Elliptical Wires Research Articles

Theory of electric field effect on the optical properties of elliptical quantum wire

In the approximation of the effective mass, the electric field effect on the optical properties of the elliptical quantum wire (EQW) was investigated. In an elliptic coordinate system, exact solutions of the Schrödinger equation for an electron in an EQW with hard walls are obtained. The electron energy spectrum consists of even and odd energies states, whose wave functions are expressed through even and odd Mathieu functions of the first kind. Using these solutions, an orthonormal basis was constructed. The influence of the electric field perpendicular to the quantum wire and parallel to the ellipse’s major axis on the energies and oscillator strength of quantum electron transitions was calculated using the matrix method. It is shown that the ellipticity of the quantum wire leads to the removal of the degeneracy of the energy spectrum of quasiparticles since the energies of even and odd electronic states depend differently on the ratio of the EQW semi-axes. The electron’s ground state is the even state, which is nondegenerate because there is no corresponding odd state. The electric field has a greater effect on energy states with a lower value of the magnetic quantum number. As the electric field strength increases, the energies of even and odd states shift to the region of lower energies.

Dynamic capture behavior of rotating matrix to paramagnetic particles in centrifugal HGMS process: Based on FEM

Centrifugal high gradient magnetic separation (CHGMS) was developed to produce a high-quality magnetic product from weakly magnetic materials. In this research, the dynamic behavior of particles in the CHGMS process and the magnetic capture of rotating wires to paramagnetic particles were analyzed through Finite Element Method (FEM). It was found that particles move spirally with slurry in the separation area of the separator, due to the stirring of magnetic wires, and the motion traces of paramagnetic particles are more tortuous and complicated than those of non-magnetic particles. The capture capacity of elliptical wire to paramagnetic particles is stronger than that of circular wire, but is weaker than that of square one. The distance from rotating wires to the center of matrix significantly influences the mass weight of paramagnetic particles captured onto the wires, and there is a clear interaction between wire layers during the capture process of rotating matrix.

The Stationary Thermal Field in a Multilayer Elliptic Cylinder

An analytical–numerical method for determining the two-dimensional (2D) thermal field in a layer-inhomogeneous elliptic cylinder (elliptical roller) was developed in the article. A mathematical model was formulated in the form of a boundary problem for Poisson equations with an external boundary condition of the third kind (Hankel’s). The conditions of continuity of temperature and heat flux increment were assumed at the inner boundaries of material layers. The eigenfunctions of the boundary problem were determined analytically. Hankel’s condition was subjected to appropriate mathematical transformations. As a result, a system of algebraic equations with respect to the unknown coefficients of the eigenfunctions was obtained. The above-mentioned system of equations was solved numerically (iteratively). As an example of an application of the aforementioned method, an analysis of the thermal field in an elliptical electric wire was presented. The system consists of an aluminum core and two layers of insulation (PVC and rubber). In addition to the field distribution, the steady-state current rating was also determined. The thermal conductivities of PVC and rubber are very similar to each other. For this reason, apart from the real model, a test system was also considered. Significantly different values of thermal conductivity were assumed in individual layers of the test model. The temperature distributions were presented graphically. The graphs showed that the temperature drop is almost linear in the insulation of an electrical conductor. On the other hand, in the analogous area of the test model, a broken line was observed. It was also found that the elliptical layer boundaries are not isothermal. The results obtained by the method presented in this paper were verified numerically.

Dispersion properties of plasmonic sub-wavelength elliptical wires wrapped with graphene

One fundamental motivation to know the dispersive or frequency dependent characteristics of localized surface plasmons (LSPs) supported by elliptical shaped particles wrapped with a graphene sheet, as well as their scattering characteristics when these elliptical LSPs are excited, is related to the design of plasmonic structures capable of manipulating light at sub-wavelength scale. The anisotropy imposed by ellipse eccentricity can be used as a geometrical tool for controlling plasmonic resonances. Unlike the metallic case, where multipolar eigenmodes are independent of each other, we find that the induced current on a graphene boundary couples multipolar eigenmodes with the same parity. In the long wavelength limit, a recursive relation equation for LSPs in terms of the ellipse eccentricity parameter is derived, and explicit solutions at lowest order are presented. In this approximation, we obtain analytical expressions for both the anisotropic polarizability tensor elements and the scattered power when LSPs are excited by plane wave incidence.

