The imaging of an imperfectly conducting cylinder buried in a three-layer structure by the genetic algorithm is investigated. An imperfectly conducting cylinder of unknown shape and conductivity buriedin the secondla yer scatters the incident wave from the first layer or the thirdla yer. We measure the scatteredfieldin the first andthird layers. Based on the boundary condition and the recorded scattered field, a set of nonlinear integral equations is derived and the imaging problem is reformulatedin to an optimization problem. The genetic algorithm is then employedto findout the global extreme solution of the cost function. Numerical results demonstrated that, even when the initial guess is far away from the exact one, goodreconstruction can be obtained. In such a case, the gradient-based methods often get trapped in a local extreme. In addition, the effect of uniform noise on the reconstruction is investigated.

Scattering by planar geometries with plane metal inclusions are analysed. The metal inclusions can be of arbitrary shape,and the material of the supporting slabs can be any linear (bianisotropic) material. We employ the method of propagators to find the solution of the scattering problem. The method has certain similarities with a vector generalisation of the transmission line theory. A general relation between the electric fields and the surface current densities on the metal inclusions and the exciting fields is found. Special attention is paid to the case of a periodic metal pattern (frequency selective structures,FSS). The method is illustrated by a series of numerical computations.

In this paper we study the electromagnetic (EM) wave propagation in a perfect magnetic medium with continuously varying magnetic permeability m(z) in one direction. We consider the inhomogeneity to be arbitrary and described by an infinite power series of z and use the Frobenious method to solve the governing differential equation of the problem in the frequency domain. We also give special attention to the first cut-off frequency of the main mode TM₁₁ and we propose a good estimation for it by means of the mean value of the magnetic permeability profile. The results from the mathematical analysis are applied to solve the direct problem of wave propagation in a system of three waveguides having two homogeneous filling materials and one that exhibits such inhomogeneous characteristics. We finally confront the inverse problem of magnetic permeability reconstruction by handling simulation data and a genetic optimization algorithm.

In this paper, we developed a general framework for the inversion of electromagnetic measurements in cases where parametrization of the unknown configuration is possible. Due to the ill-posed nature of this nonlinear inverse scattering problem, this parametrization approach is needed when the available measurement data are limited and measurements are only carried out from limited transmitter-receiver positions (limited data diversity). By carrying out this parametrization, the number of unknown model parameters that need to be inverted is manageable. Hence the Newton based approach can advantageously be used over gradient-based approaches. In order to guarantee an error reduction of the optimization process, the iterative step is adjusted using a line search algorithm. Further unlike the most available Newton-based approaches available in the literature, we enhanced the Newton based approaches presented in this paper by constraining the inverted model parameters with nonlinear transformation. This constrain forces the reconstruction of the unknown model parameters to lie within their physical bounds. In order to deal with cases where the measurements are redundant or lacking sensitivity to certain model parameters causing non-uniqueness of solution, the cost function to be minimized is regularized by adding a penalty term. One of the crucial aspects of this approach is how to determine the regularization parameter determining the relative importance of the misfit between the measured and predicted data and the penalty term. We reviewed different approaches to determine this parameter and proposed a robust and simple way of choosing this regularization parameter with aid of recently developed multiplicative regularization analysis. By combining all the techniques mentioned above we arrive at an effective and robust parametric algorithm. As numerical examples we present results of electromagnetic inversion at induction frequency in the deviated borehole configuration.

Rigorous and fast convergent analysis of a coupler slotted in common wall between two dissimilar rectangular waveguides is described by a mode-matching method combined with Fourier transform technique and consideration of the singularity of electromagnetic field around edges. Comparing with a conventional mode-matching method, the present method has two advantages. One is that it can avoid the usage of the dyadic Green's function, the other is that it can overcome the relative convergence problem. The consideration of the field singularity has greatly improved the convergence and the calculated accuracy of a solution. This analysis is rigorous and the computer cost is very low.

The Integral Equation Method (IEM) isapplied for about ten years to model the surface scattering phenomenon. Recently, Fung published in [1] an extra improved version of the IEM model. In thispap er, numerical and experimental validationsof the model are investigated. In backscattering, as in bistatic scattering, number of numerical validationsare made on a wide frequency band, by comparing IEM predictionswith a reference method results(Method of Moments). IEM results are also compared with those of some asymptotic models such as Small Perturbation Method (SPM) and Kirchhoff Model (KM) in the frequency domainswhere these latter are applicable. The improved model validation isac hieved by presenting confrontations of the simulation results with experimental data, some of them have been collected in appropriate papers, and the others come from experimentsw e conducted at the ElectroMagnetism and Radar Department (DEMR) of the Office National d'Etudes et de Recherches Aérospatiales (ONERA)-Toulouse (France).

