Lossy Dielectric Cylinder Research Articles

Electromagnetic Wave Scattering by a Multiple Core Model of Composite Cylindrical Wires at Oblique Incidence

A complex cylindrical structure consisting of a group of parallel stratified circular lossy dielectric cylinders, embedded in a dielectric circular cylindrical region and surrounded by unbounded dielectric space, is considered in this paper. The scattering of electromagnetic (EM) plane waves by the aforementioned configuration was studied; the EM waves impinged obliquely upon the structure and were arbitrarily polarized. The formulation used was based on the boundary-value approach coupled with the generalized separation of variables method. The EM field in each region of space was expanded in cylindrical wave-functions. Furthermore, the translational addition theorem of these functions was applied in order to match the EM field components on any cylindrical interface and enforce the boundary conditions. The end result of the analysis is an infinite set of linear algebraic equations with the wave amplitudes as unknowns. The system is solved by the truncation of series and unknowns and then matrix inversion; thus, we provide a semi-analytical solution for the scattered far-field and, as a consequence, for the scattering cross section of the complex cylindrical structure. The numerical results focus on calculations of the electric- and magnetic-field intensity of the far-field as well as of the total scattering cross section of several geometric configurations that fall within the aforementioned general structure. The effect of the geometrical and electrical characteristics of the structure on the scattered field was investigated. Specifically, the cylinders’ size and spacing, their conductivity and permittivity as well as the incidence direction were modified in order to probe how these variations are imprinted on scattering. Moreover, comparisons with previously published results, as well as convergence tests, were performed; all tests and comparisons proved to be successful.

Relating Forest Biomass to the Polarization Phase Difference of the Double-Bounce Scattering Component

Above-ground biomass (AGB) is a key parameter for estimating the carbon resources of forests; however, it is challenging to retrieve the AGB in tropical forests. Based on the modeling of the scattering process in an infinite-length lossy dielectric cylinder, in this work, the copolar phase difference (PPD), <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \phi _{\mathrm {tr}}$ </tex-math></inline-formula> , of the double-bounce scattering component from tree trunks was investigated. The results showed that there is an almost monotonic decrease in PPD as the trunk radius increases, meaning that the AGB can also be related to the PPD through the allometric equation. The data analyzed in this letter were obtained from the fully polarimetric P-band airborne data set acquired over Franch Guiana in 2009 as part of the European Space Agency campaign, TropiSAR. The PPD of the double-bounce scattering component was obtained using the Freeman–Durden decomposition algorithm. As expected, it was found that AGB was well correlated with the PPD, giving an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R^{2}$ </tex-math></inline-formula> value of 0.7576.

Analysis of Thin Truncated Cylinder Scatterers Using Incomplete Hankel Functions and Surface Impedance Boundary Conditions

The incomplete Hankel functions (IHFs) are employed to evaluate the scattered field from thin truncated cylinders excited by uniform plane waves or by arbitrarily oriented elemental current sources. Metallic and dielectric lossy structures are modeled by means of impedance boundary conditions (IBCs) including surface curvature effects. The scattering currents, expanded in triangular basis functions, are determined upon solving electrical field integral equations (EFIEs) by means of the point-matching method of moments (MoM). The scattered field is then expressed in closed analytical form in terms of IHFs, thus yielding highly accurate numerical results. Furthermore, accurate IHFs approximants are also derived to reduce the computational burden in the analysis of large electrical structures. The proposed approach is demonstrated in practical applications involving cylindrical dielectric structures used in planar lenses, lossy dielectric cylinders suitable to model cane-like vegetation, as well as polarization rotators featuring multiple stages composed of thin metallic wire arrays.

