no free chain ends, (b) crosslinked star polymer quasi-model networks, in which star polymers were interlinked via half of their chains, letting the other half free (dangling), and (c) shell-crosslinked polymer quasi-model networks, in which the outer part of the network contained polymer arms (dangling chains). Combination of hydrophilic and hydrophobic monomers led to amphiphilic networks whose aqueous swelling behavior was characterized gravimetrically.