Generation of nondiffracting quasi-circular polarization beams using an amplitude modulated phase hologram

We propose an approach to the generation of nondiffracting quasi-circularly polarized beams by a highly focusing azimuthally polarized beam using an amplitude modulated spiral phase hologram. Numerical verifications are implemented in the calculation of the electromagnetic fields and Poynting vector field near the focus based on the vector diffraction theory, and the polarization of the wavefront near the focal plane is analyzed in detail by calculating the Stokes polarization parameters. It is found that the electric field, magnetic field, and Poynting vector field can simultaneously be uniform and nondiverging over a relatively long axial range of ~7.23λ. In the transverse plane, the ellipticity and azimuthal angle of the local polarization ellipse varies from point to point. No polarization singularity and phase singularity are found at the beam center, which makes the bright spot possible.     

Electric field analytical formulas for single-circuit power lines with a horizontal arrangement of conductors

Analytical formulas are derived for the calculation of the electric field at any point in the vicinity of single-circuit power lines with a horizontal arrangement of conductors. The analytical formulas are appropriate for the assessment of public exposure as they allow direct calculation of the electric field. They are also suitable for assessing the dependence of the electric field on electric and geometric parameters. Initially, an accurate formula of the electric field is derived by using a proposed method. This method is based on the use of multipole expansions and double complex numbers for the representation of the electric field vector and symmetrical components analysis for the conductors' charges. Based on the accurate formula, a sensitivity analysis of the electric field is carried out with respect to the various parameters. Two simpler approximate formulas are finally developed, which provide the electric field with satisfactory accuracy in certain areas in the vicinity of the lines.     

The imaginary components of dispersion parameters and the Stokes mode dynamics in stimulated Raman scattering

The Stokes pulse dynamics during stimulated Raman scattering has been studied in the constant pumping approximation. The nonlinear problem of interaction between a pumping wave and the Stokes component is reduced to a linear equation describing propagation of an optical pulse in the amplifying medium with imaginary components of the first-and second-order dispersion parameters, the presence of which leads to the possibility of the pulse envelope propagation at a supraluminal velocity.     

Algorithms for the calculation of limit and bifurcation points using Lanczos methods

The computation of limit and bifurcation points in structural mechanics using iterative preconditioned Lanczos solvers is studied. Contrary to classical implementations of algorithms for the calculation of limit and bifurcation points, which depend in general strongly on observing the diagonal elements of the decomposed matrix – obtained by a Gauß- or Cholesky decomposition – , we use an approach of determining limit and bifurcation points by examination of the subspace spanned by the iteration vectors of the Lanczos solver. Using a multilevel preconditioning with a coarse grid solver may result in a non positive definite preconditioning matrix if the coarse grid matrix is not positive definite in the post-critical solution branch. In that case the iteration has to be performed in the complex vector space. We prove by mathematical induction that all vectors and scalars are either purely real or purely imaginary. Therefore the generalized computation can be performed with about the same number of operations as in the case of a positive definite preconditioning matrix.     

Complex unitary vectors for the direction of propagation and for the polarization of electromagnetic waves in uniaxial and absorbing dielectric media

The propagation of inhomogeneous and elliptically polarized plane waves in absorbing uniaxial anisotropic media is described using complex unitary vectors to represent the direction of propagation and the direction of polarization. Detailed expressions for electric displacement, electric field, and magnetic field vectors are obtained for the ordinary and extraordinary waves, and their geometry is discussed. According to the complex direction of propagation, three particular cases are studied: the real case (homogeneous wave), the case perpendicular to the optical axis, and the case coplanar with the optic axis. The case of isotropic media is also analyzed.     

Cutter location point calculation for five-axis surface machining with ellipse cutter

This paper presents an approach of the cutter location (CL) point calculation for five-axis surface machining with elliptic generatrix cutter. Firstly, based on the cutter contact (CC) point and its normal vector in workpiece coordinate system, the normal vector of the CC point in local coordinate system of the cutter is figured out according to the geometric relations between two coordinate systems. Secondly, the geometric properties of ellipse are analysed to obtain the local coordinate CC point with local coordinate normal vector. Thirdly, the position relation between the CC point and the ellipse centre in local coordinate system is determined. And this position relation is transformed into workpiece coordinate system according to the geometric relations between two coordinate systems. Then, the centre of the ellipse in workpiece coordinate system is calculated by the position relation and the CL point is figured out according to the ellipse centre. Finally, an example of CL point calculation with this method is carried out which proves that the method is effective.     