Flat Spring to Ensure an Elastic and Compliant Branch Connection Between Two Stents

Connecting large stents together is currently performed in two ways. The first is by overlapping, inserting a larger stent into a smaller one to obtain fixation through the radial force of the inner stent and friction between them. The second consists of laterally inserting a balloon expandable stent through a reinforced window to get fixation by plastic deformation of the stent inside a non-deformable aperture. These two approaches lead to stent protrusion through the window, or at least a vulnerable overlap zone. These connections are stiff and may predispose to late disconnection. This paper describes an innovative technology that ensures an elastic and adaptable perpendicular connection between two stents. The technology proposed here is for reconstruction of the ilio-caval confluence. The mother iliocaval stent is a laser cut nitinol conical stent that includes a window constructed as a specific braided elliptical nitinol wire, acting as a flat spring (Figure 1, Figure 2A ). The branch is a braided nitinol wire stent with a special proximal design that opens in a “floral” configuration, followed by a groove and a flare (Fig. 1B). The caval part of the mother stent is first deployed; the window is cannulated to allow insertion of the branch delivery system (Fig. 2A). The branch is delivered in three steps: the proximal “flower” inside the mother stent, the flare outside, and then the remaining branch to lock the flat spring against the groove. After complete delivery of the branch stent, the window establishes an equilibrated connection using the elastic forces applied by both the branch stent and the flat spring (Figure 1, Figure 2B).Figure 2Connection between the iliocaval stent and the iliac branch. (A) The flat spring is in a relaxed state. (B) Once the groove is open in the window, the flat spring is now compressing the groove.View Large Image Figure ViewerDownload Hi-res image Download (PPT) Prototypes have been constructed for testing to obtain a CE mark and further trialling. The next step of this technology is the application in covered stents for branched devices in the aortic arch.

Overcoming the bottleneck for quantum computations of complex nanophotonic structures: Purcell and Förster resonant energy transfer calculations using a rigorous mode-hybridization method

A calculation of the photonic Green's tensor of a structure is at the heart of many photonic problems, but for non-trivial nanostructures, it is typically a prohibitively time-consuming task. Recently, a general normal mode expansion (GENOME) was implemented to construct the Green's tensor from eigenpermittivity modes. Here, we employ GENOME to the study the response of a cluster of nanoparticles. To this end, we use the rigorous mode hybridization theory derived earlier by D. J. Bergman [Phys. Rev. B 19, 2359 (1979)], which constructs the Green's tensor of a cluster of nanoparticles from the sole knowledge of the modes of the isolated constituent. The method is applied, for the first time, to a scatterer with a non-trivial shape (namely, a pair of elliptical wires) within a fully electrodynamic setting, and for the computation of the Purcell enhancement and F\"{o}rster Resonant Energy Transfer (FRET) rate enhancement, showing a good agreement with direct simulations. The procedure is general, trivial to implement using standard electromagnetic software, and holds for arbitrary shapes and number of scatterers forming the cluster. Moreover, it is orders of magnitude faster than conventional direct simulations for applications requiring the spatial variation of the Green's tensor, promising a wide use in quantum technologies, free-electron light sources and heat transfer, among others.

Electric and magnetic field effects on the optical absorption of elliptical quantum wire

In this work, the effects of electric and magnetic fields on the linear, the third-order nonlinear and the total optical absorption coefficients of a typical GaAs/AlGaAs elliptical quantum wire are investigated. Energy eigenvalues and wave functions are calculated using the two-dimensional finite difference method and optical properties are obtained using the compact density matrix approach. The influences of the electric and magnetic fields on the probability densities are described. Results show that the resonant peak values of the optical absorption coefficients are non-monotonic functions of the external fields. Results also indicate that by applying external fields, the magnitude of total optical absorption coefficient reaches to values about 1.5 times higher than that case without external fields.

