Supramolecular Assembly of Chiral Lanthanide Triple-Decker Metallocyclophanes Ln()(L) or Tetrahedral Cages Ln()(L) and Their Chiroptical Properties.

Two new ligands (: -tris-β-diketonate and : -tris-β-diketonate) with meta and para orientations of coordinating bidentate β-diketonate units were synthesized in order to investigate their supramolecular formation behavior. When chiral ()- or ()-BINAPO (L) was used as a chiral inducer, trinuclear triple-decker metallocyclophane, Eu()(L), was formed from whereas a tetranuclear tetrahedral cage Eu()(L) was formed with . The X-ray crystal of Eu()(L) shows that all three Eu centers possess the same configuration, hence resulting in homochiral ΔΔΔ assembly.

Local diffusion theory for localized waves in open media.

We report a first-principles study of static transport of localized waves in quasi-one-dimensional open media. We find that such transport, dominated by disorder-induced resonant transmissions, displays novel diffusive behavior. Our analytical predictions are entirely confirmed by numerical simulations.

Wave transport in two-dimensional random media: the ballistic to diffusive transition and the extrapolation length.

By using a first-principles approach based on the Bethe-Salpeter equation, we study the behavior of wave propagation through a two-dimensional random slab as a function of thickness, L , in the region where L is much smaller than the localization length. A general two-dimensional vertex function for the ladder diagrams is derived from the Ward identity. We calculate both the static and the time-resolved transmitted intensities as functions of L/l , where l is the mean free path.