TMz/TEz Vector Potentials Due to an Arbitrarily Oriented Dipole in 3‐D Space in the Presence of an Infinite Dielectric Cylinder

AbstractThis manuscript provides a new formulation for the classic electromagnetic scattering problem of a point dipole source in the presence of an infinite lossy dielectric cylinder embedded within a lossy space. The formulation is in terms of the TMz and TEz vector potential components (scalar potentials) Az and Fz for an arbitrary dipole orientation. A new Bessel function identity, apparently derived here for the first time, shows that the new solution is equivalent to the previous dyadic vector wave function solutions that solve for the electric and magnetic fields directly. Expressions for the scattered potential coefficients, for a dipole inside or outside the cylinder, can be reduced to a linear set of two equations that has a simple closed‐form solution. The new potential formulation should find application in the numerical solution of various problems in electromagnetics and geophysics involving tunnels or other structures that can be modeled as cylinders.

Evaluation of SAR in a human body model due to wireless power transmission in the 10 MHz band

This study discusses a computational method for calculating the specific absorption rate (SAR) due to a wireless power transmission system in the 10 MHz frequency band. A two-step quasi-static method comprised of the method of moments and the scalar potential finite-difference method are proposed. The applicability of the quasi-static approximation for localized exposure in this frequency band is discussed by comparing the SAR in a lossy dielectric cylinder computed with a full-wave electromagnetic analysis and the quasi-static approximation. From the computational results, the input impedance of the resonant coils was affected by the existence of the cylinder. On the other hand, the magnetic field distribution in free space and considering the cylinder and an impedance matching circuit were in good agreement; the maximum difference in the amplitude of the magnetic field was 4.8%. For a cylinder–coil distance of 10 mm, the difference between the peak 10 g averaged SAR in the cylinder computed with the full-wave electromagnetic method and our quasi-static method was 7.8%. These results suggest that the quasi-static approach is applicable for conducting the dosimetry of wireless power transmission in the 10 MHz band. With our two-step quasi-static method, the SAR in the anatomically based model was computed for different exposure scenarios. From those computations, the allowable input power satisfying the limit of a peak 10 g averaged SAR of 2.0 W kg−1 was 830 W in the worst case exposure scenario with a coil positioned at a distance of 30 mm from the chest.

Development of a Scattering Model for Soybean Fields and Verification with Scatterometer and SAR Data at X-Band

This paper presents a scattering model and measurements of backscattering coefficients for soybean fields. The polarimetric radar backscatters of a soybean field were measured using the ground-based X-band polarimetric scatterometer in an angular range from <TEX>$20^{\circ}$</TEX> to <TEX>$60^{\circ}$</TEX>. The backscattering coefficients were also obtained using the COSMO-SkyMed (Spotlight mode, HH-polarization) from July to October 2010. The backscattering coefficients of the soybean field were computed using the 1st-order radiative transfer model (RTM) with field-measured input parameters. The soybean layer is composed of the stems, branches, leaves, and soybean pods. The stems, branches, and pods are modeled with lossy dielectric cylinders, the leaves are modeled with lossy dielectric disks. The estimated backscattering coefficients agree quite well with the field-measured radar backscattering coefficients.

Analytic Propagation Model for Wireless Body-Area Networks

Wave propagation in wireless body area networks (WBAN) is analytically modeled as a polarized point source close to an elliptic lossy dielectric cylinder. Using the Fourier transform along the axes, the expansion in terms of Mathieu functions in cross section, and the impedance boundary condition (IBC) on surface, the field distribution outside the cylinder can be formulated. In particular, the path gain of propagation around the human body is described in detail for 915-MHz and 2.40-GHz bands toward industrial, scientific, and medical (ISM) applications.

Accurate Modeling of Body Area Network Channels Using Surface-Based Method of Moments

An accurate method for modeling body shadowing in body area networks (BANs) is presented, based on an efficient surface-based method-of-moments (MOM) solution. The method allows the fields radiated by a transmit line current with arbitrary orientation (polarization) in the presence of a lossy dielectric cylinder of arbitrary cross section to be computed with high accuracy. The fields due to a point source are then found using Fourier transform techniques. The utility of the method for BAN modeling is demonstrated by comparing with BAN measurements on a human subject performed in a compact chamber and in an open field.