Surface Phenomena in the Hydrodynamics of an Incompressible Fluid

By taking as an example the outflow of an incompressible fluid through a hole with small geometric parameters under the conditions of supersmall pressures, we attempted to evaluate the effect of surface phenomena on its flow by the similarity method. The Navier–Stokes differential equation was supplemented by parameters allowing for the effect of surface forces. The modified Navier–Stokes equation was subjected to similarity conversion. This yielded a dimensionless group that includes the whole range of variable parameters affecting the fluid flow, namely, the generalized criterion Pv. The graphic dependence of the coefficient of the fluid flow rate on the generalized criterion Pv is presented on the basis of experimental data.     

Stokes-vector evolution in a weakly anisotropic inhomogeneous medium

The equation for evolution of the four-component Stokes vector in weakly anisotropic and smoothly inhomogeneous media is derived on the basis of a quasi-isotropic approximation of the geometrical optics method, which provides the consequent asymptotic solution of Maxwell's equations. Our equation generalizes previous results obtained for the normal propagation of electromagnetic waves in stratified media. It is valid for curvilinear rays with torsion and is capable of describing normal mode conversion in inhomogeneous media. Remarkably, evolution of the four-component Stokes vector is described by the Bargmann-Michel-Telegdi equation for relativistic spin precession, whereas the equation for the three-component Stokes vector resembles the Landau-Lifshitz equation describing spin precession in ferromagnetic systems. The general theory is applied for analysis of polarization evolution in a magnetized plasma. We also emphasize fundamental features of the non-Abelian polarization evolution in anisotropic inhomogeneous media and illustrate them by simple examples.     

Calculations of optical properties in p-doped nitrides quaternary alloys multiple quantum wells

We present theoretical photoluminescence (PL) and absorption spectra of p-doped InGaN/AlInGaN and AlInGaN/InGaN multiple quantum wells (MQWs). The calculations were performed within the k.p method by means of solving a full eight-band Kane Hamiltonian together with the Poisson equation in a plane wave representation, including exchange–correlation effects within the local density approximation. Strain effects due to the lattice mismatch and an internal electric field are also taken into account. We show that by changing the In and Al composition we can reach short and long emission wavelengths. The trends in the calculated Stokes shift, due to many-body effects within the quasi-two-dimensional hole gas (2DHG), are analyzed as a function of the acceptor doping concentration. Since the studies of optical properties of quantum wells based on nitrides quaternary alloys are at an early stage, the results reported here will provide guidelines for the interpretation of forthcoming experiments.     

Measurement of the Electromagnetic Parameters of Materials of Finite Thickness

An electrodynamic model of a dielectric plate, situated in the electromagnetic field of a slow wave, is considered. It is shown that the parameters of the plate and of the regions close to it can be represented by electric and magnetic type admittances. The relations obtained can be used to measure the thickness of thin films and to monitor the quality of radio-absorbing coatings.     

Energy flow lines for the radiation emitted by a dipole

An oscillating electric dipole emits radiation, and the flow of energy in the electromagnetic field is represented by the field lines of the Poynting vector. In the most general state of oscillation the dipole moment vector traces out an ellipse. We have evaluated analytically the field lines of the Poynting vector for the emitted light, and it appears that each field line lies on a cone, which has its axis perpendicular to the plane of the ellipse. The field lines exhibit a vortex structure near the location of the dipole, and they approach a straight line in the far field. It is shown that due to the spiraling of the field lines near the source, the asymptotic limit of a field line is displaced as compared to a ray which would come directly out of the source. Both the spatial extent of the vortex in the near field and the magnitude of the displacement of the image in the far field are of nanoscale dimension.     

