Volume Polarization Currents Research Articles

Generation of Numerical Data for the Facilitation of the Personalized Hyperthermic Treatment of Cancer with an Interstitial Antenna Array Using the Method of Symmetrical Components

The method of moments combined with the method of symmetrical components is used for the analysis of interstitial hyperthermia applicators. The basis and testing functions are both piecewise sinusoids, qualifying our technique as a Galerkin one. The dielectric coatings are modeled by equivalent volume polarization currents, which are simply related to the conduction current distribution, avoiding in that way the introduction of additional unknowns or numerical integrations. The results of our method for a four-dipole circular array, are in agreement with those already published in literature for a same hyperthermia configuration. Apart from being accurate, our approach is more general, more computationally efficient and takes into account the coupling between the antennas.

Internally Combined Volume-Surface Integral Equation for a 3-D Electromagnetic Scattering Analysis of High-Contrast Media

An internally combined volume surface integral equation (ICVSIE) for analyzing three-dimensional (3-D) electromagnetic scattering from heterogeneous high-contrast (HC) dielectric objects is proposed. Iteratively solved (generalized) volume integral equations [(g)VIEs] often converge slowly when applied to the analysis of electromagnetic interactions involving dielectric objects with permittivities much higher than those of the surrounding medium [HC breakdown] or discretized using mesh elements much smaller than the wavelength [low-frequency (LF) breakdown]. The proposed ICVSIE hybridizes a VIE and a surface integral equation (SIE) in a manner that eliminates both breakdown phenomena. Just as in previous hybrid VIE–SIE approaches, the ICVSIE invokes Huygens surface equivalence principle to transform the original problem into coupled equivalent exterior and interior scenarios. In the exterior scenario, surface currents radiate in the original surrounding medium; in the interior problem, surface and volume polarization currents radiate in a medium with permittivity closer to that of the object. By judiciously combining integral equations pertinent to both scenarios, the ICVSIE system is assembled. Numerical results show that the proposed ICVSIE is both HC and LF stable when applied to the analysis of 3-D scattering problems.

Low-Frequency Stable Internally Combined Volume-Surface Integral Equation for High-Contrast Scatterers

Volume integral equations (VIEs) are commonly used to analyze scattering from inhomogeneous dielectric objects. Unfortunately, when VIEs are applied to high-contrast scatterers, their discretization results in ill-conditioned systems of equations. Oftentimes volume-surface integral equations (VSIEs) are used to eliminate this effect. However, when the scatterer’s mesh has elements that are much smaller than the wavelength, VSIEs become ill-conditioned, too. This letter introduces a new set of internally combined VSIEs (ICVSIEs) that exhibit neither of these ill-conditioning phenomena. Just like in previous VSIE methods, surface currents are used to artificially increase the effective permittivity of the background medium in which volume polarization currents radiate. To remove ill-conditioning due to electrical size, coupling between the surface and volume is accounted for by judiciously adding contributions due to “exterior” and “interior” surface currents. Numerical data obtained by analyzing time-harmonic TE scattering from various 2-D layered cylinders suggests that discretization of the new ICVSIE yields matrices that are unaffected by the scatterer’s maximum permittivity and electrical size.

A QUASI-STATIC THEORY FOR DIELECTRIC-COATED THIN-WIRE ANTENNA STRUCTURES

Analytical investigations of the problem of dielectric- coated thin-wire antenna structures have invariably focused on the physics of developing appropriate models for the dielectric insulation on the thin-wire conductors that serve as antenna for the structure. These include the frequency domain moment-method-based approaches in which the dielectric insulation is replaced by equivalent volume polarization currents; and the time-domain analysis based on the 'equivalent radius' concept. An earlier paper gave a physical interpretation to the frequency-domain solutions to suggest that the volume polarization currents derive from an equivalent static charge distribution, which excites an essentially radially-directed quasi-static fleld, conflned to the region associated with the dielectric insulation. It is the main objective of this paper to investigate the veracity of the claims made in open literature as they concern the physics of the model for the dielectric insulation in terms of the electric fleld excited in the dielectric region. And to that end, simulation experiments were carried out, using a commercial Transmission Line Matrix (TLM) Method code, with which the characteristic features of the radial and axial components of the electric fleld within the dielectric region were investigated. The simulation results obtained from the experiments suggest that the fleld in question is not only of the quasi-static variety, but that it is also characterized by an axial component that meets the

