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.     

Surface morphology and composition of c-, a- and m-sapphire surfaces in O2 and H2 environments

This paper reports that monitoring the composition of the c(0 0 0 1), a(11–20) and m(10–10) sapphire surfaces is essential for a proper interpretation of the surface morphologies obtained after annealing at 1253 and 1473 K in ArH₂ or ArO₂ atmospheres. Our experimental investigations, which have used Auger electron spectroscopy (AES) and atomic force microscopy (AFM) on the surfaces of 99.99% pure sapphire wafers, have led to the following original conclusions: (i) Calcium segregates at the c-surface of sapphire both under ArO₂ and ArH₂. (ii) Potassium adsorption enhances the kinetics of step-bunching on the c-surface under ArO₂. (iii) The step edges on the a-surface may develop a comb-like morphology made of parallel strips along the [10–10] direction. (iv) At 1253 K, clean m-surfaces may be stable. (v) Under ArH₂, alumina surface diffusion is much slower than under ArO₂ for all surface orientations, the surface concentration of impurities is low, and the Al–O ratio of the AES signals at the surface is significantly larger.     

Modified Kolmogorov wave turbulence in QCD matched onto “Bottom-up” thermalization

We investigate modification of Kolmogorov wave turbulence in QCD calculating gluon spectra as functions of time in the presence of a low energy source which feeds in energy density in the infrared region at a time-dependent rate. Then considering the picture of saturation constraints as has been constructed in the “bottom-up” thermalization approach we revisit that picture for RHIC center-mass energy, W=130 GeV, and also extend it to LHC center-mass energy, W=5500 GeV, thus for two cases having an opportunity to calculate the equilibration time, τ_eq|therm, of the gluon system produced in a central heavy ion collision at mid-rapidity region. Thereby, at RHIC and LHC energies we can match the equilibration time, obtained from the late stage gluon spectrum of the modified Kolmogorov wave turbulence, onto that of the “bottom-up” thermalization and other evolutional approaches as well. In addition, from the revised “bottom-up” approach we find the gluon liberation coefficient to be on the average, ε0.81–1.06 at RHIC and ε0.50–0.56 at LHC. We also present other phenomenological estimates of τ_therm which, at QCD realistic couplings, yield 0.45–0.65 fmτ_therm0.97–2.72 fm at RHIC and 0.31–0.40 fmτ_therm0.86–2.04 fm at LHC. We show that the second upper-bounds of τ_therm in both cases are due to the late stage gluon spectrum of the original Kolmogorov wave turbulence in QCD, previously deduced with a low energy source which feeds in energy density at a constant rate. On the other hand, the lower-bounds and first upper-bounds of τ_therm are due to the late stage gluon spectrum of the modified QCD wave turbulence, deduced here at the specific time-dependent rate. In the latter case, at certain conditions, taking also into account both very small and realistic couplings we give estimates: 0.65 fmτ_therm1.29 fm at RHIC and 0.52 fmτ_therm1.16 fm at LHC, as well as at realistic couplings we find 0.53<τ_therm<0.7 fm at RHIC and 0.41<τ_therm<0.65 fm at LHC.     

Stimulated emission at the second order stop-zone edge of the two-dimensional opal–zinc oxide photonic crystal

The fabrication of the 2D periodic structures in ZnO thin films by magnetron sputtering on the opal matrices was developed. The microstructures were characterized by AFM and SEM. The spontaneous and stimulated emissions of the ZnO layers on opal were studied at N₂ laser excitation (λ = 337 nm). The stimulated emission near 397 nm was observed at room temperature from ZnO–opal structure. The threshold of the electron–hole plasma recombination laser process was 300 kW/cm² for this structure. This threshold is two orders of magnitude smaller of that one for the flat ZnO–SiO₂ films owing to DFB resonator effect in 2D structure.     

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.     