A circuit approach to field computation

Many design objectives can be expressed more directly in terms of circuit parameters, such as capacitance and inductance, than in terms of the field vectors E and B. A simple, although radical, change is suggested to provide a closer link between the field and circuit views. The electric potential φ and magnetic vector A are defined, in energy terms, as the primary field quantities, and they are visualized as measures of the capacitance and inductance, respectively. E and B become auxiliary symbols denoting derivatives, so that the customary roles of the potentials and field vectors are reversed. Some of the practical advantages of the change are examined and are illustrated by example     

Eddy-Currents Computation With T-$Omega$ Discrete Geometric Formulation for an NDE Problem

We propose a discrete geometric formulation based on a magnetic scalar potential and on the circulation of an electric vector potential to solve eddy-current problems for nondestructive evaluation of steel bars with longitudinal defects.     

Propagation of inhomogeneous waves in anisotropic piezo-thermoelastic media

A mathematical model for the propagation of harmonic plane waves in an anisotropic piezo-thermoelastic medium is explained through three relations. Two of them relate the stress-induced harmonic variations in temperature and electric potential to mechanical displacement of material particles. The third is a system that defines modified Christoffel equations for wave propagation in the medium. The solution of this system is ensured by a quartic equation whose complex roots explain the existence and propagation of four attenuating waves in the medium. The effects of piezoelectricity and thermoelasticity on the wave propagation are analyzed in the discussion of special cases. An angle between propagation direction and direction of maximum attenuation defines the attenuated wave as inhomogeneous wave. The complex slowness vector for each of the four attenuated waves in the medium is resolved to calculate the phase velocity and the attenuation factor for its propagation as an inhomogeneous wave along a general direction in three-dimensional space. The variations in phase velocities and attenuation factors with propagation direction are computed, for a realistic numerical model.     

An Isolated Sensor Determining the Poynting Vector in the near Field of a Radiating Antenna

A system is described comprising of an isolated sensor to measure the polarization ellipses of the electric and magnetic vectors in the near field around a transmitting antenna or a scatterer in the frequency range from 0.5 to 10 MHz. The locus of the time-dependent Poynting vector is derived by numerical calculation. Results are displayed as a stereoscopic image.     

Geometric T–Ω approach to solve eddy currents coupled to electric circuits

This paper describes a systematic geometric approach to solve magneto‐quasi‐static coupled field–circuit problems. The field problem analysis is based on formulating the boundary value problem with an electric vector potential and a scalar magnetic potential. The field–circuit coupling and the definition of potentials are formally examined within the framework of homology theory. Copyright © 2007 John Wiley & Sons, Ltd.     

Flow of electro-rheological materials

Summary An electro-rheological fluid is a material in which a particulate solid is suspended in an electrically non-conducting fluid such as oil. On the application of an electric field, the viscosity and other material properties undergo dramatic and significant changes. In this paper, the particulate imbedded fluid is considered as a homogeneous continuum. It is assumed that the Cauchy stress depends on the velocity gradient and the electric field vector. A representation for the constitutive equation is developed using standard methods of continuum mechanics. The stress components are calculated for a shear flow in which the electric field vector, is normal to the velocity vector. The model predicts (i) a viscosity which depends on the shear rate and electric field and (ii) normal stresses due to the interaction between the shear flow and the electric field. These expressions are used to study several fundamental shear flows: the flow between parallel plates, Couette flow, and flow in an eccentric rotating disc device. Detailed solutions are presented when the shear response is that of a Bingham fluid whose yield stress and viscosity depends on the electric field.     

Discrimination of globally unpolarized fields through Stokes vector element correlations

In a previous publication [J. Opt. Soc. Am. A 21, 988 (2004)], we examined theoretically joint probability distributions of Stokes vector elements and suggested the existence of various types of globally unpolarized light that could be discriminated through measurement of the Stokes vector element correlations. We now study the joint distribution of the degree of polarization and the three Stokes parameters as it relates to material properties in highly scattering, depolarizing random media. We describe numerical and experimental results of second-order Stokes vector element correlations, demonstrating the existence of various types of nonclassical, globally unpolarized light, and we suggest experimental means for discriminating between such field distributions. We also discuss the usefulness of the Stokes vector element correlations as an experimental tool for discriminating between different globally unpolarized fields and for verifying the assumption of Gaussian statistics usually invoked in the context of multiple light scattering.