400-photon-per-pulse ultrashort pulse autocorrelation measurement with aperiodically poled lithium niobate waveguides at 1.55 microm

We demonstrate ultrasensitive intensity autocorrelation measurements of subpicosecond optical pulses in the telecommunication band by using aperiodically poled lithium niobate (A-PPLN) waveguides. The tightly confined optical beam in the waveguides and the chirped poling period facilitate simultaneous high second-harmonic generation (SHG) efficiency and broad phase-matching (PM) bandwidth. The resulting measurement sensitivity is 3.2 x 10(-7) mW2, approximately 500 times better than the previous record for intensity autocorrelations. We also show that chirped A-PPLN waveguides retain nearly the same SHG efficiency as the unchirped guide as long as the PM bandwidth is not significantly broader than the input spectrum.     

Direct imaging of multimode interference in a channel waveguide

By use of a near-field scanning optical microscope in collection mode, multimode interference was directly measured in an annealed proton-exchanged LiNbO3 waveguide. Periodic transitions from a single-peaked Gaussianlike intensity distribution to a double-peaked intensity distribution were observed. The intensity distribution along the waveguide was calculated, and the results agree well with the experimental observation.     

Intramolecular Wittig Reaction: A New Synthesis of (S)‐Pyrrolam A

A straightforward synthesis of (S)‐pyrrolam A is described. The synthesis involves in situ generation of the phosphorane 3 , followed by an intramolecular Wittig reaction to furnish (S)‐pyrrolam A.     

Diode laser-based sensor for high precision measurements of ambient CO<Subscript>2</Subscript> in network applications

The increasing need for better spatial and temporal measurements of greenhouse gases, especially CO₂, to support global climate change modeling is driving the expansion of monitoring networks. Currently, networks making ambient CO₂ measurements use environmentally stabilized sensors based on non-dispersive infrared absorption spectroscopy. To expand both measurement capability and coverage, much work is underway to develop highly accurate, reliable yet economical sensors for the greenhouse gases. The US Department of Energy has created specifications for a new sensor that has high performance but at a cost that permits widespread deployment. We report on a sensor designed to meet this need. We have demonstrated a compact, automated, high precision sensor for ambient CO₂ that offers good performance in an economical package. The sensor is a near-IR diode laser-based absorption spectrometer operating near 2 μm and using Integrated Cavity Output Spectroscopy (ICOS). Field demonstrations were carried out at both the UNH/AirMap Thompson Farm Observatory and the NOAA Boulder Atmospheric Observatory. The sensor has a demonstrated precision of between 0.090 and 0.125 ppmv for a 30 sec acquisition, or 1 part in 3000 to 4000.     

Holonomy group scheme of an integral curve

Let Y be a projective variety over a field k (of arbitrary characteristic). Assume that the normalization X of Y is such that is normal, being the algebraic closure of k. We define a notion of strong semistability for vector bundles on Y. We show that a vector bundle on Y is strongly semistable if and only if its pull back to X is strongly semistable and hence it is a tensor category. In case , we show that strongly semistable vector bundles on Y form a neutral Tannakian category. We define the holonomy group scheme of Y to be the Tannakian group scheme for this category. For a strongly semistable principal G‐bundle , we construct a holonomy group scheme. We show that if Y is an integral complex nodal curve, then the holonomy group of a strongly semistable vector bundle on Y is the Zariski closure of the (topological) fundamental group of Y.     

Towards a naturally small cosmological constant from branes in 6D supergravity

We investigate the possibility of self-tuning of the effective 4D cosmological constant in 6D supergravity, to see whether it could naturally be of order 1/r⁴ when compactified on two dimensions having Kaluza–Klein masses of order 1/r. In the models we examine supersymmetry is broken by the presence of non-supersymmetric 3-branes (on one of which we live). If r were sub-millimeter in size, such a cosmological constant could describe the recently-discovered dark energy. A successful self-tuning mechanism would therefore predict a connection between the observed size of the cosmological constant, and potentially observable effects in sub-millimeter tests of gravity and at the Large Hadron Collider. We do find self-tuning inasmuch as 3-branes can quite generically remain classically flat regardless of the size of their tensions, due to an automatic cancellation with the curvature and dilaton of the transverse two dimensions. We argue that in some circumstances six-dimensional supersymmetry might help suppress quantum corrections to this cancellation down to the bulk supersymmetry-breaking scale, which is of order 1/r. We finally examine an explicit realization of the mechanism, in which 3-branes are inserted into an anomaly-free version of Salam–Sezgin gauged 6D supergravity compactified on a 2-sphere with nonzero magnetic flux. This realization is only partially successful due to a topological constraint which relates bulk couplings to the brane tension, although we give arguments why these relations may be stable against quantum corrections.     

Trapping a Silicon(I) Radical with Carbenes: A Cationic cAAC–Silicon(I) Radical and an NHC–Parent-Silyliumylidene Cation

The trapping of a silicon(I) radical with N-heterocyclic carbenes is described. The reaction of the cyclic (alkyl)(amino) carbene [cAAC_Me] (cAAC_Me=:C(CMe₂)₂(CH₂)NAr, Ar=2,6-iPr₂C₆H₃) with H₂SiI₂ in a 3:1 molar ratio in DME afforded a mixture of the separated ion pair [(cAAC_Me)₂Si:^.]⁺I⁻ ( 1 ), which features a cationic cAAC–silicon(I) radical, and [cAAC_Me−H]⁺I⁻. In addition, the reaction of the NHC–iodosilicon(I) dimer [I_Ar(I)Si:]₂ (I_Ar=:C{N(Ar)CH}₂) with 4 equiv of I_Me (:C{N(Me)CMe}₂), which proceeded through the formation of a silicon(I) radical intermediate, afforded [(I_Me)₂SiH]⁺I⁻ ( 2 ) comprising the first NHC–parent-silyliumylidene cation. Its further reaction with fluorobenzene afforded the C_Ar−H bond activation product [1-F-2-I_Me-C₆H₄]⁺I⁻ ( 3 ). The isolation of 2 and 3 confirmed the reaction mechanism for the formation of 1 . Compounds 1 – 3 were analyzed by EPR and NMR spectroscopy, DFT calculations, and X-ray crystallography.     

Krull–Schmidt reduction of principal bundles in arbitrary characteristic

Let M be an irreducible projective variety defined over an algebraically closed field k, and let E_G be a principal G-bundle over M, where G is a connected reductive linear algebraic group defined over k. We show that for E_G there is a naturally associated conjugacy class of Levi subgroups of G. Given a Levi subgroup H in this conjugacy class, the principal G-bundle E_G admits a reduction of structure group to H. Furthermore, this reduction is unique up to an automorphism of E_G.     

Selection rules and Raman spectrum of a molecule with a degenerate ground state and zero spin-orbit coupling: VCl4

Two interesting features can normally be expected in the Raman spectrum of a molecule with a degenerate electronic ground state (i) the contribution of asymmetric or even antisymmetric tensors to the Raman intensity (ii) lifting of the electronic degeneracy due to Jahn-Teller distortion. The experimental data and discussion on VCl₄, presented here, show that this molecule does not show any deviations in the Raman selection rules. Further, its Raman spectrum closely resembles that of TiCl₄ which also has T_d geometry but a nondegenerate singlet ground state. This suggests the absence of any static Jahn-Teller distortion in VCl₄. However, we have observed a broadening of the ν₂ band of VCl₄ over TiCl₄ and we attribute this to a possible dynamic Jahn-Teller splitting.