Effective dielectric constant of two-dimensional photonic crystals in optical bands

By using the Fourier expansion method, we have developed an approach to calculate the effective dielectric index of a two-dimensional photonic crystal. The approach is very general: it can take into account various Bravais lattice structure as well as arbitrary spatial variation of the dielectric index. It has been found that near a nondegenerate frequency ω_n(Γ) at Γ point, the transverse magnetic (TM) mode is ordinary, as it is independent of the propagation direction, whereas in general the transverse electric (TE) mode depends on the propagation direction, it is extraordinary. Therefore, a two-dimensional photonic crystal can always be described by an effective dielectric index for TM mode near the nondegenerate frequency ω_n(Γ). However, the TE mode is much more complicated unless the lattice structure is highly symmetric. Moreover, a two-dimensional square photonic crystal has been identified as an effective birefringent crystal having two negative refractive indexes from the perspective of Snell's law.     

Structural and phonon dynamical properties of perovskite manganites: (Tb, Dy, Ho)MnO3

A shell model has been used to study the structure, phonon dynamics and phase coexistence of perovskite manganites RMnO₃ (R=Tb, Dy, Ho). The calculated crystal structure, Raman and IR frequencies and specific heats are found to be in good agreement with the available experimental data. The phonon density of states, elastic constants, elastic stiffness, shear constants and phonon dispersion curves have been computed for these manganites. A zone center imaginary A_u mode is revealed in these phonon dispersion curves, which indicates the occurrence of the metastability of the perovskite phase. The Gibbs free energy values calculated as a function of temperature and pressure for RMnO₃ in the orthorhombic phase, when compared with those of the hexagonal phase, reveal the possibility of coexistence of these two phases in the present multiferroic manganites under ambient conditions.     

一种新型的多包层光子晶体光纤的分析方法

传统有效折射率方法只能模拟具有相同空气孔大小的单包层光子晶体光纤.针对这一问题,提出了一种改进的有效折射率法,能够计算具有不同孔径的多包层光子晶体光纤的传输特性.并用此方法对三包层光子晶体光纤的基模有效折射率和色散等特性进行了数值模拟,结果与多极法模拟出的结果符合得很好.这种改进的有效折射率法拓展了传统有效折射率法的适用范围,对快速准确地分析和设计具有不同传输特性的多包层光子晶体光纤提供了理论依据. 关键词： 光子晶体光纤 多包层 有效折射率方法 色散     

Comparative study on corona-generated audible noise and radio noise of ac long-term operating conductors with two bundle types

The corona-generated audible noise (AN) and radio noise (RN) of the long-term operating conductors with two bundle types was investigated and compared based on a corona cage measurement system. The surface morphologies of eight conductors were measured and the average surface roughness (R_a) was calculated. With the raise of conductor bundles, the maximum electric field distortion level (β₄), the relative difference of ionization intensity (γ₄) between long-term operating conductors and new conductors decreased. Adding the number of sub-conductors turned out to be an effective method to improve AN and RN of long-term operating conductors in the contaminated areas.     

Lattice dynamics and statistical mechanics of the Fm3m → I4/m structural phase transition in Rb2KInF6