Rigorous Analysis of Rectangular Dielectric Resonator Antenna With a Finite Ground Plane

A probe-fed rectangular dielectric resonator antenna (RDRA) placed on a finite ground plane is numerically investigated using method of moments (MoM). The whole structure of the antenna is exactly modeled in our simulation. The feed probe, coaxial cable and ground plane are modeled as surface electric currents, while the dielectric resonator (DR) and the internal dielectric of coaxial cable is modeled as volume polarization currents. Each of the objects is treated as a set of combined field integral equations. The associated couplings are then formulated with sets of integral equations. The coupled integral equations are solved using MoM in spatial domain. The effects of ground plane size, air gap between dielectric resonator and ground plane, probe length, and position on the radiation performance of the antenna including resonant frequency, input impedance, radiation patterns, and bandwidth are investigated. The results obtained for the antenna parameters based on the MoM investigation shows that there is a close agreement with those obtained by measurement. Moreover it is shown that the MoM results are more accurate than other simulation results using software package such as High Frequency Structure Simulator (HFSS).

A fast time domain integral equation based scheme for analyzing scattering from dispersive objects

A fast integral equation-based scheme for analyzing transient scattering from inhomogeneous dispersive bodies is presented. A time domain integral equation in terms of the electric flux inside the body is constructed by invoking the volume equivalence principle, i.e., by equating the sum of the incident electric field and that radiated by equivalent volume polarization currents to the total electric field. The proposed algorithm for solving this time domain integral equation incorporates a recursive convolution scheme that updates the polarization current from knowledge of the electric flux. To reduce the computational cost and memory requirement of the resulting marching-on-in-time scheme, it is augmented with the plane wave time domain algorithm. Numerical results that validate the proposed approach and demonstrate its accuracy are presented.

Efficient physical optics approximation for the calculation of radiation patterns of planar antennas located on a finite ground plane

A physical optics (PO) model is applied to investigate the radiation characteristics of a microstrip patch antenna located on a finite ground plane. The standard PO approach consists of the replacement of the dielectric and the ground plane by electric volume and surface polarization currents. In this paper these polarization currents are obtained as a combination of polarization currents of the infinite structure and auxiliary polarization currents, only present beyond a certain distance from the source. Simple expressions are derived for these auxiliary currents, based on the expansion wave concept. The radiation patterns consist of two terms: the radiation pattern of the antenna on the infinite ground plane and a diffraction term, which takes into consideration the finiteness of the layer structure. The diffraction term is expressed in terms of integrals containing the auxiliary polarization currents. Some of these integrals can be evaluated analytically. Numerical and experimental results are presented.

A galerkin moment method for the analysis of insulated wires above a lossy half-space

In this paper, an efficient method is proposed for the analysis of insulated wires above a lossy half-space. The reaction concept is used to formulate the electromagnetic boundary value problem. The solution is a Galerkin moment method solution with piecewise sinusoids as basis and testing functions. The influence of lossy half-space is taken into account via equivalent images, and the currents of images are related to the source current. The dielectric coating is modeled by equivalent volume polarization currents, which are simply related to the conduction current distribution. In this way, the dielectric-coating and lossy half-space cause no new unknowns to the problem solution, the size of the impedance matrix for insulated wires above lossy ground is the same as that of bare wires in free space. The insulation is accounted for entirely through a modification of the symmetric impedance matrix. The results obtained exhibit excellent agreement with those by rigorous method or experiments.

