Multimode polarization degree of mixture optical states in integrated directional couplers

Mixture multimode optical field classical states propagating in N?×?N integrated directional couplers are analyzed by using the density matrix formalism in a N-dimensional optical space. These mutimode optical fields present a kind of generalized polarization and accordingly a definition of a multimode polarization degree is proposed. It is based on the distance measure between a mixture state and an unpolarized state in a N-dimensional optical space so that in the case N=2 the standard polarization degree is recovered. It is shown that directional couplers can reduce or increase remarkably the multimode polarization degree of a mixture state. Likewise a simple measurement technique, based on Y junctions, of this multimode polarization degree is proposed. Finally all the results can be formally extended to the special case of multimode single photon quantum states.     

Simultaneous measurement of normal force and electrical resistance during isothermal crystallization for carbon black filled high-density polyethylene

The kinetics of isothermal crystallization for high-density polyethylene (HDPE) containing different volume fraction (Φ) of carbon black (CB) have been evaluated by using differential scanning calorimetry (DSC) at 123, 124, and 125 °C where the rate of crystallization is moderate. Simultaneous measurement of normal force (F _N) and electrical resistance (R) has been performed to probe the process of isothermal crystallization at strain zero. Results reveal that, at the early stage of crystallization, F _N is almost independent of time (t) while relative resistance (R/R ₀) changes slightly with increasing time t. However, a significant increment in F _N and a remarkable change in R/R ₀ can be observed at the same critical time (t _c), and the value of t _c is dependent on the crystallization temperature and CB content, which is available for describing the isothermal crystallization as a characteristic parameter. It is found that t _c is greater than induction time of crystallization (t ₀) due to the less sensitivity of mechanical and electrical responses than enthalpy to the structural changes in the composites. It is suggested that mechanical and electrical simultaneous measurement endows us a novel approach to probing the formation of percolation network involving in crystallization of polymer matrix.     

Concurrent Cholesky factorization of positive definite banded Hermitian-matrices

First the Cholesky factorization is extended to cover uniformly partitioned banded positive definite matrices of rank n which may be real symmetric or Hermitian. Then two stratagems are given for the use of the algorithm in concurrent machines where the number of processing elements is less than required to factor the matrix in as few serial steps as possible, and where uniformly high efficiency is expected from all processing elements. Expressions are given for the efficiency factor e appearing in the speed-up expression g = eN, and these are specialized for the N node hypercube machine as a function of partition size s, the number N of processing elements of the hypercube machine, and the cost μ of interelement transmission relative to computation. It is shown that efficiency factor e is inversely proportional to μ/s, and that e is almost independent of N when N is large and μ/s = 0. The task is completed in n/s serial steps with no limit on n. The half bandwidth b of the matrix is 2Ns.     

Structure and photochromism of polyoxometalates nanoparticles in cross-linked polymer networks

Cross-linked polymer (P(VP-MB)) based on N-vinylpyrrolidone (VP) and N, N′-methylene-bis-acrylamide (MB) was used as polymer matrix to construct photochromic nanocomposite thin films with entrapping the Keggin-type polyoxometalates (POM). The microstructure, photochromic behavior, and mechanism of the films were studied with transmission electron microscopy (TEM), Fourier transform infrared spectroscopy (FT-IR), ultraviolet-visible spectra (UV-vis), and electron resonance spectra (ESR). The transparent films changed from colorless to blue under UV irradiation. The films showed good reversible photochromism and could recover the colorless state gradually in the air, where oxygen plays an important role during the bleaching process. The heteropolyanions dispersed in composite films uniformly and exhibited strong coulombic interaction with cross-linked polymer. Composite films contained molybdenum had higher photochromic efficiency and slower bleaching reaction than films contained tungsten. According to ESR, the photochromic mechanism was followed by charge-transfer happened between POM and cross-linked polymer.     

Evolution of an N-level system via automated vectorization of the Liouville equations and application to optically controlled polarization rotation

The Liouville equation governing the evolution of the density matrix for an atomic/molecular system is expressed in terms of a commutator between the density matrix and the Hamiltonian, along with terms that account for decay and redistribution. To find solutions of this equation, it is convenient first to reformulate the Liouville equation by defining a vector corresponding to the elements of the density operator, and determining the corresponding time-evolution matrix. For a system of N energy levels, the size of the evolution matrix is N^2?×^?N². When N is very large, evaluating the elements of these matrices becomes very cumbersome. We describe a novel algorithm that can produce the evolution matrix in an automated fashion for an arbitrary value of N. As a non-trivial example, we apply this algorithm to a 15-level atomic system used for producing optically controlled polarization rotation. We also point out how such a code can be extended for use in an atomic system with arbitrary number of energy levels.     