Tunneling conductance in a gapped graphene-based superconducting structure: Case of massive Dirac electrons

The tunneling conductance in a NG/SG graphene junction in which the graphene was grown on a SiC substrate is simulated. The carriers in the normal graphene (NG) and the superconducting graphene (SG) are treated as massive relativistic particles. It is assumed that the Fermi energy in the NG and SG are E_FN400 meV and E_FS400 meV+U, respectively. Here U is the electrostatic potential from the superconducting gate electrode. It is seen that the Klein tunneling disappears in the case where a gap exist in the energy spectrum. As U→∞, the zero bias normalized conductance becomes persistent at a minimal value of G/G₀1.2. The normalized conductance G/G₀ is found to depend linearly on U with constant slope of , where is the size of the gap Δ opening up in the energy spectrum of the graphene grown on the SiC substrate. It is found that G/G₀2+αU for potentials in the range −270 meV<U<0 meV and G=0 for potentials U<−270 meV. As α→∞, the conductance for eV=Δ (V is the bias voltage placed across the NG/SG junction) can be approximated by a unit step function G(eV=Δ,U)/G₀2Θ(U). This last behavior indicates that a NG/SG junction made with gapped graphene could be used as a nano switch having excellent characteristics.     

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.     

Electron drag in intermediate magnetic fields with low electron density

Electron drag between two two-dimensional electron systems has been measured in intermediate magnetic fields (/τ<ω_ck_BT) with a relatively low electron density. We explore, in this sample, the unusual increase of drag in intermediate magnetic fields which was well characterized by a nearly temperature independent B³ dependence. The anomalous behavior of electron drag observed in higher density samples is found to persist for low sample density.     

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 .     

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.     

Stability of soliton lattice phase in the bilayer quantum Hall state under tilted magnetic fields

The bilayer quantum Hall (QH) state at the filling factor ν=1 shows various fascinating quantum phenomena due to the layer degree of freedom called ‘pseudospin’. We report an experimental evidence of the soliton lattice (SL) phase, which is a domain structure of pseudospin, by the appearance of a local maximum of magnetoresistance near the ν=1 QH state. We investigate the stability of the SL phase by changing B and the total electron density n_T. Detailed magnetotransport measurements under tilted magnetic fields were carried out to obtain a B–n_T plane phase diagram containing the C, IC and SL phases. We found the SL phase is only stable at low n_T region. Namely, the C–SL–IC phase transition occurs only at low n_T region as B increases. On the contrary, the C–IC phase transition directly occurs without passing through the SL phase at high n_T region.     

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).     

Entanglement evolution of a two-qubit system interacting with a quantum spin environment

We investigate the entanglement dynamics and decoherence of a two-qubit system under a quantum spin environment at finite temperature in the thermodynamics limit. For the case under study, we find different initial states will result in different entanglement evolution, what deserves mentioning here is that the state |Ψ=cosα|01+sinα|10 is most robust than other states when π/2<α<π, since the entanglement remains unchanged or increased under the spin environment. In addition, we also find the anisotropy parameter Δ can suppress the destruction of decoherence induced by the environment, and the undesirable entanglement sudden death arising from the process of entanglement evolution can be efficiently controlled by the inhomogeneous magnetic field ζ.     

Interband absorption and luminescence in small quantum dots under strong magnetic fields

Interband absorption and luminescence of quasi-two-dimensional, circularly symmetric, N_e-electron quantum dots are studied at high magnetic fields, 8B60 T, and low temperatures, T2 K. In the N_e=0 and 1 dots, the initial and final states of such processes are fixed, and thus the dependence on B of peak intensities is monotonic. For larger systems, ground state rearrangements with varying magnetic field lead to substantial modifications of the absorption and luminescence spectra. Collective effects are seen in the N_e=2 and 3 dots at “filling fractions” and .     

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.     