The static and dynamic properties of cubic Rb₂KInF₆ crystals with elpasolite structure are calculated using a nonempirical method. Calculations are performed within a microscopic ionic-crystal model taking into account the deformation and polarization of ions. The deformation parameters of ions are determined by minimizing the total energy of the crystal. The calculated equilibrium lattice parameters agree satisfactorily with the experimental data. It is found that in the cubic phase there are vibrational modes that are unstable everywhere in the Brillouin zone. The eigenvectors of the unstablest mode at the center of the Brillouin zone of the cubic phase are associated with the displacements of F ions and correspond to rotations of InF₆ octahedra. Condensation of this mode leads to a tetragonal distortion of the structure. In order to describe the Fm3m → I4/m phase transition, an effective Hamiltonian is constructed under the assumption that the soft mode whose eigenvector corresponds to octahedron rotation is local and coupled with homogeneous elastic strains. The parameters of the effective Hamiltonian are determined using the calculated crystal energy for the distorted structures due to soft-mode condensation. The thermodynamic properties of the system with this model Hamiltonian are investigated using the Monte Carlo method. The phase transition temperature is calculated to be 550 K, which is twice its experimental value (283 K). The tetragonal phase remains stable down to T=0 K; the effective Hamiltonian used in this paper thus fails to describe the second phase transition (to the monoclinic phase). Thus, the transition to the tetragonal phase occurs for the most part through octahedron rotations; however, additional degrees of freedom, first of all, the displacements of Rb ions, should be included into the effective Hamiltonian in order to describe the transition to the monoclinic phase.     

Investigation of dispersion characteristic in MI- and MII-type single mode optical fibers

Dispersion characteristic of MI and MII type single mode optical fibers is analytically investigated. For this purpose modal analysis of these fibers to obtain possible wave vectors for given system parameters are done. Then using numerical evaluation of the presented analytical relations, chromatic and waveguide dispersions are calculated. The effects of geometrical and optical parameters of the fibers on dispersion characteristics are investigated. In this analysis, we show that with increase of Δ (optical parameter) for MI structure the slope of dispersion curve is decreased and the case is reversed for MII structure. Also, with rising of Q (geometric parameter) for MI structure the slope of dispersion curve is decreased and the situation is reversed for MII structure. Finally, we show that with boosting of R₂ for MII structure the slope of dispersion is increased. As a final result, our simulations show that small values for optical parameters are better in MII structure for multi-channel optical communications. In MI structure to obtain small dispersion slope, Q can be increased that is easy for fabrication in practice. Finally, Q and R₂ are suitable parameters for control of dispersion in the proposed structures.     

A re-evaluation of the heat capacity of cerium zirconate (Ce2Zr2O7)

The heat capacity of cerium zirconate pyrochlore, Ce₂Zr₂O₇, was measured from 0.4 to 305 K by hybrid adiabatic relaxation method for various magnetic field strengths. Magnetisation measurements were performed on the sample also. The results revealed a low-temperature anomaly that showed Schottky-type characteristics with increasing magnetic field strength. The estimated entropy due to the magnetic ordering of the two Ce³⁺ moments is 1.37R, close to the theoretical value for a doublet ground state (1.39R). The enthalpy increments relative to 298.15 K were measured by drop calorimetry from 531 to 1556 K. The obtained results significantly differ from those reported in the literature; the origin of the discrepancy is due to the probable oxidation of the pyrochlore structure into fluorite.     

Spin-injection efficiency and magnetoresistance in a hybrid ferromagnetic-semiconductor trilayer with interfacial barriers

We present a self-consistent model of spin transport in a ferromagnetic (FM)-semiconductor (SC)-FM trilayer structure with interfacial barriers at the FM-SC boundaries. The SC layer consists of a highly doped n²⁺ AlGaAs-GaAs 2DEG while the interfacial resistance is modeled as delta potential (δ) barriers. The self-consistent scheme combines a ballistic model of spin-dependent transmission across the δ-barriers, and a drift-diffusion model within the bulk of the trilayer. The interfacial resistance (R_I) values of the two junctions were found to be asymmetric despite the symmetry of the trilayer structure. Transport characteristics such as the asymmetry in R_I, spin-injection efficiency and magnetoresistance (MR) are calculated as a function of bulk conductivity σ_s and spin-diffusion length (SDL) within the SC layer. In general a large σ_s tends to improve all three characteristics, while a long SDL improves the MR ratio but reduces the spin-injection efficiency. These trends may be explained in terms of conductivity mismatch and spin accumulation either at the interfacial zones or within the bulk of the SC layer.     