Foliage Attenuation Over Mixed Terrains in Rural Areas for Broadband Wireless Access at 3.5 GHz

This paper reports the modeling of foliage attenuation for a broadband wireless access system deployed over mixed terrains in rural areas at 3.5 GHz. The foliage is composed of leaves and leafstalks, and are the dominant scatterers along the transmission paths. The foliage attenuation is determined using the Torrico-Lang model combined with digital topography information. In this model, leaves are modeled as thin lossy circular dielectric discs whereas leafstalks (petioles) are modeled as thin lossy dielectric cylinders. Three measurement campaigns were performed using the mobile WiMAX system (IEEE 802.16 e) deployed in Hetzwege/Abbendorf during winter, spring and mid-summer. Using the winter data as a baseline, the foliage loss due to different degrees of foliation in spring and in winter is studied. The derived foliage loss is then verified and compared with an empirical exponential decay model.

Channel Simulator for Land Mobile Satellite Channel Along Roadside Trees

We study the signal fading for the land mobile satellite channel caused by roadside trees. A channel simulator is developed which takes into account the signal fading caused by position-dependent tree scattered fields and by swaying tree components. In the model, the tree canopy is modeled as a vertically oriented cylindrical volume containing randomly distributed and oriented leaves and branches. The tree trunk is modeled as a finite lossy dielectric cylinder. Leaves are modeled as thin lossy dielectric disks and branches as finite lossy dielectric cylinders. The scattering pattern of the new model has a narrow forward lobe with an isotropic background which is comparable to the one found using the radiative energy transfer theory. In addition, the variation of the specific attenuation with frequency of the model is fairly similar to the one given in the ITU Recommendation. The model is validated using measurements at 2 GHz in terms of the cumulative distribution functions of the received signal and the Ricean K-factor, average fade duration and level crossing rate. Good agreement is found between the measured and simulated statistics.

Assessment of Optical Absorption in Carbon Nanotube Photovoltaic Device by Electromagnetic Theory

An electromagnetic (EM) scattering model is built for a kind of single-walled carbon nanotube (SWCNT) photovoltaic device excited by light. In this model, the exciting light is treated as classical EM wave with a very high frequency, and the SWCNTs in the device were treated as a lossy dielectric cylinder with frequency-dependent complex permittivity. Based on the EM scattering model, the Foldy-Lax multiple-scattering equation for the SWCNT cylinders can be derived, and then, the absorbed power of SWCNTs can be estimated. We also use EM simulation software - high frequency structure simulator (HFSS) - to extract the optical absorption of SWCNTs, and then the property of optical absorption of the device is studied more carefully; and the EM scattering model is also validated through HFSS simulation. From the results, some advices are given for the design of such kind of device.

A Full-Wave 2.5D Volume Integral Equation Solver for 3D Millimeter-Wave Scattering by Large Inhomogeneous 2D Objects

A two-and-a-half dimensional full-wave forward solver to compute the three-dimensional (3D) electromagnetic field scattered by an infinitely long inhomogeneous (lossy) dielectric cylinder with arbitrary cross-sectional shape under a given 3D time-harmonic illumination is presented. The relevant set of linear equations, obtained after performing a spatial Fourier transform of the fields along the axial direction and applying a method of moments discretization to the two-dimensional contrast source volume integral equation, is solved iteratively with a stabilized biconjugate gradient fast Fourier transform method. In this way, objects with cross-sectional dimensions of several to many wavelengths can be handled in a very fast way. Furthermore, a vectorial 3D Gaussian beam illumination, usually employed in active millimeter-wave (mm-wave) imaging systems, is implemented using a complex source Gaussian beam formulation. The validity of the method is proved by comparison with analytic results and with the results from a full-wave 3D solver. Finally, the method is applied to a millimeter-wave imaging example, showing the scattering from an object hidden under clothing on a human body.

