Convexity and the Average Curvature of Plane Curves

The average curvature of a rectifiable closed curve in R2 is its total absolute curvature divided by its length. If a rectifiable closed curve in R2 is contained in the interior of a convex set D then its average curvature is at least as large as the average curvature of the simple closed curve D which bounds the convex set.     

High-energy single-transverse-mode Q-switched fiber laser based on a multimode large-mode-area erbium-doped fiber

We demonstrate that appropriately designed doped multimode fibers provide robust single-mode output when used within a fiber laser cavity. Using a novel large-mode-area fiber, we demonstrate what we believe to be record single-mode (M(2) <1.2) pulse energies of >0.5 mJ from a Q -switched fiber laser and even higher pulse energies (as high as 0.85 mJ) with slightly compromised spatial-mode quality (M(2)<2.0) . This approach offers significant scope for extending the range of single-mode output powers and energies that are achievable from fiber-laser-amplifier systems.     

Interrogation of fiber grating sensor arrays with a wavelength-swept fiber laser

We demonstrate a novel application of a wavelength-swept fiber laser to fiber Bragg grating sensor-array interrogation. The laser provides high signal powers of >3 mW with <0.1-nm spectral resolution over a 28-nm wavelength span. Using time-interval counting, we demonstrate static-dynamic strain measurements with a resolution of 0.47mu? rms at a sampling rate of 250 Hz.     

Optical parametric oscillation in periodically poled lithium niobate driven by a diode-pumped Q-switched erbium fiber laser

We describe what is to our knowledge the first nanosecond periodically poled lithium niobate (PPLN) optical parametric oscillator (OPO) driven by a fiber laser. The source was frequency doubled by a PPLN sample before pumping a second, 20-mm-long, PPLN crystal. The OPO threshold was <10muJ, with pump depletions of as much as 45% and a tunable signal range of 945-1450 nm (1690-4450-nm idler range). We demonstrated 130-nm signal tuning by varying the pump wavelength and doubling crystal's temperature. Also, we achieved 15-nm tuning with all crystals at a constant temperature. The results demonstrate the potential of the fiber laser:PPLN combination for practical, versatile, and tunable sources.     

All-optical AND gate based on coupled gap-soliton formation in a fiber Bragg grating

We experimentally demonstrate an all-optical AND gate based on coupled gap-soliton formation in an apodized fiber Bragg grating. A switching contrast of better than 17 dB is obtained with an incident pulse peak power of 2.5 kW.     

An Inscribing Model for Random Polytopes

For convex bodies K with boundary in ℝ ^d , we explore random polytopes with vertices chosen along the boundary of K. In particular, we determine asymptotic properties of the volume of these random polytopes. We provide results concerning the variance and higher moments of this functional, as well as an analogous central limit theorem. The research of V.H. Vu was done under the support of A. Sloan Fellowship and an NSF Career Grant. The research of L. Wu is done while the author was at University of California San Diego.     

4,5-di(2-pyridyl)-1,2,3-triazolate: the elusive member of a family of bridging ligands that facilitate strong metal-metal interactions

The new click-adduct 4,5-di(2-pyridyl)-1,2,3-triazole acts as a doubly-chelating anionic bridging ligand that forms dinuclear ruthenium(II) complexes which exhibit strong metal-metal interactions.     

Optimisation of chemical protein cleavage for erythropoietin semi-synthesis using native chemical ligation

Selective protein cleavage at methionine residues is a useful method for the production of bacterially derived protein fragments containing an N-terminal cysteine residue required for native chemical ligation. Here we describe an optimised procedure for cyanogen bromide-mediated protein cleavage, and ligation of the resulting fragments to afford biologically active proteins.