Tuning quadratic nonlinear photonic crystal fibers for zero group-velocity mismatch

We consider an index-guiding silica photonic crystal fiber with a triangular hole pattern and a periodically poled quadratic nonlinearity. By tuning the pitch and the relative hole size, second-harmonic generation with zero group-velocity mismatch is found for any fundamental wavelength above 780 nm. The nonlinear strength is optimized when the fundamental has maximum confinement in the core. The conversion bandwidth allows for femtosecond-pulse conversion, and 4%-180%W(-1)cm(-2) relative efficiencies were found.     

On convergence of wavelet packet expansions

It is well known that the-Walsh-Fourier expansion of a function from the block space ([0, 1 ) ), 1 ＜q≤∞, converges pointwise a.e. We prove that the same result is true for the expansion of a function from in certain periodixed smooth periodic non-stationary wavelet packets bases based on the Haar filters. We also consider wavelet packets based on the Shannon filters and show that the expansion of Lp-functions, 1＜p＜∞, converges in norm and pointwise almost everywhere.     

Imaging and quantifying transverse flow velocity with the Doppler bandwidth in a phase-resolved functional optical coherence tomography

The Doppler bandwidth extracted from the standard deviation of the frequency shift in phase-resolved functional optical coherence tomography (F-OCT) was used to image the velocity component that is transverse to the optical probing beam. It was found that above a certain threshold level the Doppler bandwidth is a linear function of flow velocity and that the effective numerical aperture of the optical objective in the sample arm determines the slope of this dependence. The Doppler bandwidth permits accurate measurement of flow velocity without the need for precise determination of flow direction when the Doppler flow angle is within +/-15 degrees perpendicular to the probing beam. Such an approach extends the dynamic range of flow velocity measurements obtained with the phase-resolved F-OCT.     

Investigation of Brillouin effects in small-core holey optical fiber: lasing and scattering

We demonstrate for what is believed to be the first time a Brillouin laser based on a holey fiber (HF). Using a simple Fabry-Perot resonator scheme containing a 73.5-m-long highly nonlinear HF with an effective area of 2.85 microm(2) , we obtain a threshold of 125 mW and a slope efficiency of ~70% . Stimulated and spontaneous Brillouin scattering effects are investigated in the HF, and we show that the high lasing threshold is due mainly to reduction of the effective gain coefficient caused by structural nonuniformity along the fiber length.     

Fiber Bragg gratings for pure dispersion-slope compensation

Single-fiber Bragg gratings designed to compensate for pure third-order dispersion are demonstrated. The devices are designed by use of a layer-peeling inverse-scattering technique and exhibit dispersion profiles across their reflection bandwidths of -20, +/- 40, and -225 ps/nm2 over bandwidths of 4.5, 6, and 3 nm, respectively. Furthermore, they have almost constant peak reflectivities of approximately 75% and are, respectively, only 8, 23, and 40 mm long.     

Synthesis of linear and tripoidal oligo(phenylene ethynylene)-based building blocks for application in modular DNA-programmed assembly

Rigid linear and tripoidal organic modules based on the oligo(phenylene ethynylene) backbone having salicylaldehyde-derived termini are synthesized. A highly functionalized 5-iodosalicyl aldehyde was prepared and coupled to each ethynyl group of 1,4-diethynylbenzene or 1,3,5-triethynylbenzene in Sonogashira couplings. The two or three termini of the compounds are functionalized for incorporation in linear and branched oligonucleotide strands. For the linear module (LM), the two termini are equipped with amide spacers, and one of these was functionalized with a DMTr (dimethoxytrityl)-protected hydroxy group and the other with a phosphoramidite. One of the tripoidal modules is prepared with DMTr groups in two of its three termini. A tripoidal module is also synthesized with three different groups on its hydroxy termini: a phosphoramidite, a DMTr group, and an Fmoc group. Extended studies have shown that these rigid linear and tripoidal organic modules can be incorporated into short oligonucleotides. Several of these modules can be applied for DNA-directed assembly and covalent coupling into structures of predetermined connectivity. Such structures have potential application for molecular electronics and nanotechnology.     

Nonlinear Approximation with Dictionaries I. Direct Estimates

We study various approximation classes associated with m-term approximation by elements from a (possibly redundant) dictionary in a Banach space. The standard approximation class associated with the best m-term approximation is compared to new classes defined by considering m-term approximation with algorithmic constraints: thresholding and Chebychev approximation classes are studied, respectively. We consider embeddings of the Jackson type (direct estimates) of sparsity spaces into the mentioned approximation classes. General direct estimates are based on the geometry of the Banach space, and we prove that assuming a certain structure of the dictionary is sufficient and (almost) necessary to obtain stronger results. We give examples of classical dictionaries in L^p spaces and modulation spaces where our results recover some known Jackson type estimates, and discuss some new estimates they provide.     

The topology of interbank payment flows

We explore the network topology of the interbank payments transferred between commercial banks over the Fedwire^®${}^{\circledR }$ Funds Service. We find that the network has both a low average path length and low connectivity. The network includes a tightly connected core of banks to which most other banks connect. The degree distribution is scale free over a substantial range. We find that the properties of the network changed considerably in the immediate aftermath of the events of September 11, 2001.     

A thermally stable Pt/Y-based metal-organic framework: Exploring the accessibility of the metal centers with spectroscopic methods using H2O, CH3OH, and CH3CN as probes

A metal-organic framework (MOF) based on Pt, Y, and 2,2'-bipyridine-5,5'-dicarboxylate (BPDC), stable up to 400 degrees C, has been synthesized and characterized. In this MOF, the Pt centers are coordinated to Cl and the N atoms of the BPDC unit, giving a local environment similar to that found in a series of Pt-organic complexes with catalytic activity toward C-H bond cleavage of alkanes. This new material is a heterogeneous counterpart to the corresponding metal-organic complex. The structure, determined by single-crystal XRD data, is the repetition of three covalently bonded layers. These layers form a block, which is stacking as an (a)(b)(c) sequence along the crystallographic b-axis. Each layer contains the Pt-organic unit, while Y atoms represent the connection between adjacent layers. No covalent connection is present between layer (a) of a block and layer (c) of an adjacent block. EXAFS (BM29 at the ESRF) analysis supports the XRD data. As this MOF crystallizes under hydrothermal conditions, water acts both as solvent and as a direct ligand of Y. Accessibility to the metal centers is demonstrated by reversible water desorption/readsorption, as determined by TPA/TPD, FTIR, UV-vis, EXAFS, and XANES. Importantly, the results show that the as-synthesized material will not suffer a permanent loss in porosity upon solvent removal. In addition to water, methanol, ethanol, and acetonitrile can also access the internal void of the dehydrated phase.