Improved radiation pattern computation of finite microstrip antennas

A refined method to compute the radiation characteristics of microstrip antennas on finite substrates is presented. Electric surface and volume polarization currents are approximately calculated using the Green's function of an infinite dielectric slab. A comparison with measured radiation patterns shows that the excitation via coaxial probe needs to be included in the calculations for more accurate results. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 23: 263–265, 1999.

Moment method analysis of dielectrically loaded antennas

The method of moments is used to analyse the impact of square cylindrical dielectric loading on electrically thin circular cylindrical wire antennas. The dielectric inhomogeneity is modelled by equivalent volume polarization currents with the conduction currents on the wire and the polarization currents in the dielectric being treated as independent unknowns. The technique is very efficient in terms of computation time and can be used to analyse arbitrary dielectric loading on a wide variety of antenna structures.

Radiation and scattering from infinite periodic printed antennas with inhomogeneous media

The hybrid method of moments (MoM)/Green's function method technique is applied to infinite periodic printed antenna arrays containing dielectric inhomogeneities. The solution uses an integral equation for an infinite periodic printed array on or over a homogeneous dielectric substrate, coupled with equivalent volume polarization currents for dielectric inhomogeneities on top of the homogeneous substrate. Volume pulse-basis functions were used to expand the volume polarization currents. A hybrid MoM/Green's function method solution was then obtained through the matrix form of the problem. The two-dimensional (2-D) solution of plane wave scattering from a grounded dielectric slab was used to validate the reaction impedance of the dielectric inhomogeneity. Several infinite periodic printed dipole arrays with dielectric supports and overlays were studied with this solution and good agreement was observed between the hybrid MoM/Green's function method and waveguide simulator experiments.

Moment method analysis of the electric shielding factor of a conducting TM shield at ELF

This paper presents an integral equation and method of moments (MM) solution to the problem of TM transmission by a metallic conducting shield at extremely low frequencies (ELF). To obtain an accurate and efficient solution, the equivalent volume polarization currents representing the shield are expanded in terms of physical basis functions, corresponding to two planewaves propagating normal to the surface of the shield. ELF approximations are used to obtain closed form expressions for certain crucial elements in the MM matrix equation where extreme accuracy between the relative magnitudes of self and mutual impedance terms are required. Numerical data will illustrate that despite the fact that the equivalent polarization currents are being computed very accurately, the method is not capable of computing the extreme near zone electric fields of these currents with sufficient accuracy to compute the electric shielding factor. An alternate method, based upon the use of the volume equivalence theorem to directly compute the total electric field in the shield is devised, and is found to accurately compute the electric shielding factor.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Scattering by a Chiral Cylinder of Arbitrary Cross Section in the Presence of a Half-Plane

An integral equation and method of moments/Green's function solution to the problem of scattering by a chiral cylinder of arbitrary cross section in the presence of a perfectly conducting half-plane is presented. The volume equivalence theorem for chiral media is used to formulate a pair of coupled vector integral equations for the equivalent electric and magnetic volume polarization currents representing the chiral cylinder. The presence of the half-plane is accounted for by including the half-plane Green's function in the kernel of the integral equations, and efficient techniques for accurately evaluating the integrals in this Green's function are presented. Numerical results illustrate that a chiral cylinder surrounding the half-plane edge can significantly modify the scattering from the edge. The chiral cylinder is also seen to produce significant cross-polarized scattered fields, which are a direct result of the rotation of field polarization in a chiral medium.

