Further observations on the variation with dielectric constant and thickness of the reflectance and phase change on reflection of films

Studies of the behaviour with ₁, ₂ and film thickness of the optical functions reflectance (R) and phase change on reflection (Φ_r) have previously been made for both very thin and very thick films. Abelès [J. Opt. Soc. Amer. 47 (1957) 473] has formulated equations for very thin films where functions of ₁ and ₂ are the coefficients of a power series of the optical thickness, x(2πd/λ) up to x², whilst in the case of very thick films (solids) the relationships between ₁ and ₂ can be represented in polar coordinates L and α by ₁=L cos α, ₂=L sin α where L_R=2y²₀W²(1+cos α−1/W²) [W=(1+R)/(1−R)] and L_Φr=2(y₀/ tan Φ_r)²(1−cos α+tan ² Φ_r) [Ward, Opt. and Laser Tech. 27 (1995) 125]. The present study is concerned with films of intermediate optical thicknesses (1.0<2πd/λ<solid) and has revealed that the polar-type relationships previously noted for solid materials are augmented by secondary structures of maxima and minima whose position and amplitude can be predicted by adapting the exact equations for R and Φ_r.     

Wavelength and temperature dependence properties of human blood-serum

For biological importance and general scientific interest, the present paper studies the physical properties dependent on wavelength and temperature, for six different samples of human blood-serum, at two different laser wavelengths (514.5 and 632.8 nm). The properties are described in terms of scalar quantities, viz. refractive index or optical permittivity, optical and dielectric dispersion. A modified and high accurate laser Mach–Zehnder interferometric technique is used for measurement of the refractive index (n) and its gradient with temperature (dn/dT). The values of n and dn/dT are applied to calculate the optical permittivity () and its gradient with temperature d/dT. The refractive properties such as the variation of n, , −dn/dT and, −d/dT as a functions of wavelengths are determined. On the other hand, the optical properties such as reflectance, transmittance and absorptance as a function of light incident angle, temperature and wavelength are studied. Additionally the following dielectric parameters are calculated: specific refractivity, specific dispersivity, polarizability per unit volume, wave impedance, volume expansion coefficient and the electric susceptibility.     

Contours of constant Δ and Ψ in the 2–4 plane for the ellipsometric functions

Contour graphs of ₂ vs ₄ for different film thicknesses and a range of angles of incidence have been plotted for the ellipsometric functions Δ and Ψ in both the reflection and transmission modes. In the case of reflection ellipsometry, when the plots for Δ_R and Ψ_R are superimposed, the two sets of contours cross nearly at right angles over a large part of the field, this being indicative of the high accuracy obtainable in using this technique to determine ₄ and ₂ and hence the optical constants, n and k, for the film material. The reflection ellipsometric technique is accurate over angles of incidence between 30° and 75° and for a range of film thicknesses between λ/30 and 5λ. Transmission ellipsometry is less useful, due to anomalies in both X_s and X_p where sudden phase changes of ±π occur in regions of interest. There is also the possibility of multiple solutions, although the use of a multiangle technique would enable the “correct” values to be more easily determined.     

Functionalization of multiwalled carbon nanotubes for reinforcing of poly(l-lactide-co--caprolactone) biodegradable copolymers

Up to now, synthetic polymers and biomacromolecules have been grafted or assembled onto the convex surface of carbon nanotubes (CNTs) via covalent bonds or chemisorptions. In this research, poly(l-lactide-co--caprolactone)-functionalized multiwalled carbon nanotubes (MWCNT-OH-g-PCLA)s are synthesized by in situ ring-opening copolymerization of l-lactide (LA) and -caprolactone (CL) using stannous octanoate and hydroxylated MWCNTs (MWCNT-OHs) as the initiating system. The pristine MWCNTs are modified to possess carboxyl groups and then hydroxyl groups. MWCNT-OHs are used as coinitiators to polymerize LA and CL by the surface-initiated ring-opening polymerization. The FT-IR spectra, SEM and TEM micrographs revealed that the PCLA grafted form the sidewall of MWCNTs strongly. The TGA analysis indicates that about 75 wt% of functionalized MWCNTs with PCLA belongs to grafted PCLA and the remaining 25 wt% to the initial MWCNT-OH.     

Multiscaling for classical nanosystems: Derivation of Smoluchowski & Fokker–Planck equations

Using multiscale analysis and methods of statistical physics, we show that a solution to the N-atom Liouville equation can be decomposed via an expansion in terms of a smallness parameter , wherein the long scale time behavior depends upon a reduced probability density that is a function of slow-evolving order parameters. This reduced probability density is shown to satisfy the Smoluchowski equation up to O(²) for a given range of initial conditions. Furthermore, under the additional assumption that the nanoparticle momentum evolves on a slow time scale, we show that this reduced probability density satisfies a Fokker–Planck equation up to O(²). This approach has applications to a broad range of problems in the nanosciences.     

