On the electromagnetic field of one- and two-dimensional gratings of large cylinders--Part III: Nonpermeable cylinders in uniform field

The electromagnetic flow pattern in one-and two-dimensional gratings of large nonconducting circular cylinders in an external uniform field is studied. It is shown that the cylinders can be replaced by suitable arrangement of pairs of dipoles opposite in sense and placed on an axis perpendicular to the external field. The relation between the spacing of the dipoles and the cylinder radius R yields the complex potential as a function of R, with the imaginary part used to describe the flow pattern. Solutions for unit cells of square, rectangular, and infinite-strip geometry are discussed, with details in tables and plots. In the same context, a uniform field obliquely oriented toward the grating is considered, as is the flux pattern.     

On the electromagnetic field of one- and two-demensional gratings of large cylinder--Part I: Alternating potential

The field of gratings of large cylinders in a unit cell of square, rectangular, or infinite-strip pattern is studied. Solutions are provided for alternating potential use being made of suitable arrangements of line charges. The complex potential corresponding to a given cylinder is found by correlation of the spacing of the line charges and the size of the cylinder. This method is also suitable for solution of fields of one-dimensional gratings of elliptical cylinders at alternating potential. Detailed results are presented in tables as well as in plots of typical field configurations.     

Enhanced transmission due to nonplasmon resonances in one- and two-dimensional gratings

Enhanced transmission through subwavelength slit gratings and hole arrays is studied in view of its application in the far-infrared and microwave domains. Because for perfectly conducting gratings, plasmon resonances are not expected to produce an enhanced transmission, other kinds of resonance, such as Fabry-Perot, waveguide-mode, and cavity-mode resonances, are studied. The possibility of reaching 100% transmittivity for some particular wavelengths is established when two superimposed identical gratings are used while each of them transmits approximately 1% off resonance. A similar transmission is obtained with hole arrays. The study of the field map inside the groove region allows our establishing the nature of the resonance, that is involved. Comparison of the bandwidth with respect to the wavelength or incidence given by various kinds of resonance is presented.     

Numerical expansion-iterative method for analysis of integral equation models arising in one- and two-dimensional electromagnetic scattering

Most integral equations of the first kind are ill-posed, and obtaining their numerical solution needs often to solve a linear system of algebraic equations of large condition number. So, solving this system may be difficult or impossible. Since many problems in one- and two-dimensional scattering from perfectly conducting bodies can be modeled by Fredholm integral equations of the first kind, this paper presents an effective numerical expansion-iterative method for solving them. This method is based on vector forms of block-pulse functions. By using this approach, solving the first kind integral equation reduces to solve a recurrence relation. The approximate solution is most easily produced iteratively via the recurrence relation. Therefore, computing the numerical solution does not need to directly solve any linear system of algebraic equations and to use any matrix inversion. Also, the method practically transforms solving of the first kind Fredholm integral equation which is inherently ill-posed into solving second kind Fredholm integral equation. Another advantage is low cost of setting up the equations without applying any projection method such as collocation, Galerkin, etc. To show convergence and stability of the method, some computable error bounds are obtained. Test problems are provided to illustrate its accuracy and computational efficiency, and some practical one- and two-dimensional scatterers are analyzed by it.     

Generalized theory of magnetic field diffusion in superconducting cylinders: II

We present the results of nonperturbative calculations of the total transition time for the magnetically induced phase transition in a long superconducting cylinder of type I material. We investigate the behavior of the transition time in the field range H_c to 100H _c and show that there are two stages in the kinetics of the transition. Previous theories were based on a quasiequilibrium approach whose validity is restricted to the field rangeH _c <H ₀ 2H _c . Our results are in very good agreement with experimental values obtained with 6–9's pure indium cylinders.     

Microwave transmission amplitude-frequency characteristic of two-dimensional composite electromagnetic crystal based on copper cylinders

The amplitude-frequency characteristic of the coefficient of microwave transmission of a two-dimensional composite electromagnetic crystal comprising gypsum (CaSO₄ · 2H₂O) matrix with a regular structure of conducting cylinders has been experimentally studied.     

A fast numerical method for analysis of one- and two-dimensional electromagnetic scattering using a set of cardinal functions

Since many problems in one- and two-dimensional scattering from perfectly conducting bodies can be modeled by linear Fredholm integral equations, the main focus of this paper is to present a fast numerical method for solving them. The method uses Whittaker cardinal functions as a set of basis functions. By using the properties of these cardinal functions together with an appropriate quadrature rule, the computational cost of the method becomes low and the calculations are done quickly. This is due to the fact that the method uses just sampling of functions instead of integration. To show computational efficiency of this approach, some practical one- and two-dimensional scatterers are analyzed by it and the results are compared with those of two other numerical methods.     