Electromagnetic modelling of curved lossy dielectric surface and cylinder

A new electromagnetic model for curved dielectric surfaces and cylinder has been introduced. The model considers scatterers as a lossy dielectric body. The theoretical and simulation results have been compared with the literature and the model agrees with the published results of the hollow cylinder for which an exact solution exists. Figures of relative error versus ka and kT of hollow cylinder (a) single- (b) three-layered cylinder are used for the parameters. The curved dielectric scatterer is discretised to N small element, and then the contributions of each element are sum up coherently to find the total response. Finally, the simulations for curved cylinder and convex surfaces of arbitrary shape are presented.

Torque and longitudinal force exerted by eigenmodes on circular waveguides

It is demonstrated that rotating waveguide eigenmodes may exert a longitudinal force, positive or negative, as well as a torque on the guiding structure itself or part of it. Configurations that are considered include a lossy dielectric cylinder bounded by a hollow waveguide, and a lossy dielectric fiber. Both propagating and evanescent eigenmodes are considered. The analysis is based on a general formulation of the linear and angular momentum currents flowing in the waveguide. The results of this study suggest a novel type of light-driven machine.

On the Schur complement form of the Dirichlet-to-Neumann operator

The Dirichlet-to-Neumann operator relates the values of the normal derivative of a scalar field to the values of the field itself on the boundary of a simply connected domain. Although it is easy to prove analytically that the Dirichlet-to-Neumann operator is self-adjoint, the discretization of the pertinent Green’s integral equation by means of the usual Galerkin approach generally results in a non-symmetric matrix representation of that operator. In this paper we remedy this by means of a Hamiltonian Schur complement method and compare it with other symmetrization approaches. It is also shown that the problem of E-wave scattering by a lossy dielectric cylinder can be nicely simplified by means of the Dirichlet-to-Neumann operator. A numerical Galerkin implementation demonstrates the strength and versatility of the present approach.

Multigrid Optimization Method Applied to Electromagnetic Inverse Scattering Problem

An iterative reconstruction algorithm of accelerating the estimation of the complex relative permittivity of a cylindrical dielectric object based on the multigrid optimization method (MGOM) is presented. A cost functional is defined by the norm of a difference between the scattered electric fields measured and calculated for an estimated contrast function, which is expressed as a function of the complex relative permittivity of the object. Then the electromagnetic inverse scattering problem can be treated as an optimization problem where the contrast function is determined by minimizing the cost functional. We apply the conjugate gradient method (CGM) and the frequency-hopping technique (FHT) to the minimization of the cost functional, and also employ the multigrid method (MGM) with a V-cycle to accelerate the rate of convergence for getting the reconstructed profile. The reconstruction scheme is called the multigrid optimization method. Computer simulations are performed for lossy and inhomogeneous dielectric circular cylinders by using single-frequency or multifrequency scattering data. The numerical results demonstrate that the rate of convergence of the proposed metod is much faster than that of the conventional CGM for both noise-free and noisy cases.

ITERATIVE SOLUTION TO THE TM SCATTERING BY TWO INFINITELY LONG LOSSY DIELECTRIC ELLIPTIC CYLINDERS

An analytic solution to the problem of a plane electromagnetic wave scattering by two infinitely long lossy dielectric elliptic cylinders is presented using an iterative procedure to account for the multiple scattered field between the cylinders. To compute the higher order terms of the scattered fields, the translation addition theorem for Mathieu functions is implemented to express the field scattered by one lossy dielectric cylinder in terms of the elliptic coordinate system of the other cylinder in order to impose the boundary conditions. Scattered field coefficients of various orders are obtained and written in matrix form. Numerical results are obtained for the scattered field in the far zone for different axial ratios, electrical separations, relative dielectric constants, and angles of incidence.

