Piecewise linear current density recursive convolution FDTD implementation for anisotropic magnetized plasmas

The piecewise linear current density recursive convolution (PLCDRC) finite-difference time-domain (FDTD) method for isotropic dispersive media greatly improves accuracy over recursive convolution (RC) and current density recursive convolution (CDRC) FDTD approaches but retains its speed and efficiency advantages. This letter extends this approach to anisotropic magnetoactive plasmas which incorporates both anisotropy and frequency dispersion at the same time, enabling the transient solutions of electromagnetic wave propagation in anisotropic magnetoactive plasmas. The high efficiency and accuracy of the method are confirmed by computing the reflection and transmission through a magnetized plasma layer, with the direction of propagation parallel to the direction of the biasing field. A comparison to frequency-domain analytic results and CDRC FDTD results is included.     

FDTD Analysis of Electromagnetic Reflection by Conductive Plane Covered with Magnetized Inhomogeneous Plasmas

A novel finite-difference time-domain (FDTD) methodology which incorporates both anisotropy and frequency dispersion at the same time is developed for electromagnetic wave propagation in anisotropic magnetoactive plasmas in this paper. The numerical verification of the method are confirmed by computing the reflection and transmission of right-handed/left-handed circularly polarized (RCP/LCP) wave through a magnetized plasma layer, with the direction of propagation parallel to the direction of the biasing field. And, the right-handed / left-handed polarized wave reflection coefficients for electromagnetic signals normally incident upon a conductive plane covered with a layer of magnetized plasma are computed using the new FDTD method. The parabolic electron-number density profile varies only in the direction perpendicular to the plane. The function dependence of reflection coefficients on the number density, collision frequency and external magnetic field is studied.     

Reflecting Rubber Characteristics of Anisotropic Sheets and Measurement of Complex Permittivity Tensor

Complex values of the permittivity tensor of robber sheets which are manufactured by the rolling process were estimated by the least-squares method using the reflection coefficient measured for normal incidence. First, the frequency characteristics of the reflection coefficients of a rubber sheet backed by thin aluminum were measured from 8.5 to 10.5 GHz by changing the rolling angle relative to the incident electric field. Next, the elements of the permittivity tensor were determined by the least-squares method from many data of measured reflection coefficients of the samples. Five kinds of rubber sheets containing carbon particles or fibers were selected, and circular pieces 30 cm in diameter were measured by this method. The complex permittivity tensors including off-diagonal elements were thus obtained, and the principal directions of the tensor were calculated from the measured permittivity tensor. The following facts were found through this analysis: The permittivity element in the rolling direction is about five times larger and the off-diagonal elements are small compared with the diagonal elements. The principal direction of the real part is different from that of the imaginary part for a certain kind of rubber sheet mixed with carbon particles.     

A frequency-dependent finite-difference time-domain formulation fortransient propagation in plasma

Previous FDTD (finite-difference time-domain) formulations were not capable of analyzing plasmas for two reasons. First, FDTD requires that at each time step the permittivity and conductivity be specified as constants that do not depend on frequency, while even for the simplest plasmas these parameters vary with frequency. Second, the permittivity of a plasma can be negative, which can cause terms in FDTD expressions to become singular. A novel FDTD formulation for frequency-dependent materials (FD)²TD has been developed. It is shown that (FD) ²TD can be applied to compute transient propagation in plasma when the plasma can be characterized by a complex frequency-dependent permittivity. While the computational example presented is for a pulse normally incident on an isotropic plasma slab, the (FD)²TD formulation is fully three-dimensional. It can accommodate arbitrary transient excitation, with the limitation that the excitation pulse must have no zero frequency energy component. Time-varying electron densities and/or collision frequencies could also be included. The formulation presented is for an isotropic plasma, but extension to anisotropic plasma should be fairly straightforward     

Frequency-dependent FDTD modeling of optically controlleddielectric resonators

A theoretical analysis is carried out to describe the performance of optically controlled dielectric resonators. A previously developed frequency-dependent finite-difference-time domain (FDTD) formulation has been used to estimate the effect that solid state plasmas have on the resonant frequency on dielectric resonators. Optical generation of plasmas in contact with dielectric resonators is being considered here as a possible means of controlling the resonator's frequency. The effect that carrier diffusion and recombination-generation have on plasma permittivity and penetration depth are taken into account in this analysis. The results are compared with measurement and are shown to yield a quantitative estimate of the optically induced dielectric resonator frequency shift as a function of the illumination, properties of the plasma host semiconductor, and the properties of the dielectric resonator     

JEC-FDTD for 2-D conducting cylinder coated by anisotropic magnetized plasma

The JE convolution finite-difference-time-domain (JEC-FDTD) method is extended to the anisotropic magnetized plasma which incorporates both anisotropy and frequency dispersion at the same time, enabling the transient solution of the electromagnetic wave propagation in anisotropic magnetized plasmas. Two-dimensional JEC-FDTD formulations for magnetized plasma are derived. The back scattering radar cross section (RCS) of a perfectly conducting cylinder coated by a layer of magnetized plasmas is calculated.     