Synthesis, characterization and fluorescence property of CdS/P(N-iPAAm) nanocomposites

A novel nanocomposite in which CdS nanoparticles were embedded in poly(N-isopropylacrylamide) (P(N-iPAAm)) matrix have been fabricated. The particle size of CdS nanoparticles ranged from 10 nm to 40 nm could be adjusted with the varying of the inorganic contents. The nanocomposites have been characterized by X-ray diffraction (XRD), transmission electron microscope (TEM), thermo-gravimetric analysis (TGA), high resolution transmission electron microscope (HRTEM), UV-vis absorption and fluorescence spectra (FLS) measurements. The cell volume of CdS nanoparticles embedded in polymer matrix was smaller than the standard value and the nanocomposites with 12.0% inorganic content showed a good fluorescence property.     

Solid-phase extractant with dipicolinic acid N,N’-diethyl-N,N’-di(p-tolyl)diamide for preconcentration and separation of actinides and lanthanides

The sorption ability of a solid-phase extractant with dipicolinic acid N,N’-diethyl-N,N’-di(p-tolyl) diamide groups on fibrous polyacrylonitrile (PAN) matrix was studied. The conditions for immobilization of the reagent on PAN disks were determined, and the possibility of sorption preconcentration and separation of U(VI), Pu(IV), Am(III), and Eu(III) from 2–6 M HNO₃ solutions was examined. The solid-phase extractant obtained exhibits good kinetic properties and can be used for separation of Am(III) + EU(III).     

n-Fold Polarization Measures and Associated Thermodynamic Entropy of N Partially Coherent Pencils of Radiation

An n-fold (n=2,…,N) measure of the degree of polarization associated with an N×N coherency matrix characterizing N pencils of radiation is discussed. The measure is cast in terms of the N possible scalar invariants of the coherency matrix and automatically takes into account possible rank deficiency. When N = 2, the single polarization measure reduces to the usual expression for polarization as the fraction of the intensity contained in the polarized component. The N = 3 case is discussed as an illustrative example, with special reference to the rank deficiency of a plane wave arbitrarily oriented with respect to the given coordinate system. Finally, these results are used to redevelop von Laue's theory of the thermodynamic entropy of partially coherent pencils of radiation.     

Preparation,characterization and photocatalytic properties of nanoplate Bi<Subscript>2</Subscript>MoO<Subscript>6</Subscript> catalysts

Bismuth molybdate (Bi₂MoO₆) nanoplates have been successfully synthesized by a simple hydrothermal process. The nanoplates were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), Raman spectroscopy, and IR spectroscopy. The effects of hydrothermal temperature and reaction time on the structures and morphologies of the nanoplates were investigated. On the basis of TEM observation of time series samples, a possible formation mechanism of the nanoplates was proposed. Optical absorption experiments revealed that Bi₂MoO₆ nanoplates had absorption in visible-light region, but a blue shift appeared compared with the corresponding bulk materials. Photocatalytic experiments showed that the nanoplates exhibited good photocatalytic activities for degradation of N,N,N′,N′-tetraethylated rhodamine (RhB) under visible-light irradiation (λ > 420 nm).     

Development and characterisation of SiAlON composites with TiB2, TiN, TiC and TiCN

30 vol% of TiB₂, TiCN, TiN or TiC was added to a sialon matrix with an X-phase sialon (Si₁₂Al₁₈O₃₉N₈) and an Al₂O₃–Si₃N₄ (77/23 wt%) starting powder composition and hot pressed at 1650°C in vacuum. The microstructures of the obtained composites were characterised by means of X-ray diffraction and electron microscopy, and the mechanical properties; E-modulus, hardness, bending strength and fracture toughness were measured and evaluated.Fully dense composites with an X-phase sialon or a polyphase Al₂O₃–-sialon–X-sialon matrix with 30 vol% of TiB₂, TiN and TiCN were obtained. TiC, added as a dispersed phase, however reacts with the nitrogen from the Si₃N₄ during liquid phase sintering, with the formation of TiC_1–x N _x , SiC and a changed sialon matrix composition. In the case of the X-phase sialon starting composition, a mullite matrix is obtained after sintering. The microstructural observations with respect to the sialon-TiC composites are found to be in agreement with the thermodynamic calculations.