On the quantization of the electromagnetic field in conducting media

In this work we investigate the quantization of electromagnetic waves propagating through homogeneous conducting linear media with no charge density. We use Coulomb's gauge to reduce the problem to that of a time-dependent harmonic oscillator, which is described by the Caldirola–Kanai Hamiltonian. Furthermore, we obtain the corresponding exact wave functions with the help of quadratic invariants and of the dynamic invariant method. These wave functions are written in terms of a particular solution of the Milne–Pinney equation. We also construct coherent and squeezed states for the quantized electromagnetic waves and evaluate the quantum fluctuations in coordinates and momentum as well as the uncertainty product for each mode of the electromagnetic field.     

Ultrashort pulse propagation in uniform and nonuniform waveguide long-period gratings

We conduct a detailed theoretical analysis of ultrashort pulse propagation through waveguide long-period grating (LPG) structures operating in the linear regime. We first consider the case of uniform LPGs, and we also investigate the effect of the typical grating nonuniformities, e.g., grating profile apodization, grating period chirping, and discrete phase shifts, on the spectral and temporal behavior of LPG structures. The two interacting modes are analyzed separately, and advanced representation tools, namely, space-wavelength and space-time diagrams (where space refers to the longitudinal grating dimension), are used to provide a deeper insight into the physics that determines the pulse evolution dynamics through the grating structures under analysis. In addition to its intrinsic physical interest, our study reveals the strong potential of LPG-based devices for optical pulse reshaping operations in the subpicosecond regime.     

Analysis of difference diagrams stability approximating a class of one- and two-dimensional non-linear–parabolic field equations

This paper describes the stability conditions for difference diagrams applied to the approximation of one- and two-dimensional non-linear field equations. The one-dimensional electromagnetic field is described by vector B and vector E , and the two-dimensional field by magnetic vector potential A . It has been proved that the presence of a lower order of derivatives has a decisive influence on the stability condition of the considered diagrams.     

Current-induced destruction of type I superconductivity: The role of the one- and two-dimensional mixed state

New experimental and theoretical results on the current-induced phase transition in cylindrical wires (tin) are presented: The London model for the intermediate state of current-carrying superconductors has been modified, taking into account magnetoresistance, and has been extended to hollow cylinders. Evidence for the one- and two-dimensional mixed state first proposed by Landau has been obtained from the study of the quasistatic voltage-current curves of solid and hollow cylindrical specimens, respectively. The kinetic phenomena during the current-induced destruction of superconductivity in solid cylindrical wires have previously been studied by Posada and Rinderer, but only measurements on hollow wires of high purity presented in this paper confirm the isothermal electromagnetic theory of Rothen and Bestgen for a current-induced phase transition. For currents close to Silsbee's critical current, in pure specimens as well as for impure specimens, for any current above the critical, the dynamic destruction of superconductivity in wires is no longer isothermal. For these cases the nonisothermal theory of Posada and Rinderer has been extended to the case of hollow cylinders and successfully compared with experiments.This work was supported financially by the Fonds National Suisse pour la Recherche Scientifique.     

Operator approach to electromagnetic coupled-wave calculations of lamellar gratings: infrared optical properties of intrinsic silicon gratings

The system of coupled-wave equations for electromagnetic calculations of lamellar gratings is transformed to a new operator-vector form. The numerical procedure is based on truncation of the transformed system and proves to be stable, to be free of ill conditioning, and to preserve the power-conservation requirement for a lossless dielectric with high accuracy. To execute the procedure a very compact MATLAB-based program is developed, and numerical simulations for thick intrinsic silicon gratings are performed. Zero-reflectance phenomena at normal incidence for both TE and TM polarizations are studied. The ratios of the grating dimensions to be wavelengths at which these anomalies occur are found numerically. It is shown that by keeping the period- and slot-width-towavelength ratios constant and by increasing the slot depth one can repeat the anomalies. An antiblazing property at oblique incidence is also considered. The connection with recent directional polarized-emission experiments on intrinsic silicon g atings is discussed.     

AC susceptibilities of conducting cylinders and their applications in electromagnetic measurements

We present accurate calculations and tabulations of the volume and midplane-averaged complex ac susceptibilities of nonmagnetic conducting cylinders with aspect ratio ranging from 0.1 to 10 as functions of a dimensionless frequency. We discuss their features in terms of eddy-current demagnetizing effect. We explain their applications in high-sensitivity, low-temperature, and high-field ac susceptometers and contactless conductivity measurements.     