In the first part of this work we show that, by working in Fourier space, the Bohren decomposition and the Helmholtz's decomposition can be combined into one decomposition. This yields a completely mathematical decomposition, which decomposes an arbitrary vector field on â„œ³ into three components. A key property of the decomposition is that it commutes both with the curl operator and with the time derivative. We can therefore apply this decomposition to Maxwell's equations without assuming anything about the media. As a result, we show that Maxwell's equations split into three completely uncoupled sets of equations. Further, when a medium is introduced, these decomposed Maxwell's equations either remain uncoupled, or become coupled depending on the complexity of the medium. In the second part of this work, we give a short introduction to contact geometry and then study its relation to electromagnetism. By studying examples, we show that the decomposed fields in the decomposed Maxwell's equations always seem to induce contact structures. For instance, for a plane wave, the decomposed fields are the right and left hand circulary polarized components, and each of these induce their own contact structure. Moreover, we show that each contact structure induces its own Carnot-Carathéodory metric, and the path traversed by the circulary polarized waves seem to coincide with the geodesics of these metrics. This article is an abridged version of the author's master's thesis written under the instruction of Doctor Kirsi Peltonen and under the supervision of Professor Erkki Somersalo.

Recently non-relativistic boundary conditions based on the Lorentz force formulas have been introduced. It was shown that to the first order in the relative velocity v/c the results are in agreement with the exact relativistic formalism. Specific boundary value problems have been solved to get concrete results and demonstrate the feasibility of implementing the formalism. These included examples involving plane and cylindrical interfaces. Presently the velocity-dependent Mie problem, viz. scattering of a plane wave by a moving sphere, is investigated. The sphere is assumed to move in a material medium without mechanically affecting the medium. The analysis follows closely the solution for the cylindrical case, given before. The mathematics here (involving spherical vector waves and harmonics) is more complicated, and therefore sufficient detail and references are provided. The interesting feature emerging from the present analysis is that the velocity-dependent effects induce higher order multipoles, which are not present in the classical Mie solution for scattering by a sphere at rest. The formalism is sufficiently general to deal with arbitrary moving objects.

This paper demonstrates how the error of a measured or simulated antenna radiation pattern can be decreased by calculating a spherical wave expansion (SWE) with an optimised truncation mode index. Four radiation pattern examples are examined for which the analytical expression of the electrical field is known. Upon adding random and Φ-alignment errors to the exact electric fields, the SWEs are determined and compared with the corresponding ones for the exact fields. These comparisons show that the accuracy of the calculated SWE is much better than the accuracy of the original inaccurate field. Resting on the calculated examples, a method is created which can be used to determine the optimal truncation index from the modal power distribution of a SWE without knowing the exact field. Finally, the method developed is applied to measured antenna radiation patterns.

The analysis was developed for a coaxial waveguide for two configurations - one in which the central conductor is corrugated in axial slot-wedges, with ridge-wedges between them, and the other in which the outer conductor is provided with radial metal vane-wedges. Azimuthal harmonics were considered in the structure regions, the effects of which were ignored in earlier published analyses based on the surface impedance model to replace the interface between the two structure regions by a homogeneous reactive surface. For both the structure configurations, one and the same form of the dispersion relation with proper interpretation of the symbol for the radius of the ridge/vane was obtained. The dispersion relation obtained by the present analysis was validated against that obtained by other analytical methods reported in the literature. The shape of the dispersion characteristics is found uncontrollable by the structure parameters, and therefore the structure cannot be used for broadbanding a gyro-TWT. However, the plot of the eigenvalue versus the ratio of the outer conductor to ridge/vane radii strongly depended on the ridge/vane parameters. Thus the structure with its cross section tapered and ridge/groove parameters optimized has the potential for providing mode rarefaction in high-power, over-sized, over-moded gyrotrons.

We study the scattering problem for a thin cylindrical target that is placed with arbitrary orientation in a rectangular TE₁₀ waveguide and subjected to an imposed electromagnetic field. The scattered far-field is expressed in terms of the scattered field inside the target and the far-field expansion of the dyadic Green's function for the waveguide. In order to capture features of interest in microwave heating applications, we allow the target material's electrical properties to be arbitrary functions of position along the thin cylindrical target's axis. Reflection and transmission coefficients for such a target, and an expression for the rate of deposition of electromagnetic energy within it are derived.

A novel image solution for the canonical electrostatic problem of a point charge in an anisotropic half-space bounded by an anisotropic surface is presented. The image source is obtained in operator form by using Fourier-transformed Maxwell equations and transmission line theory. After applying methods from Heaviside operator calculus, the image operator can be interpreted as a combination of a point charge and a line-charge-bounded sector of planar charge density. The new theory is shown to coincide with the previously known image solutions of less general anisotropic media. In addition to being applicable to any physically feasible anisotropic medium of electrostatics, the method can be used for steady-current conductivity problems via a duality transformation.

