Control of orbital angular momentum of light with optical fibers

We present a fiber-based method for generating vortex beams with a tunable value of orbital angular momentum from -1? to +1? per photon. We propose a new (to our knowledge) method to determine the modal content of the fiber and demonstrate high purity of the desired vortex state (97% after 20 m, even after bends and twists). This method has immediate utility for the multitude of applications in science and technology that exploit vortex light states.     

Tempered distributions in infinitely many dimensions

In the present paper we continue investigating spaces of tempered distributions in infinitely many dimensions. In particular, we prove that those linear homogeneous transformations of the canonical pair of field operators, which preserve the commutation relations, can be implemented by an essentially unique intertwining operator. The dependence of this operator on the transformation is studied.     

Investigation of the mesoscopic Aharonov–Bohm effect in low magnetic fields

We have investigated the Aharonov–Bohm effect in mesoscopic semiconductor GaAs/GaA1As rings in low magnetic fields. The oscillatory magnetoconductance of these systems is systematically studied as a function of electron density. We observe phase shifts of π in the magnetoconductance oscillations, and halving of the fundamental h/e period, as the density is varied. Theoretically, we find agreement with the experiment, by introducing an asymmetry between the two arms of the ring.     

Studies on peroxycompounds—XXVI: “SN2”-type decarbethoxylation of o-benzoyltartronates and benzoyloxycyanoacetates. New synthons for 2-hydroxycarboxylic esters and aldehydes

Diethyl O-benzoyl-R-tartronates 1; RH, C₂H₅, Ph undergo S_N2-type dealkylation and subsequent CO₂ elimination at 175–190°C in anhydrous or wet DMSO, with or without inorganic salts as catalysts giving the corresponding 2-benzoyloxyesters 2. Ethyl 2-benzoyloxy-2-benzylcyanoacetate 4 also undergoes decarbethoxylation (140°C, DMSO or wet DMSO) giving 6 in small yields (1–6%). The best yields of 6 (82%) were found when pyridine was the solvent and LiI the catalyst.     

Optimal control based NCO and NCA experiments for spectral assignment in biological solid-state NMR spectroscopy

We present novel pulse sequences for magic-angle-spinning solid-state NMR structural studies of (13)C,(15)N-isotope labeled proteins. The pulse sequences have been designed numerically using optimal control procedures and demonstrate superior performance relative to previous methods with respect to sensitivity, robustness to instrumental errors, and band-selective excitation profiles for typical biological solid-state NMR applications. Our study addresses specifically (15)N to (13)C coherence transfers being important elements in spectral assignment protocols for solid-state NMR structural characterization of uniformly (13)C,(15)N-labeled proteins. The pulse sequences are analyzed in detail and their robustness towards spin system and external experimental parameters are illustrated numerically for typical (15)N-(13)C spin systems under high-field solid-state NMR conditions. Experimentally the methods are demonstrated by 1D (15)N-->(13)C coherence transfer experiments, as well as 2D and 3D (15)N,(13)C and (15)N,(13)C,(13)C chemical shift correlation experiments on uniformly (13)C,(15)N-labeled ubiquitin.     

On Rank One Convex Functions that are Homogeneous of Degree One

We show that positively 1-homogeneous rank one convex functions are convex at 0 and at matrices of rank one. The result is a special case of an abstract convexity result that we establish for positively 1-homogeneous directionally convex functions defined on an open convex cone in a finite dimensional vector space. From these results we derive a number of consequences including various generalizations of the Ornstein L¹ non inequalities. Most of the results were announced in (C R Acad Sci Paris Ser I 349:407–409,2011).     

Relaxed fabrication tolerance for self-imaging photonic crystal waveguide splitters using a tapered multimode interference region

The power imbalance between different waveguide outputs is compensated by manipulating the dispersion of the guided propagation in the multimode interference (MMI) region. This is attainable using a tapered region at the beginning of the MMI region that has been verified through simulation and experiment. From this, the fabrication tolerance for the diameters of holes in a tapered 1×3 photonic crystal waveguide (PhCW) splitter is relaxed up to a range of at least 27 nm. The output power is well-balanced to within 1 dB. The effective bandwidth of the splitters shifts only around 13 nm, for a reduction of 10 nm in the diameter of the PhCW holes. The optimized component is an outstanding ultracompact 1×3 splitter for the photonic integrated circuit (PIC).     

Photoelectron spectroscopy studies of the functionalization of a silicon surface with a phosphorylcholine-terminated polymer grafted onto (3-aminopropyl)trimethoxysilane

The structure of a biomimetic phosphorylcholine (PC)-functionalized poly(trimethylene carbonate) (PC-PTMC-PC), linked to a silicon substrate through an aminolysis reaction at 120 degrees C with (3-aminopropyl)trimethoxysilane (APTMS), was studied using photoelectron spectroscopy. Two chemical states were found for the unreacted APTMS amine, a neutral state and a protonated state, where the protonated amine on average was situated closer to the silicon substrate than the neutral amine. The experiments also indicated the presence of a third chemical state, where amines interact with unreacted silanol groups. The PTMC chains of the grafted films were found to consist of only 2-3 repeat units, with the grafted chains enriched in the zwitterionic end group, suggesting that these groups are attracted to the surface. This was further supported by the experiments showing that the PC groups were situated deeper within the film.