Scattering from cylinders using the two-dimensional vector plane wave spectrum: addendum

The solution for the vector plane wave spectrum scattering from multiple cylinders by Pawliuk and Yedlin [J. Opt. Soc. A28, 1177 (2011)] only provided the single scattering coefficients for the TM polarization case. The TE solution is similar except for the form of the single scattering coefficients. Here we describe the single scattering coefficients for both polarizations and three types of cylinders: dielectrics, perfect electric conductors, and perfect magnetic conductors.     

Effect of porous lining on the MHD flow between two concentric rotating cylinders under the influence of a uniform magnetic field

Summary Bénard-Marangoni instabilities are theoretically discussed: emphasis is placed on the role of negative Rayleigh and Marangoni numbers. Marginal, supercritical and subcritical instabilities are respectively examined.The first part is concerned with the response of an unbounded fluid layer with respect to small disturbances. A variational principle describing marginal stability is proposed. Rayleigh-Ritz method is used to obtain approximate solutions for the critical Rayleigh and Marangoni numbers. In a second part, corrections to the linear theory, by including weak nonlinearities, are introduced. The amplitude of the supercritical temperature and velocity fields are calculated in the framework of Stuart's shape approximation. Finally, the possibility of subcritical instability with respect to disturbances of arbitrary amplitude is investigated by the method of energy.With 5 Figures     

Construction and performance of one- and two-dimensional large position-sensitive liquid and plastic scintillation detectors — an application to a neutron polarimeter

Large one- and two-dimensional position-sensitive neutron detectors have been developed. Their shapes are a long block and a square and their sizes are 100×10×7.5 cm³ and 100×100×10 cm³ for one- and two-dimensional detectors, respectively. Both liquid and plastic scintillators are employed as detector materials. Position resolutions are examined by using monoenergetic neutron beams with energies of 61.6 MeV. The obtained position resolutions in FWHM are 3–5 cm and 4–14 cm for one- and two-dimensional detectors, respectively. Position resolutions are poor near the corner of the two-dimensional detector irrespective of scintillator materials. Scintillation light responses have been compared with predictions of Monte Carlo calculations. Neutron polarimeters at an intermediate energy have been developed by utilizing the position sensitivity of these detectors.     

Fractional Talbot field and of finite gratings: compact analytical formulation

We present a compact analytical formulation for the fractional Talbot effect at the paraxial domain of a finite grating. Our results show that laterally shifted distorted images of the grating basic cell form the Fresnel field at a fractional Talbot plane of the grating. Our formulas give the positions of those images and show that they are given by the convolution of the nondistorted cells (modulated by a quadratic phase factor) with the Fourier transform of the finite-grating pupil.     

Intrinsic dynamics of the boundary of a two-dimensional uniform vortex

The link between the shape of a two-dimensional, uniform vortex and self-induced velocities on its boundary is investigated through a contour-dynamics approach. The tangent derivative of the velocity along the boundary is written in a complex form, which depends on the analytic continuation of the tangent unit vector outside the vortex boundary. In this way, a classical analysis in terms of Schwarz's function of the boundary, due to Saffman, is extended to vortices of arbitrary shape. Time evolution of intrinsic quantities (tangent unit vector, curvature and Fourier's coefficients for the vortex shape) is also analyzed, showing that it depends on tangent derivatives of the velocities, only. Furthermore, a spectral method is proposed, aimed at investigating the dynamics of nearly-circular vortices in an inviscid, isochoric fluid. Comparisons with direct numerical simulations are also established.     

Application of asymptotic expansions to model two-dimensional induction heating systems. Part I: calculation of electromagnetic field distribution

We analyze the effect of a radio-frequency alternating magnetic field generated in the vicinity of solid or liquid electrically conducting components, such as used in induction heating processes. The field can penetrate only into a thin magnetic skin located beneath the conductor surface, where the generated heat and stresses are concentrated. This most often leads to major numerical difficulties, especially for very thin magnetic skins. Therefore, we have developed a mathematical model of the electromagnetic field distribution inside the conductors for planar and axisymmetric configurations by using a matched asymptotic expansion technique. Among other features, our method takes the curvature of the conductor surfaces into account. A practical numerical implementation of our model is detailed here, and numerical calculations are carried out in order to extend the model to limiting cases such as curvature discontinuities and corners. These calculations compare successfully with complete numerical computations.