Electric and magnetic losses and gains in determining the sign of refractive index

Within the framework of classic electromagnetic theories, we have studied the sign of refractive index of optical medias with the emphases on the roles of the electric and magnetic losses and gains. Starting from the Maxwell equations for an isotropic and homogeneous media, we have derived the general form of the complex refractive index and its relation with the complex electric permittivity and magnetic permeability, i.e. , in which the intrinsic electric and magnetic losses and gains are included as the imaginary parts of the complex permittivity and permeability, respectively, as  = _r + i_i and μ = μ_r + iμ_i. The electric and magnetic losses are present in all passive materials, which correspond, respectively, to the positive imaginary permittivity and permeability _i > 0 and μ_i > 0. The electric and magnetic gains are present in materials where external pumping sources enable the light to be amplified instead of attenuated, which correspond, respectively, to the negative imaginary permittivity and permeability _i < 0 and μ_i < 0. We have analyzed and determined uniquely the sign of the refractive index, for all possible combinations of the four parameters _r, μ_r, _i, and μ_i, in light of the relativistic causality. A causal solution requires that the wave impedance be positive Re{Z} > 0. We illustrate the results for all cases in tables of the sign of refractive index. One of the most important messages from the sign tables is that, apart from the well-known case where simultaneously  < 0 and μ < 0, there are other possibilities for the refractive index to be negative n < 0, for example, for _r < 0, μ_r > 0, _i > 0, and μ_i > 0, the refractive index is negative n < 0 provided μ_i/_i > μ_r/_r.     

High-Order Nonreflecting Boundary Conditions without High-Order Derivatives

A wave problem in an unbounded domain is often treated numerically by truncating the infinite domain via an artificial boundary , imposing a so-called nonreflecting boundary condition (NRBC) on , and then solving the problem numerically in the finite domain bounded by . A general approach is devised here to construct high-order local NRBCs with a symmetric structure and with only low (first- or second-) order spatial and/or temporal derivatives. This enables the practical use of NRBCs of arbitrarily high order. In the case of time-harmonic waves with finite element discretization, the approach yields a symmetric C⁰ finite element formulation in which standard elements can be employed. The general methodology is presented for both the time-harmonic case (Helmholtz equation) and the time-dependent case (the wave equation) and is demonstrated numerically in the former case.     

A rapid measurement of : The DECPMG sequence

The Driven-Equilibrium Carr–Purcell Meiboom–Gill (DECPMG) pulse sequence is a rapid method for obtaining the average ratio of longitudinal to transverse relaxation times T₁/T₂ as a function of T₂. Since this is a one-dimensional experiment, the T₁/T_2T2 ratio can be acquired, potentially, in just two scans; the second scan being a reference CPMG measurement. Conventionally, T₁/T₂ is determined from a two-dimensional T₁-T₂ relaxation correlation experiment. The method described here offers a significant reduction in experimental time without a reduction in signal-to-noise. The T₁/T₂ ratio is useful for comparing the behaviour of liquids in porous media. Here we demonstrate the application of the DECPMG sequence to the study of oil-bearing rocks by differentiating oil or water saturated rock cores, and by observing the relative strengths of surface interaction for water in two types of rock by measuring T₁/T₂ as a function of magnetic field strength.     

Asymmetric di-jet production in polarized hadronic collisions

Using the collinear QCD factorization approach, we study the single-transverse-spin dependent cross section Δσ(S) for the hadronic production of two jets of momenta P₁=P+q/2 and P₂=−P+q/2. We consider the kinematic region where the transverse components of the momentum vectors satisfy PqΛ_QCD. For the case of initial-state gluon radiation, we show that at the leading power in q/P and at the lowest non-trivial perturbative order, the dependence of Δσ(S) on q decouples from that on P, so that the cross section can be factorized into a hard part that is a function only of the single scale P, and into perturbatively generated transverse-momentum dependent (TMD) parton distributions with transverse momenta .     