Green formulation for studying electromagnetic scattering from graphene-coated wires of arbitrary section

We present a rigorous electromagnetic method based on Green's second identity for studying the plasmonic response of graphene-coated wires of arbitrary shape. The wire is illuminated perpendicular to its axis by a monochromatic electromagnetic wave and the wire substrate is homogeneous and isotropic. The field is expressed everywhere in terms of two unknown source functions evaluated on the graphene coating which can be obtained from the numerical solution of a coupled pair of inhomogeneous integral equations. To assess the validity of the Green formulation, the scattering and absorption efficiencies obtained numerically in the particular case of circular wires are compared with those obtained from the multipolar Mie theory. An excellent agreement is observed in this particular case, both for metallic and dielectric substrates. To explore the effects that the break of the rotational symmetry of the wire section introduces in the plasmonic features of the scattering and absorption response, the Green formulation is applied to the case of graphene-coated wires of elliptical section. As might be expected from symmetry arguments, we find a two-dimensional anisotropy in the angular optical response of the wire, particularly evident in the frequency splitting of multipolar plasmonic resonances. The comparison between the spectral position of the enhancements in the scattering and absorption efficiency spectra for low-eccentricity elliptical and circular wires allows us to guess the multipolar order of each plasmonic resonance. We present calculations of the near field distribution for different frequencies which explicitly reveal the multipolar order of the plasmonic resonances. They also confirm the previous guess and serve as a further test on the validity of the Green formulation.

98.08 The moment of inertia of an elliptical wire

98.08 The moment of inertia of an elliptical wire

Effect of polarization charges on impurity binding energy in elliptical quantum wire

The binding energy of hydrogenic impurity located at the center of elliptical quantum wire using the effective mass approximation and an appropriate coordinate transformation is calculated for CdS/SiO2 structure. The effect of surface polarization charges due to impurity on the impurity binding energy is considered. The results clearly indicate that the binding energy depends not only on the polarization charges but also on the ellipticity constant.

Simulation of magnetic suspensions for HGMS using CFD, FEM and DEM modeling

Properties of magnetic suspensions depend on the fluid, the particles and the magnetic background field. The simulation is aimed at understanding the influence of magnetic properties in High Gradient Magnetic Separation processes. In HGMS magnetic particles are collected on magnetic wires for separation. External magnetic forces are calculated or simulated using the Finite Element Method and embedded first in a Computational Fluid Dynamics simulation. In the simulation, elliptic and rectangular wires aligned in field direction reach higher separation efficiencies than cylindrical wires. Magnetic forces from FEM with implemented dipole forces in a Discrete Element Method code show magnetically induced agglomeration and yield an acceptable agreement with experiments. Particle deposition on wires is investigated under the influence of different parameters. The porosity of the deposit is dependent on the magnetization of the wire and particles. A centrifugal force of 60g has an important influence.

Linearly Polarized, Single-Mode Spontaneous Emission in a Photonic Nanowire

We introduce dielectric elliptical photonic nanowires to funnel efficiently the spontaneous emission of an embedded emitter into a single optical mode. Inside a wire with a moderate lateral aspect ratio, the electromagnetic environment is largely dominated by a single guided mode, with a linear polarization oriented along the ellipse major axis. The resulting monomode spontaneous emission is maintained over a broad wavelength range, a key asset of this 1D photonic structure. Our theoretical analysis is completed by an experimental study of GaAs elliptical photonic wires with embedded InAs quantum dots. In particular, the fraction of collected photons with the desired linear polarization can exceed 95%.

Free vibration analysis of cylindrical helical springs with noncircular cross-sections

The free vibration analysis of cylindrical helical springs with noncircular cross-sections is carried out by means of an analytical study. In the governing equations of motion of a spring, all displacement functions and a generalized warping coordinate are defined at the centroidal principal axis. The effects of the rotational inertia, axial and shear deformations, including torsion-related warping deformations, are also considered in the formulations. Explicit analytical expressions that give the vibrating mode shapes are derived by rigorous application of the symbolic computing package MATHEMATICA, and the Muller root search method is used to determine the natural frequencies. Numerical examples are provided for springs with elliptic, rectangular and equilateral triangular cross-sections, and subjected to clamped–clamped and clamped–free boundary conditions. The natural frequencies are presented for a range of geometric parameters. In the case of elliptical wires, results are presented for the aspect ratio λ= a/ b ranging from 3/5 to 5/3, the helix pitch angle α ¯ from 5 to 12.5, the number of active turns n from 6 to 12, and the ratio of cylinder radius to minor axis R/2 a ranging from 20/3 to 50/3. Validation of the proposed model has been achieved through comparison with a finite element model using three-dimensional solid elements and the results available in published literature, which in these cases indicates a good correlation.

