Resonant-induced transparency and coupled modes in layered metamaterials

We present an overview of some of our work on transmission properties and mode characteristics of layered metamaterials and their potential applications. In particular, we will show how layered metamaterials exhibit unusual transmission properties and unconventional features of guided modes, such as resonance-induced transparency in multilayer structures and slope reversal of dispersion curves in coupled waveguides. PACS 78.67.-n; 73.21.Ac; 61.46.+w; 42.25.Bs; 42.82.Et     

The isomerization of optically-active propargyl alcohols to terminal acetylenes.

The isomerization of optically-active secondary propargyl alcohols, RCHOHCC(CH₂)_nCH₃, to terminal acetylenic alcohols, RCHOH(CH₂)_n+1 C=CH, by potassium 3-aminopropylamide (KAPA) proceeds without loss of configuration at the hydroxy center.     

Cucurbit[7]uril Disrupts Aggregate Formation Between Rhodamine B Dyes Covalently Attached to Glass Substrates

Dye aggregation is detrimental to the performance of high optical density dye-doped photonic materials. To overcome this challenge, the ability of cucurbit[7]uril (CB7) as a molecular host to disrupt aggregate formation on glass substrates was examined. Rhodamine B was covalently attached to glass slides by initially coating the surface with azidohexylsiloxane followed by copper-catalyzed “click” triazole formation with rhodamine B propargyl ester. The absorption and emission spectra of rhodamine B coated slides in water indicated diverse heterogeneous properties as surface dye density varied. Fluorescence quenching due to dye aggregation was evident at high surface dye density. Addition of aqueous cucurbit[7]uril (CB7) to the surface-tethered dyes perturbed the spectra to reveal a considerable reduction in heterogeneity, which suggested that the presence of a surface in close proximity does not significantly impair CB7’s ability to complex with tethered rhodamine B.     

Conformational interconversions in [2]catenanes containing a wide rigid bis(p-benzyl)methyl spacer

The conformational interconversions of four [2]catenanes (1-4) containing a dibenzo-34-crown-10 ether (BPP34C10) interlocked with rings containing two 4,4'-dipyridiniums tethered by 1,3-bis(ethyloxy)phenyl and bis(p-benzyl)methyl spacers have been studied by VT 1H NMR spectroscopy. Symmetrically placed blocking groups on thickened tethers enabled either pathway for circumrotation of the BPP34C10 between isoenergetic sites to be blocked. On the basis of chemical shifts of the BPP34C10, its internal p-hydroquinone forms pi-pi-stacking interactions with only one 4,4'-dipyridinium ring at a time. The activation barrier for migration along either open tether was approximately 11.5 kcal/mol. This study demonstrates an ability to select the pathway for conformational interconversions in these [2]catenanes containing the rigid bis(p-benzyl)methyl tether and the lowering the barrier for interconversion through destabilization of the ground state structures.     

Resonances of nanocylinders with gap defects

We have investigated the plasmonic resonance characteristics of canonical circular and square cylinders, with gap defects, that are illuminated by a plane wave. The circular and square cylinders have vee shaped gaps and constant width gaps, respectively. The electric and magnetic fields are obtained by solving the Lippmann–Schwinger equation from which we compute the far-field scattering cross-section and near-field local electromagnetic energy density.Numerical results are given for numerous wavelength and gap dimensions to qualitatively present the effects of gap defects on the scattering cross-section and local electromagnetic energy density.     

Chaotic Expansion of Elements of the Universal Enveloping Algebra of a Lie Algebra Associated with a Quantum Stochastic Calculus

The functional Ito formula, in the form df() = f( + d ) –f(),is formulated and proved in the context of a Lie algebra L associatedwith a quantum (non-commutative) stochastic calculus. Here fis an element of the universal enveloping algebra U of L, andf() + d() – f() is given a meaning using the coproductstructure of U even though the individual terms of this expressionhave no meaning. The Ito formula is equivalent to a chaoticexpansion formula for f() which is found explicitly. 1991 MathematicsSubject Classification: primary 81S25; secondary 60H05; tertiary18B25.