Studies of the spin-Hamiltonian parameters, d–d transitions and defect structures for two tetragonal Cu centers in Ba2ZnF6:Cu crystal

Two theoretical methods, the perturbation theory method (PTM) and the complete diagonalization (of energy matrix) method (CDM), are applied to calculate the spin-Hamiltonian parameters (g-factors g, g and hyperfine structure constants A, A, obtained from electron paramagnetic resonance (EPR) spectra) and d–d transitions (obtained from optical spectra) for two tetragonal Cu²⁺ centers in Ba₂ZnF₆:Cu²⁺ crystals. The Cu²⁺(I) ion replaces the Zn²⁺ ion at tetragonally compressed octahedral coordination and has the ground state ²A₁(|d_z²), whereas the Cu²⁺(II) ion is at an interstitial site with a square-planar F⁻coordination and has the ground state ²B₂(|d_x²-y²). The calculated spin-Hamiltonian parameters and d–d transitions from the PTM and CDM coincide and are in reasonable agreement with the experimental values. This suggests that both methods are effective for the theoretical studies of EPR and optical spectral data for 3d⁹ ions in tetragonal symmetry with different ground states. The defect structures of the two Cu²⁺ centers in Ba₂ZnF₆:Cu²⁺ are also estimated.     

Dielectric/piezoelectric properties and temperature dependence of domain structure evolution in lead free single crystal

(K_0.5Na_0.5)NbO₃ (KNN) single crystals were grown using a high temperature flux method. The dielectric permittivity was measured as a function of temperature for [001]-oriented KNN single crystals. The ferroelectric phase transition temperatures, including the rhombohedral–orthorhombic T_R−O, orthorhombic–tetragonal T_O−T and tetragonal–cubic T_C were found to be located at −149  C, 205 C and 393 C, respectively. The domain structure evolution with an increasing temperature in [001]-oriented KNN single crystal was observed using polarized light microscopy (PLM), where three distinguished changes of the domain structures were found to occur at −150  C, 213 C and 400 C, corresponding to the three phase transition temperatures.     

The extraction of total cross section from

We report on the first measurement of the differential cross section of -meson photoproduction for the d(γ,pK⁺K⁻)n exclusive reaction channel. The experiment was performed using a tagged-photon beam and the CEBAF Large Acceptance Spectrometer (CLAS) at Jefferson Lab. A combined analysis using data from the d(γ,pK⁺K⁻)n channel and those from a previous publication on coherent production on the deuteron has been carried out to extract the −N total cross section, σ_N. The extracted −N total cross section favors a value above 20 mb. This value is larger than the value extracted using vector-meson dominance models for photoproduction on the proton.     

A Roe Scheme for Ideal MHD Equations on 2D Adaptively Refined Triangular Grids

In this paper we present a second order finite volume method for the resolution of the bidimensional ideal MHD equations on adaptively refined triangular meshes. Our numerical flux function is based on a multidimensional extension of the Roe scheme proposed by Cargo and Gallice for the 1D MHD system. If the mesh is only composed of triangles, our scheme is proved to be weakly consistent with the condition …B=0. This property fails on a cartesian grid. The efficiency of our refinement procedure is shown on 2D MHD shock capturing simulations. Numerical results are compared in case of the interaction of a supersonic plasma with a cylinder on the adapted grid and several non-refined grids. We also present a mass loading simulation which corresponds to a 2D version of the interaction between the solar wind and a comet.     

Velocity of electroweak bubble walls

We study the velocity of bubble walls in the electroweak phase transition. For several extensions of the Standard Model, we estimate the friction and calculate the wall velocity, taking into account the hydrodynamics. We find that deflagrations are generally more likely than detonations. Nevertheless, for models with extra bosons, which give a strongly first-order phase transition, the deflagration velocity is in general quite high, 0.1v_w0.6. Therefore, such phase transitions may produce an important signal of gravitational waves. On the other hand, models with extra fermions which are strongly coupled to the Higgs boson may provide a strongly first-order phase transition and small velocities, 10⁻²v_w10⁻¹, as required by electroweak baryogenesis.     

Enhancement of surface morphology and optical properties of nanocolumnar ZnO films

Nanocolumnar ZnO films were prepared by electrodeposition (ED) on a glass substrate covered with a conductive layer of thin oxide doped with fluorine (FTO). After deposition the samples were annealed in oxidizing or reducing atmosphere, at temperatures between 100 to 500 C, in order to follow the evolution of optical properties and morphology. The optical properties of these films were studied by means of photoluminescence spectroscopy (PL) and the morphology by scanning electron microscopy (SEM). Films annealed at 300 C exhibit a higher ultraviolet emission peak, originating from exciton transitions. A green band related to deep-level emission centered at 500 nm, shows a drastic increase at 500 C. These results are independent of the annealing atmosphere. An increase of coalescence is also observed after annealing at 500 C. These results are explained taking into account the contribution of different point defects.     