Confined and interface optical phonons in the semiconductor elliptic quantum wire with the axial heterostructure

Confined and interface optical phonons in the semiconductor elliptic quantum wire with the axial heterostructure

Crystal structure and optical properties of silver nanorings

We report the polyol synthesis and crystal structure characterization of silver nanorings, which have perfect circular shape, smooth surface, and elliptical wire cross-section. The characterization results show that the silver nanorings have well-defined crystal of singly twinned along the whole ring. The spatial distribution of the scattering of a silver nanoring with slanted incidence reveals the unique focus effect of the nanoring, and the focus scattering varies with the incident wavelength. The silver nanorings with perfect geometry and well-defined crystal have potential applications in nanoscaled photonics, plasmonic devices, and optical manipulation.

An asymptotic solution of the Schrödinger equation for the elliptic wire in the magnetic field

An asymptotic solution of the Schrödinger equation with non-separable variables is obtained for a particle confined to an infinite elliptic cylinder potential well under an applied uniform longitudinal magnetic field. Using the standard-problem method, dimension-quantized eigenvalues have been calculated when the magnetic length is large enough in comparison with the half of the distance between the boundary ellipse focuses. In semi-classical approximation, the confined electron (hole) states are divided into the boundary states (BS), ring states (RS), hyperbolic caustic states (HCS) and harmonic oscillator states (HOS). For large angular momentum quantum numbers and small radial quantum numbers, the BS and RS are grouped into the ‘whispering gallery’ mode. They associate with particles moving along the wire cross section boundary. The motion is limited from the wire core by the elliptic caustic. Consisting of the HCS and HOS, the ‘jumping ball’ modes correspond to the states of particle moving along a wire diameter when the angular momentum quantum number is much less than the radial quantum number. In this case, the motion is restricted by the hyperbolic caustics and two boundary ellipse arcs. For excited hole states in a Bi wire, the energy spectrum and space probability distribution are analyzed.

Electronic structure and optical gain of wurtzite ZnO nanowires

The electronic structure and optical gain of wurtzite ZnO nanowires are investigated in the framework of effective-mass envelope-function theory. We found that as the elliptical aspect ratio e increases to be larger than a critical value, the hole ground states may change from optically dark to optically bright. The optical gain of ZnO nanowires increases as the hole density increases. For elliptical wire with large e, the y-polarized mode gain can be several thousand cm−1, while the x-polarized mode gain may be 26 times smaller than the former, so they can be used as ultraviolet linearly polarized lasers.

Electron energy spectrum in core-shell elliptic quantum wire

The electron energy spectrum in core-shell elliptic quantum wire and elliptic semiconductor nanotubes are investigated within the effective mass approximation. The solution of Schrodinger equation based on the Mathieu functions is obtained in elliptic coordinates. The dependences of the electron size quantization spectrum on the size and shape of the core-shell nanowire and nanotube are calculated. It is shown that the ellipticity of a quantum wire leads to the break of degeneration of quasiparticle energy spectrum. The dependences of the energy of odd and even electron states on the ratio between semiaxes are of a nonmonotonous character. The anticrosing effects are observed at the dependences of electron energy spectrum on the transversal size of the core-shell nanowire.

Electron energy spectra in an elliptic quantum wire and elliptic nanotube

In the effective mass approximation, the electron spectra in an elliptic quantum wire and elliptic semiconductor nanotube are investigated. An exact electron energy spectrum in the GaAs elliptic quantum wire and elliptic semiconductor nanotube with impenetrable walls is obtained and an approximate solution of the Schrodinger equation is derived for a finite potential barrier height in the GaAs/AlxGa1−xAs elliptic quantum wire. It is demonstrated that the ellipticity of the quantum wire and nanotube results in removal of degeneration of the quasiparticle energy spectrum. Dependences of energies of even and odd states on the ratio of the ellipse semiaxes are nonmonotonic in character. In the limiting case of degeneration of elliptic quantum wires and nanotubes into circular ones, the quasi-particle energy spectrum coincides with the corresponding spectrum in cylindrical nanosystems.

Electron energy spectrum in elliptic quantum wire and elliptic nanotube

Electron energy spectrum in elliptic quantum wire and elliptic nanotube