Phase-matched nonlinear diffraction

We report on a new (to our knowledge) configuration incorporating both birefringence and quasi-phase-matching, enabling efficient phase-matched nonlinear diffraction in one-dimensional periodically poled nonlinear crystals. We demonstrate the method experimentally, showing an efficient nonlinear diffraction to the first few orders in two types of crystals, MgO doped congruent lithium niobate and congruent lithium niobate, and characterize its efficiency dependence on the fundamental power, the propagation angle, and the crystal temperature. This configuration can increase efficiencies observed in nonlinear diffraction experiments, enables ferroelectric domain characterization by nonlinear microscopy, and can be used to determine the duty cycles of periodically poled nonlinear crystals.     

Polarization-mixing optical parametric oscillator

We report the experimental realization of a new type of optical parametric oscillator in which oscillation is achieved by polarization rotation in a linear retarder, followed by nonlinear polarization mixing. The mixing is performed by a type II degenerate parametric downconversion in a periodically poled KTP crystal pumped by a 1064 nm pulsed Nd:YAG pump. A single, linearly polarized beam, precisely at the degenerate wavelength is generated. The output spectrum has a narrow linewidth (below the instrumentation bandwidth of 1 nm) and is highly stable with respect to variations in the crystal temperature.     

Non‐symmetric bent‐core mesogens with one terminal vinyl group

Two series of non‐symmetric banana‐shaped compounds, both with one alkyl and one alkenyl terminal tail, have been synthesized and studied. Both series were compared with the corresponding series with two saturated terminal alkyl tails. All the compounds have a bent central 1,3‐phenylene bis(4‐benzoyloxy)benzoate core; their mesophases were characterized by polarizing optical microscopy, differential scanning calorimetry, X‐ray diffraction and switching current response experiments. In all four series one of the terminal tails is varied from OC₈H₁₇ to OC₁₆H₃₃. The other terminal tails are OC₁₁H₂₃, O(CH₂)₉CH?=?CH₂, OC₁₀H₂₁ and O(CH₂)₈CH?=?CH₂. The short‐tailed compounds show monotropic or enantiotropic B₁ phases and the long‐tailed compounds the B₂ phase. The introduction of one terminal vinyl group slightly lowers the transition temperatures. The introduction of a second terminal vinyl group further suppresses the liquid crystalline properties. All compounds with B₂ phases have layer spacings that suggest a tilt of ～45° of the bent molecules in the layers, and their switching behaviour is antiferroelectric.     

Nonmonotonicity in the quantum-classical transition: chaos induced by quantum effects

The classical-quantum transition for chaotic systems is understood to be accompanied by the suppression of chaotic effects as the relative variant Planck's over 2pi is increased. We show evidence to the contrary in the behavior of the quantum trajectory dynamics of a dissipative quantum chaotic system, the double-well Duffing oscillator. The classical limit in the case considered has regular behavior, but as the effective variant Planck's over 2pi is increased we see chaotic behavior. This chaos then disappears deeper into the quantum regime, which means that the quantum-classical transition in this case is nonmonotonic in variant Planck's over 2pi.     

A Voltage-Responsive Synthetic Cl−-Channel Regulated by pH

Transmembrane protein channels are an important inspiration for the design of artificial ion channels. Their dipolar structure helps overcome the high energy barrier to selectively translocate water and ions sharing one pathway, across the cell membrane. Herein, we report that the amino-imidazole (Imu) amphiphiles self-assemble via multiple H-bonding to form stable artificial Cl⁻-channels within lipid bilayers. The alignment of water/Cl⁻ wires influences the conduction of ions, envisioned to diffuse along the hydrophilic pathways; at acidic pH, Cl⁻/H⁺ symport conducts along a partly protonated channel, while at basic pH, higher Cl⁻/OH⁻ antiport translocate through a neutral channel configuration, which can be greatly activated by applying strong electric field. This voltage/pH regulated channel system represents an unexplored alternative for ion-pumping along artificial ion-channels, parallel to that of biology.     

Mean dimension of $${\mathbb{Z}^k}$$-actions

Mean dimension is a topological invariant for dynamical systems that is meaningful for systems with infinite dimension and infinite entropy. Given a \({\mathbb{Z}^k}\)-action on a compact metric space X, we study the following three problems closely related to mean dimension.

1. (1)
   When is X isomorphic to the inverse limit of finite entropy systems?
    
2. (2)
   Suppose the topological entropy \({h_{\rm top}(X)}\) is infinite. How much topological entropy can be detected if one considers X only up to a given level of accuracy? How fast does this amount of entropy grow as the level of resolution becomes finer and finer?
    
3. (3)
   When can we embed X into the \({\mathbb{Z}^k}\)-shift on the infinite dimensional cube \({([0,1]^D)^{\mathbb{Z}^k}}\)?
    

These were investigated for \({\mathbb{Z}}\)-actions in Lindenstrauss (Inst Hautes Études Sci Publ Math 89:227–262, 1999), but the generalization to \({\mathbb{Z}^k}\) remained an open problem. When X has the marker property, in particular when X has a completely aperiodic minimal factor, we completely solve (1) and a natural interpretation of (2), and give a reasonably satisfactory answer to (3).A key ingredient is a new method to continuously partition every orbit into good pieces.     

The multiplicative version of the Wiener index

The classical Wiener index, W(G), is equal to the sum of the distances between all pairs of vertexes of a (molecular) graph, G. We now consider a related topological index, pi(G), equal to the product of distances between all pairs of vertexes of G. The basic properties of the pi index are established and its possible physicochemical applications examined. In the case of alkanes, pi and W are highly correlated; a slightly curvilinear correlation exists between In pi and W.     

Molecular assemblies from imidazolyl-containing haloalkenes and haloalkynes: competition between halogen and hydrogen bonding

The structural characterization of molecular assemblies constructed from imidazolyl-containing haloalkenes and haloalkynes is reported. 1-(3-Iodopropargyl)imidazole (2) and 1-(2,3,3-triiodoallyl)imidazole (5) were synthesized from 1-propargylimidazole (1). In the solid state, these wholly organic modules self-assemble through N...I halogen-bonding interactions, thus giving rise to polymeric chains. The N...I interaction observed in 2 (d(N...I)=2.717 A, angle-spherical C(sp)-I...N=175.8 degrees) is quite strong relative to previously reported data. The N...I interaction in 5 (d(N...I)=2.901 A, angle-spherical C(sp2)-I...N=173.6 degrees) is weaker, in accordance with the order C(sp)-X<--base>C(sp2)-X<--base. Compound 5 was found to give a 1:1 cocrystal 4 with morpholinium iodide (6). In the X-ray crystal studies of 4, N...I halogen-bonding interactions similar to those observed in 5 were shown not to be present, as the arrangement of the molecules is governed by two interwoven hydrogen-bonding networks. The first network involves N-H...O interactions between nearby morpholinium cations, and the second network is based on N-H...N hydrogen bonding between morpholinium cations and imidazolyl groups. Both hydrogen-bonding schemes are charge-assisted. Halogen bonding is not completely wiped out, however, as the triiodoalkene fragment forms a halogen bond with an iodide anion in its vicinity (d(I...I)=3.470 A, angle-spherical C(sp2)-I...I=170.7 degrees). X-ray crystal studies of 6 show a completely different arrangement from that observed in 4, namely, N-H...O interactions are not present. In crystalline 6, morpholinium cations are interconnected through C-H...O bridges (d(H...O)=2.521 and 2.676 A), and the NH2+ groups interact with nearby iodide anions (d(H...I)=2.633 and 2.698 A).