Lattice dynamics, ferroelectric and antiferroeelctric instabilities, and the ferroelectric phase transition in disordered PbB′1/2B″1/2O3 (B′ = Ga, In, Lu; B″ = Nb, Ta) solid solutions

The lattice vibration spectra, rf permittivity, and dynamic Born charges of disordered PbB′_1/2B″_1/2O₃ (B′ = Ga, In, Lu; B″ = Nb, Ta) solid solutions are calculated in terms of the generalized Gordon-Kim model. All the compounds are found to have soft modes related to the center (Γ₁₅) and boundary point R (R ₁₅) of the Brillouin zone; the frequencies of these modes are close. The ferroelectric phase transition temperatures and the spontaneous polarization in the ferroelectric phase are calculated for the solid solutions using a model Hamiltonian in the local mode approximation and the Monte Carlo method. These temperatures for the tantalum compounds are found to be higher than for the niobium compounds, and temperature t _s increases with the atomic number of ion B′. A model where the antiferroelectric state is related to the condensation of modes Γ₁₅ and R ₁₅ is proposed. It is found that, for all compounds except for PbSc_1/2Nb_1/2O₃ and PbSc_1/2Ta_1/2O₃, the ferroelectric phase, which is only related to the condensation of mode R ₁₅, and the antiferroelectric phase have similar energies. In PbIn_1/2Ta_1/2O₃, the antiferroelectric phase turns out to be energetically favorable.     

Collective gyromagnetic ratio from density dependent hartree-fock calculations: (II). Odd nuclei

The collective gyromagnetic ratio and moment of inertia of deformed odd-proton and oddneutron axially symmetric nuclei have been calculated in the cranking approximation using wave functions obtained with the Skyrme force SIII. Good agreement with experiment is found for g_R. Our parameter-free cranking results are better than those of Prior, Boehm and Nilsson where effective charges were used. The cranking formula leads to better results than the projection method (in which one simply takes the expectation value of the relevant operator in the deformed HF ground state, neglecting corrections of relative order 1/〈J²〉. In particular, the cranking results follow nicely the exceptionally large/small g_R for the odd-proton/neutron nuclei around mass 153–167.     

The properties of two-dimensional photonic crystals bandgap structure with rhombus lattice

The relative bandgap ω_R of photonic crystals structure with rhombus lattice for both TE and TM modes is studied by the plane wave expansion method. Based on the analysis, a bending waveguide of U type can be easily obtained. The steady-state distribution of the electric field with ω = 0.4765(a/λ) of TM mode is given by FDTD method and the transmission is obtained by FFT of the time domain field. All of the sufficient analysis shows the conceptual framework of the proposed rhombus lattice PCs and its great potential application in photonic integration circuit.     

Structural instability in BaZrO3 crystals: Calculations and experiment

The phonon spectrum of cubic barium zirconate is calculated from first principles using the density functional theory. An unstable R ₂₅ phonon mode observed in the phonon spectrum indicates an instability of the BaZrO₃ structure with respect to the oxygen octahedra rotations. It is shown that the symmetry of the ground-state structure of the crystal is I4/mcm. The local structure of BaZrO₃ is studied by the EXAFS spectroscopy at the BaL _III absorption edge at 300 K to search for the instability predicted by calculations. Anomalously high values of the Debye-Waller factor for the Ba-O atomic pairs (σ ₁ ² ～ 0.015 Ų) are attributed to the appearance of this structural instability. The average amplitude of the octahedra rotations caused by thermal vibrations is estimated from the measured σ ₁ ² value to be ～4° at 300 K. The closeness of the calculated energies of various distorted phases resulting from the condensation of the R ₂₅ mode suggests a possible formation of the structural glass state in BaZrO₃ as the temperature is lowered. It explains the origin of the disagreement between the results of calculations and diffraction experiments.     