TE-scattering from dense homogeneous infinite dielectric cylinders of arbitrary cross-section

A numerical approach to obtain the fields scattered by a homogeneous dielectric cylinder of arbitrary cross section which is illuminated by a TE plane wave is presented. The equivalence theorem is used to transform the problem of solving Maxwell's equations in the whole space, subject to the conditions imposed by the presence of the cylinder and the incident field, into an operator equation for the volume polarization currents in the cylinder. A set of expansion functions is then used to solve the problem using Galerkin's technique. These expansion functions are obtained by dividing the cylinder cross-section into a number of triangular patches and defining, for each node in the mesh of triangles, a basis function which depends on the dimensions of the triangles attached to it. This basis function is divergence-free for all the internal nodes, with surface charges associated to the external nodes only. The computed results include the radar cross sections. Several geometries are studied, and the computed results are compared with exact or numerical results.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Equivalence of integral and integrofunctional equations in electrodynamic problems of diffraction by inhomogeneous bodies

Relations for fields with specified distributions of volume electric and magnetic currents are investigated. The dependence of the term outside the integral on the limit method for calculation of improper integrals is shown; an evaluation method is proposed. The relations are used to establish equivalence between integral equations with volume polarization currents and integrofunctional equations of the standard boundary-value problem of electrodynamic for an inhomogeneous ferrite body. It is shown that the solutions of both types of equations satisfy the boundary conditions. The practical use of integrofunctional equations in the form of systems of integral equations of the second kind and functional equations is discussed.

An integral equation approach to the analysis of finite microstrip antennas: volume/surface formulation

An E-field integral equation for the analysis of finite printed circuit antennas with multiple dielectric regions is developed. In this analysis, the ground plane is considered to be finite. The dielectric substrates may be either lossless or lossy, and they may be inhomogeneous but must be finite. The equivalence principle is used to replace all conducting bodies by equivalent surface electric currents and all dielectrics by equivalent volume polarization currents. The respective boundary conditions on the dielectrics and the conductors are utilized to solve for the electric current on the entire structure. Typical results are presented to illustrate the potential of this method. >

Scattering by a chiral cylinder of arbitrary cross section

An integral equation and method-of-moments (MM) solution to the problem of scattering by an inhomogeneous chiral cylinder of arbitrary cross section is presented. The volume equivalence theorem for chiral media is developed and used to formulate a set of coupled integral equations for the electric and magnetic volume polarization currents representing the chiral cylinder. These coupled integral equations are solved using a standard pulse basis and point-matching MM solution. Numerical results, including echo width and internal fields, are presented for the scattering by chiral slabs and circular cylinders. These results are compared to exact solutions when available.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Analysis of microstrip antennas using moment methods

The method of moments is used to analyze microstrip antennas of rectangular and nonrectangular shape. Surface currents are used to model the microstrip patch and volume polarization currents for the dielectric slab. The method requires unusually precise computation of the impedance matrix but is capable of accurately predicting currents, impedance, and resonant frequency of the antenna.

Wire antennas in the presence of a dielectric/ferrite inhomogeneity

A moment method solution for treating thin-wire antennas in the presence of an arbitrary dielectric and/or ferrite inhomogeneity is presented. The wire is modeled by an equivalent surface current density, and the dielectric/ferrite inhomogeneity is modeled by equivalent volume polarization currents. The conduction currents on the wire and the polarization currents in the dielectric/ferrite inhomogeneity are treated as independent unknowns and determined in the moment method solution. The method is applied to the problem of a loop antenna loaded with dielectric or ferrite. Numerical results are presented, and are in good agreement with measurements and previous calculations.

H-plane sectoral dielectric horn antenna

The purpose of this paper is to investigate theoretically and experimentally the radiation aspect of a H-plane sectoral dielectric horn antenna. In the theoretical analysis, the radiated field at a distant point from this antenna is evaluated by determining separately the field from the waveguide in absence of the scatterers (scatterers are flares of the horn) and the scattered field and then adding the two fields at the point. In order to simplify the problem, the volume polarization currents are approximated with sheet currents for thin dielectric flares.The experimental study is carried out at X-band with 10°, 20°, and 30° dielectric (εr = 2.62) horns and also with 25° dielectric (εr = 3.0) horn at 1λ and 2λ axial lengths in all cases. The results of the experimental investigation show fairly good agreement with the predicted pattern. Limitations of the theory are also discussed.