Scanning tunneling microscopy/spectroscopy on multi-layered cuprate superconductor Ba2Ca5Cu6O12 (O1−x Fx)2

Scanning tunneling microscopy/spectroscopy (STM/STS) measurements on multi-layered cuprate superconductor Ba₂Ca₅Cu₆O₁₂ (O_1−x F_x)₂ are carried out. STM topographies show randomly distributed bright spot structures with a typical spot size of 0.8 nm. These bright spots are occupied about 28% per one unit cell of c-plane, which is comparable to the regular amount of apical oxygen of 20% obtained from element analysis. Tunneling spectra simultaneously show both the small and the large gap structures. These gap sizes at 4.9 K are about Δ 15 meV and 90 meV, respectively. The small gap structure disappears at the temperature close to T_C, while the large gap persists up to 200 K. Therefore, these features correspond to the superconducting gap and pseudogap, respectively. These facts give evidence for some ordered state with large energy scale even in the superconducting state. For the superconducting gap, the ratio of 2Δ/K_BT_C = 4.9 is obtained with T_C = 70 K, which is determined from temperature dependence of the tunneling spectra.     

Far-field properties and beam quality of vectorial Hermite–Laguerre–Gaussian beams beyond the paraxial approximation

The far-field properties and beam quality of vectorial nonparaxial Hermite–Laguerre–Gaussian (HLG) beams are studied in detail, where, instead of the second-order-moments-based M² factor, the extended power in the bucket (PIB) and βparameter are used to characterize the beam quality in the far field and the intensity in the formulae is replaced by the z component of the time-averaged Poynting vector S_z. It is found that the S_z PIB and βparameter of vectorial nonparaxial HLG beams depend on the mode indices n, m, αparameter and waist-width-to-wavelength ratio w₀/λ and the PIB and βparameter are additionally dependent on the bucket's size taken.     

On the theory of temporal aberrations for cathode lenses

A new approach to the theory of temporal aberration for cathode lenses is given in the present paper. A definition of temporal aberration is given in which a certain initial energy of electron emission along the axial direction ε_z1 (0ε_z1ε_0max) is considered. A new method to calculate the temporal aberration coefficients of cathode lenses named “direct integral method” is also presented. The “direct integral method” gives new expressions of the temporal aberration coefficients which are expressed in integral forms. The difference between “direct integral method” and “τ-variation method” is that the “τ-variation method” needs to solve the differential equations for the three of temporal geometrical aberration coefficients of second order, while the “direct integral method” only needs to carry out the integral calculation for all of these temporal aberration coefficients of second order.All of the formulae of the temporal aberration coefficients deduced from “direct integral method” and “τ-variation method” have been verified by an electrostatic concentric spherical system model, and contrasted with the analytical solutions. Results show that these two methods have got identical solutions and the solutions of temporal aberration coefficients of the first and second order are the same as with the analytical solutions. Although some forms of the results seem different, but they can be transformed into the same form. Thus, it can be concluded these two methods given by us are equivalent and correct, but the “direct integral method” is related to solve integral equations, which is more convenient for computation and could be suggested for use in practical design.     

Generation of laser-polarized xenon using fiber-coupled laser-diode arrays narrowed with integrated volume holographic gratings

Volume holographic gratings (VHGs) can be exploited to narrow the spectral output of high-power laser-diode arrays (LDAs) by nearly an order of magnitude, permitting more efficient generation of laser-polarized noble gases for various applications. A 3-fold improvement in ¹²⁹Xe nuclear spin polarization, P_Xe, (compared to a conventional LDA) was achieved with the VHG-LDA’s center wavelength tuned to a wing of the Rb D₁ line. Additionally, an anomalous dependence of P_Xe on the xenon density within the OP cell is reported—including high P_Xe values (>10%) at high xenon partial pressures (1000 torr).     

Effect of Ca doping on the superconducting properties of GdBaSrCu3O7−δ bulk samples

Gd_1−xCa_xBaSrCu₃O_7−δ samples (0  x  0.1) were prepared via solid-state reaction. Four-point probes method was used for resistance versus temperature measurements. Results show decrease in T_c by increasing x content. This variation is assumed to be irrelevant to the different phases or impurity effects since X-ray patterns show all samples are tetragonal single-phase. Ca doping decreases the oxygen content and lattice parameters of the samples. It is suggested that Ca prevents the dislocation of oxygen, and then disrupts the hole concentration of the system and antiferromagnetic correlation at CuO₂ planes. Subsequently, destroys the superconductivity of the samples.