Improvement of cubic silicon carbide crystals grown from solution

Cubic-silicon carbide crystals have been grown from carbon-rich silicon solutions using the travelling-zone method. To improve the growth process, we investigated the effect of controlling more tightly some of the growth parameters. Using such improved growth conditions, our best sample is a 12 mm diameter and 3 mm long 3C–SiC crystal. It is grown on a (0001) 2 off, 6H–SiC seed and has 111-orientation. The low amount of silicon inclusions results in a reduced internal stress, which is demonstrated by the consideration of μ-Raman spectra collected at room temperature on a large number of samples.     

Transport properties of single crystal

Transport properties of BaNi₂P₂ single crystals prepared by high-pressure synthesis method have been investigated. The temperature dependence of the resistivity is that of a typical metal with the anisotropy ratio ρ/ρ of 6.3 and suggests that electron–phonon interaction dominates the scattering mechanism. We have also found that the Hall effect and the magnetoresistance can be explained by a two-carrier model which is consistent with a multiple-band structure with both hole and electron characters.     

Effects of linear birefringence inside sensing head upon bulk glass current sensors’ sensitivity

The effects of the linear birefringence inside a bulk glass current sensing element and the incident polarizing angle upon the performance of a bulk glass optical current sensor are derived and analyzed theoretically. The investigation results show that the linear birefringence will modify the scale factor of the system with a sample function; it can also affect the extent of the influence of the incident polarizing angle, at the same time. When the incident polarizing angle has some special values such as 0, 45, or 90, its effect on the system will be zero. These results might provide some useful reference to the researchers and designers of bulk glass optical current sensors.     

Critical Casimir amplitudes for n-component models with -symmetry breaking quadratic boundary terms

Euclidean n-component ⁴ theories whose Hamiltonians are O(n) symmetric except for quadratic symmetry breaking boundary terms are studied in the film geometry . The boundary terms imply the Robin boundary conditions at the boundary planes at z=0 and at z=L. Particular attention is paid to the cases in which m_j of the n variables associated with plane take the special value corresponding to critical enhancement while the remaining ones are larger and hence subcritically enhanced. Under these conditions, the semi-infinite system with boundary plane has a multicritical surface–bulk point, called m_j-special, at which an O(m_j) symmetric critical surface phase coexists with the O(n) symmetric bulk phase, provided d is sufficiently large. The L-dependent part of the reduced free energy per cross-section area behaves asymptotically as Δ_C/L^d−1 as L→∞ at the bulk critical point. The Casimir amplitudes Δ_C are determined for small =4−d in the general case where m_c,c components _α are critically enhanced at both boundary planes, m_c,D+m_D,c components are enhanced at one plane but satisfy asymptotic Dirichlet boundary conditions at the respective other, and the remaining m_D,D components satisfy asymptotic Dirichlet boundary conditions at both . Whenever m_c,c>0, the corresponding small- expansions involve, besides integer powers of , also fractional powers ^k/2 with k3 modulo powers of logarithms. Results to order ^3/2 are given for general values of m_c,c, m_c,D+m_D,c, and m_D,D. These are used to estimate the Casimir amplitudes Δ_C of the three-dimensional Heisenberg systems with surface spin anisotropies for the cases with (m_c,c,m_c,D+m_D,c)=(1,0), (0,1), and (1,1).     

Experimental and numerical investigation of the hetero-/homogeneous combustion of lean propane/air mixtures over platinum

The pure heterogeneous and the coupled hetero-/homogeneous combustion of fuel-lean propane/air mixtures over platinum have been investigated at pressures 1 bar  p  7 bar, fuel-to-air equivalence ratios 0.23  φ  0.43, and catalytic wall temperatures 723 K  T_w  1286 K. Experiments were performed in an optically accessible catalytic channel-flow reactor and involved 1-D Raman measurements of major gas-phase species concentrations across the reactor boundary layer for the assessment of catalytic fuel conversion and planar laser induced fluorescence (LIF) of the OH radical for the determination of homogeneous ignition. Numerical predictions were carried out with a 2-D elliptic CFD code that included a one-step catalytic reaction for the total oxidation of propane on Pt, an elementary C₃ gas-phase chemical reaction mechanism, and detailed transport. A global catalytic reaction step valid over the entire pressure–temperature-equivalence ratio parameter range has been established, which revealed a p^0.75 dependence of the catalytic reactivity on pressure. The aforementioned global catalytic step was further coupled to a detailed gas-phase reaction mechanism in order to simulate homogeneous ignition characteristics in the channel-flow reactor. The predictions reproduced within 10% the measured homogeneous ignition distances at pressures p  5 bar, while at p = 7 bar the simulations overpredicted the measurements by 19%. The overall model performance suggests that the employed hetero-/homogeneous chemical reaction schemes are suitable for the design of propane-fueled catalytic microreactors.