First-principles study of the structural properties and magnetism of R2CoIn8 (R=Y,Pr, Nd,and Dy) intermetallic compounds

The electronic structure of R₂CoIn₈ (R=Y, Pr, Nd, and Dy) intermetallic compounds is calculated from first principles based on the density functional theory (DFT). The Kohn–Sham single-particle equations of the DFT are solved using two independent computational methods, namely APW+lo and FPLO. First the structural properties of Y₂CoIn₈ are studied. Good agreement of calculated equilibrium volume and c/a ratio with the experimental data is found. Also we minimize the forces at equilibrium volume and calculate the symmetry-free structural parameters of the space group P4/mmm for Y₂CoIn₈. In Y₂CoIn₈, the Co 3d states are almost fully occupied and situated below the Fermi level. We applied the fixed-spin-moment method and a stable paramagnetic ground state for Y₂CoIn₈ was found. Finally, the crystal field (CF) parameters were calculated for R=Pr, Nd and Dy from first principles. The microscopic tetragonal CF Hamiltonian was diagonalized and the obtained eigenvalues and eigenfunctions were used to predict the anisotropy of the magnetic properties of R₂CoIn₈ single crystals.     

On the vacancy in a metal

The self-consistent calculations of spatial distributions of electrons and potentials in an isolated spherical cavity (with atomic radius R _WS) of the Wigner-Seitz cell, the energy of the vacancy formation, and the vacancy contribution to the electrical resistance have been performed in terms of the modified Kohn-Sham method and the stabilized jellium model. The energy shift of the ground state of electrons in the Wigner-Seitz cell with radius R _v ? R _WS (where R _v is the average distance between vacancies), the contribution of vacancies to the electron work function, and the effective mass of electrons have been found using the calculated phase shifts of the scattering wave functions and the representation of a system of vacancies as a “superlattice” in a metal.     

Design and fabrication of antireflective GaN subwavelength grating structures using periodic silica sphere monolayer array patterning

We designed and fabricated gallium nitride (GaN) subwavelength grating (SWG) structures on GaN/sapphire via patterning using the periodic silica sphere monolayer array as an etch mask and a subsequent dry etching for efficient antireflection coatings. Theoretical optimization of GaN SWG structures was performed in terms of their geometrical parameters by the rigorous coupled-wave analysis simulation using a theoretical structural model. The bullet-like parabola-shaped SWGs with a large height-to-diameter ratio (R _H/D) yielded good broadband and wide-angle antireflective surface properties. Considering the R _H/D, the GaN SWG structure using 320-nm silica spheres theoretically and experimentally exhibited the most efficient antireflection property because it provided a linearly graded effective refractive index profile with relatively long relaxation length. For various geometries of the fabricated GaN SWGs on GaN/sapphire, the calculated reflectance results showed a similar tendency with the experimental results.     

Design of highly birefringent chalcogenide glass PCF: A simplest design

In this article, a new simplified structure of a highly birefringent chalcogenide As₂Se₃ glass photonic crystal fiber (PCF) is designed and analyzed by using fully vectorial finite element method. The effective indices, confinement loss, birefringence, and chromatic dispersion of fundamental polarized mode are calculated in the proposed PCF for a wide wavelength range. To maintain the polarization in chalcogenide As₂Se₃ glass PCF, we enlarged two of the central air holes and reduced two transverse air holes for achieving high birefringence. This helps in creating an effective index difference between the two orthogonal polarization modes. It is also shown that As₂Se₃ glass PCF provides lower chromatic dispersion and less confinement loss compared to silica PCF of the same structure in wavelength range 1.3 to 1.8 μm and hence such chalcogenide As₂Se₃ glass PCF have high potential to be used in dispersion compensating and birefringence application in optical communication systems. In addition to this, the polarization mode dispersion (PMD) result of the proposed PCF is also reported.     

