Frequency stabilization of a frequency-doubled 1556-nm source to the 5S(1/2) ? 5D (5/2) two-photon transitions of rubidium

Improvements in the power level of sources near 1550 nm and in the efficiency of waveguide frequency doublers enabled us to lock a frequency-doubled source directly to the 5S(1/2) ? 5D(5/2) two-photon transitions near 778 nm. We obtained a sufficiently powerful second-harmonic signal, exceeding 2 mW, by doubling an external-cavity diode laser that was amplified by an erbium-doped fiber amplifier in a periodically poled LiNbO(3) channel waveguide. Our experimental scheme can be used for realizing compact, high-performance frequency standards near 1550 nm for fiber-optic communication and sensing applications.     

Microstrain in hydroxyapatite carbon nanotube composites

Synchrotron radiation diffraction data were collected from hydroxyapatite–carbon nanotube bioceramic composites to determine the crystallite size and to measure changes in non‐uniform strain. Estimates of crystallite size and strain were determined by line‐profile fitting of discrete peaks and these were compared with a Rietveld whole‐pattern analysis. Overall the two analysis methods produced very similar numbers. In the commercial hydroxyapatite material, one reflection in particular, (0 2 3), has higher crystallite size and lower strain values in comparison with laboratory‐synthesized material. This could indicate preferential crystal growth in the [0 2 3] direction in the commercial material. From the measured strains in the pure material and the composite, there was a degree of bonding between the matrix and strengthening fibres. However, increasing the amount of carbon nanotubes in the composite has increased the strain in the material, which is undesirable for biomedical implant applications.     

Selective Lanthanides Sequestration Based on a Self‐Assembled Organosilica

In this paper, we investigate the cation‐exchange properties of a self‐assembled hybrid material towards trivalent ions, lanthanides (La³⁺, Eu³⁺, Gd³⁺, Yb³⁺) and Fe³⁺. The bis‐zwitterionic lamellar material was prepared by sol–gel process from only 3‐aminopropyltriethoxysilane (APTES), succinic anhydride, and ethylenediamine. In ethanol heated under reflux, the exchange ethylenediammonium versus Ln³⁺ proved to be complete by complexometry measurements and elemental analyses, one Cl^? ion per one Ln^III remaining as expected for charge balance. In aqueous solution at 20 °C, the material was found to be selective towards lanthanide in spite of the similarity of their ionic radii. The cation uptake depends on the nature of the salt, the difference between two lanthanides reaching up to 20 % in some cases. Finally, ion‐exchange reaction with FeCl₃ was chosen as a probe to get more information on the material after incorporation of trivalent ions. Based on Mössbauer spectroscopic investigations on the resulting material in conjunction with the XRD analysis of materials containing trivalent ions, a structural model was proposed to describe the incorporation of trivalent ions by exchange reaction within the original zwitterionic material.     

Signatures of non-Abelian statistics in nonlinear Coulomb blockade transport

Signatures of the non-Abelian statistics of quasiparticles in the ν=5/2 quantum Hall state are predicted to be present in the current-voltage characteristics of tunneling through one or two quantum Hall puddles of Landau filling ν(a) embedded in a bulk of filling ν(b) with (ν(a),ν(b))=(2,5/2) and (ν(a),ν(b))=(5/2,2).     

Adiabatic frequency conversion of ultrafast pulses

A new method for efficient, broadband sum and difference frequency generation of ultrafast pulses is demonstrated. The principles of the method follow from an analogy between frequency conversion and coherent optical excitation of a two-level system. For conversion of ultrafast pulses, the concepts of adiabatic conversion are developed further in order to account for dispersion and group velocity mismatch. The scheme was implemented using aperiodically poled nonlinear crystals and a single step nonlinear mixing process, leading to conversion of near-IR (∼790 nm) ultrafast pulses into the blue (∼450 nm) and mid-IR (∼3.15 μm) spectral regions. Conversion bandwidths up to 15 THz FWHM and efficiencies up to 50% are reported.     

Multiple coupling of surface plasmons in quasiperiodic gratings

Whereas periodic gratings enable us to couple light into a surface plasmon polariton only at a specific angle and wavelength, we show here that quasiperiodic gratings enable the coupling of light at multiple wavelengths and angles. The quasiperiodic grating can be designed in a systematic manner using the dual-grid method, thereby enabling us to control the coupling strength and grating dimensions. We verified the method experimentally by efficiently coupling light into a surface plasmon from several different illumination angles using a single quasiperiodic grating.     

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.     

Cubic symmetric polynomials yielding variations of the Erdős–Ginzburg–Ziv theorem

Let p be a prime and let $\varphi\in\mathbb{Z}_{p}[x_{1},x_{2},\ldots, x_{p}]$ be a symmetric polynomial, where  $\mathbb {Z}_{p}$ is the field of p elements. A sequence T in  $\mathbb {Z}_{p}$ of length p is called a φ-zero sequence if φ(T)=0; a sequence in $\mathbb {Z}_{p}$ is called a φ-zero free sequence if it does not contain any φ-zero subsequence. Motivated by the EGZ theorem for the prime p, we consider symmetric polynomials $\varphi\in \mathbb {Z}_{p}[x_{1},x_{2},\ldots, x_{p}]$ , which satisfy the following two conditions: (i) every sequence in  $\mathbb {Z}_{p}$ of length 2p?1 contains a φ-zero subsequence, and (ii) the φ-zero free sequences in  $\mathbb {Z}_{p}$ of maximal length are all those containing exactly two distinct elements, where each element appears p?1 times. In this paper, we determine all symmetric polynomials in $\mathbb {Z}_{p}[x_{1},x_{2},\ldots, x_{p}]$ of degree not exceeding 3 satisfying the conditions above.     

Counting commensurability classes of hyperbolic manifolds

Gromov and Piatetski-Shapiro proved existence of finite volume non-arithmetic hyperbolic manifolds of any given dimension. In dimension four and higher, we show that there are about v ^v such manifolds of volume at most v, considered up to commensurability. Since the number of arithmetic ones tends to be polynomial, almost all hyperbolic manifolds are non-arithmetic in an appropriate sense. Moreover, by restricting attention to non-compact manifolds, our result implies the same growth type for the number of quasi-isometry classes of lattices in SO(n, 1). Our method involves a geometric graph-of-spaces construction that relies on arithmetic properties of certain quadratic forms.