Image brightening in samples of high dielectric constant

An analytic solution is given for the electromagnetic problem of a lossy dielectric cylinder of infinite length, irradiated by a circularly polarized radiofrequency (RF) magnetic field; the NMR-active components of the field inside the cylinder are projected out by transforming the RF Hamiltonian to the rotating frame and retaining only those terms independent of time; it is noted that the resulting cartesian field components are required to be real. The squared magnitude of the NMR-active fields are then used to calculate the gradient-recalled images of the cylinder, for small tip angles of the magnetization; and the result is shown to predict almost quantitatively the intensity patterns of experimental proton images at 3.0 and 4.0 T, in a cylindrical phantom of radius 9.25 cm, filled with 0.05 M aqueous NaCl. In particular, the artifactual brightening at the center of the recorded image is convincingly reproduced in a simulation, whose underlying model excludes wave propagation along the direction of the cylinder axis. Formation of the artifact is explained in terms of the focussing of the RF magnetic field at the center of the cylinder, as illustrated by contour plots showing the time evolution of the rotating flux. An extended electromagnetic model—having the dielectric cylinder enclosed in a long, shielded volume resonator (e.g., of bird cage type)—is then sketched. The mathematical details appear in Appendix A; and the simulated images are shown to be virtually indistinguishable from those of the simpler original model. The theory of the Q, or quality factor, of the dielectric cylinder—considered itself as a resonant object—is developed for the enclosed cylinder model, where flux containment by the shield permits an unambiguous treatment of both the stored energy and the radiative losses. This is extended to treat the Q of a lossy dielectric sphere without shielding. Further plots of flux contours are given for the sphere, excited at 208 MHz with a uniform circularly polarized field, as well as by a surface coil, and for the enclosed cylinder in the range 140–160 MHz. It is then argued that the center brightening artifacts in magnetic resonance images are due to the underdamped dielectric resonance of the sample, i.e., at Q>0.5, while the overdamped condition, Q<0.5, leads to exclusion of flux from the center, i.e., to the classic skin effect. The term ‘dielectric resonance’ is shown to require careful interpretation for mixed-mode excitation, such as occurs with a surface coil. An extended reciprocity formula for NMR reception, valid for an arbitrary electromagnetic Green’s function, is also given in Appendix B.

Physical optics models for the backscatter response of road-surface faults and roadside pebbles at millimeter-wave frequencies

Theoretical models, based on the physical optics (PO) approximation, are presented to predict the backscatter response of road-surface faults and roadside pebbles. Two types of surface faults are considered, cracks and potholes. By applying the PO model, the backscattering coefficients of a road-surface crack are approximated by the radar cross section (RCS) per unit length of a lossy dielectric cylinder. For a road-surface pothole with a simple geometry, its RCS is estimated by the coherent sum of the backscattered fields from the pothole edges with significant backscatterers. The backscatter response of roadside pebbles is a combination of the surface scattering from surface roughness and the volume scattering from a layer of rock particles. The surface scattering is depicted by the integral equation method, a simplified second-order iterative physical optics approximation. The hybrid scattering model based on the theory of vector radiative transfer is employed to predict the volume scattering. The validity of the theoretical models is examined by comparing the simulation results with experimental data from the University of Michigan, where backscatter measurements at W-band frequencies were conducted on road-surface faults and roadside pebbles at near grazing incidence angles (74/spl deg/-88/spl deg/) (Sarabandi, K. et al., ibid., vol.45, p.1679-88, 1997; Li and Sarabandi, ibid., vol.47, p.851-61, 1999).

The 2.5-D multidomain pseudospectral time-domain algorithm

A 2.5-D multidomain pseudospectral time-domain (PSTD) method with a suitable well-posed perfectly matched layer is developed as an accurate and flexible tool for the simulation of electromagnetic wave propagation and scattering in conductive and inhomogeneous media. This approach allows for an accurate treatment of curved geometries with a high efficiency. Numerical results show an excellent agreement with analytical solutions for lossy dielectric cylinders. The 2.5-D multidomain PSTD algorithm is applied to several scattering and waveguiding problems.