Theory of an Fm3m→I4/m structural phase transition in an Rb2KScF6 crystal

An Rb₂KScF₆ crystal having an elpasolite structure undergoes a sequence of Fm3m→I4/m→P12₁/n1 structural phase transitions where the transition to the tetragonal phase is associated with “rotation” of the ScF₆ octahedron. An effective Hamiltonian is constructed to describe the Fm3m→I4/m transition using the approximation of a local mode for which we selected a “soft mode” whose eigenvector corresponds to the rotation of the octahedron. The effective Hamiltonian also includes the relationship between the local mode and the homogeneous elastic strains. The parameters of the effective Hamiltonian were determined using the generalized Gordon-Kim model of an ionic crystal which allows for the deformability and polarizability of the ions. The thermodynamic properties of a system with this model Hamiltonian were investigated using the Monte Carlo method. The calculated phase transition temperature of 250 K is almost the same as the experimental value (252 K). The tetragonal phase remains stable as far as T=0 K and a second transition (to the monoclinic phase) cannot be obtained using this effective Hamiltonian. This suggests that if the transition to the tetragonal phase is mainly associated with “rotations” of the octahedrons, in order to describe the phase transition to the monoclinic phase the effective Hamiltonian must allow for additional degrees of freedom mainly associated with the motion of rubidium ions.     

Modulation spectroscopy on metamorphic InAs quantum dots

The modulation spectroscopy on 1.45 μm metamorphic InAs quantum dots (QDs) with In_0.3Ga_0.7As capping layer grown on GaAs substrate by molecular beam epitaxy (MBE) has been investigated by differential absorption (Δα), electro-reflectance (ER), and photo-reflectance (PR) spectra at different reverse bias. The optical transitions of the ground state, excited states, and wetting layers were identified and discussed. The micro-structure characterization was also analyzed by TEM and AFM. The variation of refractive index spectra (Δn) by calculating Δα spectra through Kramers–Kronig transform is obtained to study the electro-absorption behaviors. Additionally, a simple physical model is proposed to explain the experimental values between the Δn and ΔR spectra performed by two different modulation spectroscopies (Δα and ER). The built-in electric field of metamorphic InAs QDs structure was determined to analyze the Franz–Keldysh Oscillation (FKO) extreme in PR spectra with different bias.     

Estimation of Permeability by Integrating Nuclear Magnetic Resonance (NMR) Logs with Mercury Injection Capillary Pressure (MICP) Data in Tight Gas Sands

It has been a great challenge to determine permeability in tight gas sands due to the generally poor correlation between porosity and permeability. The Schlumberger Doll Research (SDR) and Timur–Coates permeability models, which have been derived for use with nuclear magnetic resonance (NMR) data, also lose their roles. In this study, based on the analysis of the mercury injection experiment data for 20 core plugs, which were drilled from tight gas sands in the Xujiahe Formation of central Sichuan basin, Southwest China, two empirical correlations between the pore structure index ( $ \sqrt {{K \mathord{\left/ {\vphantom {K \varphi }} \right. \kern-0em} \varphi }} $ , defined by the square root of the ratio of rock permeability and porosity) and the R ₃₅ (the pore throat radius corresponding to 35.0 % of mercury injection saturation), the pore structure index and the Swanson parameter have been developed. To consecutively estimate permeability in field applications, based on the study of experimental NMR measurements for 36 core samples, two effective statistical models, which can be used to derive the Swanson parameter and R ₃₅ from the NMR T ₂ logarithmic mean value, have been established. These procedures carried out on the experimental data set can be extended to reservoir conditions to estimate consecutive formation permeability along the intervals with which NMR logs were acquired. The processing results of several field examples using the proposed technique show that the classification scale models are effective only in tight gas reservoirs, whereas the SDR and Timur–Coates models are inapplicable. The R ₃₅-based model is of significance in thin sands with high porosity and high permeability, but the predicted permeability curves in tight gas sands are slightly lower. In tight gas and thin sands, the Swanson parameter model is all credible.