关于各向异性基本电子元件欧姆定律的两种形式

由于各向异性电阻元件的导电各向异性，使电流密度方向和电场强度方向不一致，从而欧姆定律表现为两种形式：电流密度方向的欧姆定律和电场强度方向的欧姆定律。相应地存在一个二阶电阻张量和一个二阶电导张量。并给出了它们的计算公式。分析表明各向异性电阻元件的欧姆定律具有近似性。     

Self-Adjoint Vector Variational Formulation for Lossy Anisotropic Dielectric Waveguide

This paper presents the derivation of a new self-adjoint variational formula for complex propagation constant in a lossy anisotropic dielectric waveguide, in terms of the magnetic field and real frequency. The ability to include loss and anisotropy (into the permittivity tensor) while preserving the self-adjointness of the system is achieved by using the less common real-type inner product. When used as a basis of Rayleigh-Ritz or finite-element methods, the formula leads to the canonical eigenvalue eqnation of the form Ax= gamma/sup 2/Bx.     

各向异性介质在三维ADI-FDTD中的应用

该文研究一种减小三维交替方向隐式时域有限差分法(ADI-FDTD)数值色散的新方法。通过在三维空间中合理添加各向异性介质,达到调整相速的目的,从而减小数值色散,使计算结果更加精确。首先对添加各向异性介质后的三维ADI-FDTD迭代公式进行变形,并得到新的数值色散关系,从而求解得到各向异性介质的相对介电常数。以空心波导和具有介质不连续性的波导作为数值算例,分析不同的各向异性介质和添加方法对计算精度的影响,并与传统ADI-FDTD得到的结果和计算资源占用情况进行比较。结果表明通过正确选择各向异性介质和添加方法,可以有效地减小三维ADI-FDTD数值色散。     

Anisotropic permittivity and attenuation extraction frompropagation constant measurements using an anisotropic full-wave Green'sfunction solver for coplanar ferroelectric thin-film devices

In this paper, a full-wave spectral-domain integral-equation technique is used to study double substrate layer coplanar devices with the ferroelectric thin film adjacent to the conductor guiding interfacial surface. The Green's function is used in the anisotropic situation for anisotropic permittivities. In examining specific laboratory data, going from an unbiased static electric field to the biased case, the permittivity tensor is allowed to go from a unity tensor to a uniaxial one. Consistent with this permittivity tensor behavior, the attenuation trend with frequency and its amplitude is also found     

Application of the radio-frequency interferometry method to a stratifield anisotropic medium

Interference patterns are calculated for a horizontal dipole laid on the surface of a stratified medium with both anisotropic permittivity and permeability tensors. The anisotropy in permitivity affectts the radiated fields in the endfire direction, and the anisotropy in permeability affects those in the broadside direction. The effects of anisotropy are illustrated for various cases.     

Inverse scattering of inhomogeneous biaxial materials coated on aconductor

The inverse scattering of inhomogeneous biaxial materials coated on a perfectly conducting cylinder with known cross section is investigated. A group of unrelated incident waves is used to illuminate the cylinder. By properly arranging the direction and polarization of various unrelated incident waves, the difficulties of ill-posedness and nonlinearity were circumvented and the permittivity tensor distribution can be reconstructed through simple matrix operations. For theoretical formulation based on the boundary condition, a set of integral equations is derived and solved by the moment method as well as the unrelated illumination method. Numerical results show that the permittivity tensor distribution of the materials can be successfully reconstructed even when the permittivity is fairly large. Good reconstruction has been obtained both with and without Gaussian noise in measured data. In addition, the effect of noise contamination on imaging is also examined     

Split frequencies in planar axisymmetric gyroelectric resonators

Axisymmetric gyroelectric disk, ring, and composite resonator structures have been characterized for both InSb and GaAs semiconductors at 77 K. The calculations assume that these materials can be represented by the tensor permittivity derived from the Drude model of cyclotron motion in a plasma. Resonance and loss regions are identified and the sensitivity of normal mode splitting and onset frequencies to material and geometrical variables are graphed and tabulated. The information is presented in terms of signal frequency and the bias field to permit a direct comparison with results from ferrimagnetic structures. Semiconductor calculations show two extraordinary wave resonances and predict excellent symmetrical wide-band normal mode splitting. Field plots for the semiconductor disk and ring are included to explain coupled mode behaviour between modes in different bias regions     

Shielding Properties of a Wire-Medium Screen

The shielding performance of a planar metamaterial wire-medium (WM) screen under plane-wave illumination is studied. The screen consists of a finite number of periodic layers of thin conducting cylinders embedded in a dielectric matrix; in the low-frequency limit and for waves with the electric field polarized along the wire direction, such a screen can be modeled as a homogeneous slab with a plasma-like dispersive permittivity. In particular, well below the plasma frequency, the effective relative permittivity is negative and very large in absolute value, giving rise to high values of the shielding effectiveness. A comparison with a conventional planar metal screen is reported, showing how the proposed structure can be designed to be advantageous in terms of low density and weight saving. In order to be effective against arbitrarily polarized waves, the original structure is modified, adding a second WM screen with wires orthogonally oriented with respect to the first one. Numerical results are provided that illustrate the validity of the homogenized model in predicting field levels both near to and far from the screen and show the shielding performance attainable with the proposed metamaterial screen in both single- and double-layer configurations at normal incidence.     