The multi-resolution time domain (MRTD) technique for electromagnetic field equations was proposed by Krumpholz, Katehi et al., using Battle-Lemarie wavelets. The basis principle behind the MRTD is the wavelet-Galerkin time domain (WGTD) approach. Despite its effectiveness in space discretization, the complexity ofthe MRTD makes it unpopular. Recently, the WGTD was significantly simplified by Cheong et al. based on the approximate sampling property ofthe shifted versions ofthe Daubechies compactly supported wavelets. In this paper, we provide a rigorous analysis ofthe MRTD, employing positive sampling functions and their biorthogonal dual. We call our approach as the sampling biorthogonal time-domain (SBTD) technique. The introduced sampling and dual functions are both originated from Daubechies scaling functions of order 2 (referred as to D₂), and form a biorthonormal system. This biorthonormal system has exact interpolation properties and demonstrates superiority over the FDTD in terms ofmemory and speed. Numerical examples and comparisons with the traditional FDTD results are provided.

The 3D Berenger's and uniaxial perfectly matched layers used for the truncation of the FDTD computations are theoretically investigated respectively in the discrete space, including numerical dispersion and impedance characteristics. Numerical dispersion for both PMLs is different from that of the FDTD equations in the normal medium due to the introduction of loss. The impedance in 3D homogeneous Berenger's PML medium is the same as that in the truncated normal medium even in the discrete space, however, the impedance in 3D homogenous UPML medium is different, but the discrepancy smoothly changes as the loss in the UPML medium slowly change. Those insights acquired can help to understand why both 3D PMLs can absorb the outgoing wave with arbitrary incidence, polarization, and frequency, but with different efficiency.

In this work, we summarize the existing theoretical methods based on statistical and quanty theory and give some non-standard mathematical approaches based on such theories to explain the principal scalar and vector electrodynamic problems for future applications to acoustic, radio and optical wave propagation in homogeneous, isotropic, anisotropic and inhomogeneous media. We show of how the statistical description of wave equations can be evaluated based on quantum field theory with presentation of Feynman's diagrams by a limited-to-zero finite set of expanded Green functions according to perturbation theory for single, double, triple, etc, scattering phenomenon. It is shown that at very short wavelengths, the Green's function is damped over a few wavelengths if the refractive index fluctuations in the medium are strong; at long wavelengths the effective phase velocity of electromagnetic waves may be increased. It is shown, that the coupling between different wave modes and the energy transfer between different wave modes, may be important, even for week random fluctuations of parameters of the medium, but it takes a very long time.

Malvar wavelets are often referred to as smooth local cosine (SLC) functions. In this paper the SLC functions are employed as the basis and testing functions in the Galerkin-based Method of Moments (MoM) for the Pocklington equation of thin-wire antennas and scatterers. The SLC system has rapid convergence and is particularly suitable to handle electrically large scatterers, where the integral kernel behaves in a highly oscillatory manner. Numerical examples demonstrate the scattering ofelectromagnetic waves from a thin-wire scatterer as well as wave radiation from the gull-shaped antenna. A comparison ofthe new approach versus the traditional MoM is provided.

The hemispherical dielectric resonator antenna (DRA) excited by a single-arm spiral slot is studied theoretically in this paper. The Green's function technique is employed to formulate an integral equation for the spiral slot current. The moment method with piecewise sinusoidal (PWS) basis and testing functions is used to convert the integral equation into a matrix equation by using a deltagap exciting source. The input impedance, return loss, axial ratio and radiation pattern are calculated. Numerical results demonstrate that the analysis is efficient.

The objective of the paper is to develop a compact and broadband microstrip patch antenna for the IMT-2000 mobile handset application. By parasitically coupling two shorted semi-disc patches with a single shorting-post each and employing Styrofoam substrate with low dielectric constant, an overall impedance bandwidth of 17.8% has been achieved to cover the frequency spectra of 1.862-2.225 GHz. The overall dimension of this proposed antenna is 44.4mm(length) × 37.8mm(width) × 7mm (thickness), and it would be suitable for the IMT-2000 mobile handset application. The typical antenna characteristics are presented and analysed theoretically and experimentally.

The field-to-cable coupling cross section is proposed to evaluate the coupling performance of a single-braided coaxial cable. In addition, a new definition for the coax shielding effectiveness is suggested. Both the coupling cross section and the shielding effectiveness of a 1.25 m-length RG 58 C/U 50Ω coax are measured byemplo ying both the mode-tuned reverberation chamber and GTEM cell methodologies. The detailed measurement set-ups and results are presented. The mode-tuned reverberation chamber methodologyis proven to be beneficial for assessing the cable shielding and coupling characteristics over a wide frequencyrange.

The finite element hybridized with the boundary integral method is a powerful technique to solve the scattering problem, especially when the fast multipole method is employed to accelerate the matrix-vector multiplication in the boundary integral method. In this paper, the multifrontal method is used to calculate the triangular factorization of the ill conditioned finite element matrix in this hybrid method. This improves the spectral property of the whole matrix and makes the hybrid method converge very fast. Through some numerical examples including the scattering from a real-life aircraft with an engine, the accuracy and efficiency of this improved hybrid method are demonstrated.