Analysis and Calculations on Dispersion Relation and Coupling Resistance of Periodic Plasma-Cavities

The plasma tensor dielectric permittivity and electromagnetic field accurate expressions in the external axial magnetic field are obtained from the Maxwell’s equations and the double component plasma particle linear movement equations. Further, the flux of energy inside the plasma-cavity drift channel is presented. Based on them, some of the property of cavity passband dispersion and coupling resistance of plasma-filled coupled-cavities slow wave structure in different plasma density and magnetic field conditions is analyzed according to the numerical calculation.     

FDFD analysis of electromagnetic scattering in anisotropic mediausing unconstrained triangular meshes

A method using finite differences in the frequency domain (FDFD) for modeling field interaction and propagation in anisotropic media with generalized tensor permittivity and permeability, and with complex geometry, is presented. The method uses an unconstrained mesh with triangular cells, which provides an efficient discrete approximation of curved surfaces. The two-dimensional problem with transverse field excitation is studied. Computed results comparing this algorithm to published data for the former case show excellent agreement. The analysis provides information for all view angles simultaneously at a single frequency. The method can be adapted to a time-domain formulation to analyze the effects of wave pulses and multiple frequencies at a single observation angle     

Propagation of ELF waves below an inhomogeneous anisotropic ionosphere

The ionospheric anisotropy is considered with horizontal magnetic field either for transverse (East-West or West-East) or for longitudinal (South-North) propagation. For transverse propagation in a vertically stratified medium the differential equations of the various field components are uncoupled and a closed form solution is given for identical exponential height variation of the components of tensor conductivity. For arbitrary height variation of the tensor conductivity numerical solutions are obtained after expressing the surface impedance below the ionosphere in terms of a Riccati-type differential equation. The West-East direction of propagation exhibits a lower attenuation constant than the East-West direction forf < 1000cps. This is contrary to the expectations based on a model of a homogeneous anisotropic ionosphere. For longitudinal propagation the differential equations of the various field components are coupled, with the coupling being particularly strong above theDregion. The differential equations are simplified by assuming no coupling in the lower ionosphere and strong coupling above a pre-selected altitudey_{1}. For exponential height variation of the tensor conductivity components the closed form solution differs negligibly from the isotropic case. For arbitrary height varition of the tensor conductivity numerical solutions are obtained similarly as for the transverse propagation. Over most of the frequency range the attenuation figures for South-North propagation are intermediate between the corresponding figures for West-East and East-West propagation.     

A General Three-Dimensional Tensor FDTD-Formulation for Electrically Inhomogeneous Lossy Media Using the Z-Transform

A general three-dimensional tensor finite-difference time-domain (TFDTD) formulation is derived to model electrically inhomogeneous lossy media of arbitrary shapes. The time domain representation of electric losses is achieved using Z-transforms. The regular cubical grid structure is maintained everywhere in the calculation domain by defining a 3-D face-fraction based 3 x 3 permittivity tensor on the interfaces that describes the relationship between the (known) average flux density vector and the (unknown) local electric field vector. For electrically lossy media, this tensor is complex in the frequency domain. However, it can be modified for use with the Z-transform. Only this modified real form is inverted, then transformed from the frequency into the Z-domain, and finally into the time domain. Furthermore, a local interface matrix is used to describe the relationship between the local electric field in the grid node and its counterpart on the other side of the interface. This matrix is complex in the frequency domain for lossy media. By applying the Z-transform, this matrix can also be transformed into the time domain using only real modified matrix elements. The accuracy of the method is confirmed by comparisons with analytical solutions.     

Macroscopic characterisation of a two-fluid anisotropic warm plasma

Two `compressivity tensors? are suggested, which, together with the permittivity tensor and the permeability, with characterise the macroscopic electromagnetic properties of an anisotropic warm plasma under the two-fluid model. A new set of four governing equations is formulated, which is both mathemathematically concise and amenable to meaningful physical interpretation.     

High-frequency EM scattering by edges in artificially hard and softsurfaces illuminated at oblique incidence

Uniform high-frequency expressions describing the field scattered by edges in anisotropic impedance surfaces illuminated at oblique incidence are provided. The specific anisotropic impedance boundary condition considered here exhibits a vanishing surface impedance along a principal anisotropy axis and an arbitrary one in the orthogonal direction. In certain circumstances, this tensor surface impedance may represent an accurate model for describing the scattering properties of artificially hard and soft surfaces. In order to simplify the analysis but without losing pertinence with real problems, in all canonical configurations we consider a face of the wedge to be perfectly conducting. The anisotropic impedance face is characterized by a tensor surface impedance with the principal anisotropy axes parallel and perpendicular to the edge