ELECTROMAGNETIC WAVES PROPAGATION IN COMPLEX MATTER Edited by Ahmed A... Electromagnetic Waves Propagation in Complex Matter Edited by Ahmed A.. Used under license from Shutterstock.
Trang 1ELECTROMAGNETIC WAVES PROPAGATION IN
COMPLEX MATTER
Edited by Ahmed A. Kishk
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Electromagnetic Waves Propagation in Complex Matter
Edited by Ahmed A Kishk
Published by InTech
Janeza Trdine 9, 51000 Rijeka, Croatia
Copyright © 2011 InTech
All chapters are Open Access articles distributed under the Creative Commons
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referencing or personal use of the work must explicitly identify the original source Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher No responsibility is accepted for the accuracy of information contained in the published articles The publisher assumes no responsibility for any damage or injury to persons or property arising out
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First published June, 2011
Printed in Croatia
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Electromagnetic Waves Propagation in Complex Matter, Edited by Ahmed A Kishk
p cm
ISBN 978-953-307-445-0
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Contents
Preface IX Part 1 Solutions of Maxwell's Equations
in Complex Matter 1
Chapter 1 The Generalized Solutions
of a System of Maxwell's Equations for the Uniaxial Anisotropic Media 3
Seil Sautbekov Chapter 2 Fundamental Problems
of the Electrodynamics of Heterogeneous Media with Boundary Conditions Corresponding
to the Total-Current Continuity 25
N.N Grinchik, O.P Korogoda, M.S Khomich, S.V Ivanova, V.I Terechovand Yu.N Grinchik Chapter 3 Nonlinear Propagation of
ElectromagneticWaves in Antiferromagnet 55
Xuan-Zhang Wang and Hua Li Chapter 4 Quasi-planar Chiral Materials
for Microwave Frequencies 97
Ismael Barba, A.C.L Cabeceira, A.J García-Collado, G.J Molina-Cuberos, J Margineda and J Represa Chapter 5 Electromagnetic Waves in Contaminated Soils 117
Arvin Farid, Akram N Alshawabkeh and Carey M Rappaport
Part 2 Extended Einstein’s Field Equations
for Electromagnetism 155
Chapter 6 General Relativity Extended 157
Gregory L Light
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Part 3 High Frequency Techniques 185
Chapter 7 Field Estimation through Ray-
Tracing for Microwave Links 187
Ada Vittoria Bosisio Chapter 8 High Frequency Techniques: the Physical
Optics Approximation and the Modified Equivalent Current Approximation (MECA) 207
Javier Gutiérrez-Meana, José Á Martínez-Lorenzo and Fernando Las-Heras
Part 4 Propagation in Guided Media 231
Chapter 9 Electrodynamics of Multiconductor
Transmission-line Theory with Antenna Mode 233
Hiroshi Toki and Kenji Sato Chapter 10 Propagation in Lossy Rectangular Waveguides 255
Kim Ho Yeap, Choy Yoong Tham, Ghassan Yassin and Kee Choon Yeong
Part 5 Numerical Solutions based on Parallel Computations 273
Chapter 11 Optimization of Parallel FDTD Computations Based
on Program Macro Data Flow Graph Transformations 275
Adam Smykand Marek Tudruj
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Preface
This book is based on the contributions of several authors in electromagnetic waves propagations. Several issues are considered. The contents of most of the chapters are highlighting non classic presentation of wave propagation and interaction with matters. This book bridges the gap between physics and engineering in these issues. Each chapter keeps the author notation that the reader should be aware of as he reads from chapter to the other. The author’s notations are kept in order to eliminate any possible unintentional errors that might lead to confusion. We would like to thank all authors for their excellent contributions.
In chapter 1, the problem of radiation of arbitrarily distributed currents in boundless uniaxial anisotropic media is considered through the method of generalized solutions
of the system of Maxwell’s equations in an exact form. The solution resolves into two
independent solutions. The first corresponds to the isotropic solution for currents directed along the crystal axis, while the second corresponds to the anisotropic
solution when the currents are perpendicular to the axis. The independent solutions
define the corresponding polarization of electromagnetic waves. The generalized solutions obtained in vector form by the fundamental solutions of the Maxwell’s equations are valid for any values of the elements of the permeability tensor, as well as for sources of the electromagnetic waves described by discontinuous and singular functions. The solutions can be also represented with the help of vector potentials by the corresponding fundamental solutions. The problems for tensors of the dielectric and magnetic permeabilities are considered separately. In particular, the solutions for elementary electric and magnetic dipoles have been deduced. Through the use of the expressions for current density of the point magnetic and electric dipoles using delta‐ function representations, the formulae for the radiated electromagnetic waves, as well
as the corresponding radiation patterns, are derived. The obtained solution in the anisotropic case yields the well‐known solutions for the isotropic case as a limiting case. The radiation patterns for Hertz radiator and point magnetic dipole are represented. Directivity diagrams of radiation of point magnetic and electric dipoles are constructed at parallel and perpendicular directions of an axis of a crystal.Validity
of the solutions has been checked up on balance of energy by integration of energy flow on sphere. The numerical calculation of the solution of Maxwell’s equations shows that it satisfies the energy conservation law, i.e. the time average value of
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energy flux through the surface of a sphere with a point dipole placed at its center remains independent of the radius of the sphere. Numerical calculation shows that its values keep with the high accuracy. The rigorous solving of system of Maxwell equations in an anisotropic media can be used in construction of the integral equations for solving the class of respective boundary problems.
In chapter 2, the consistent physic‐mathematical model of propagation of an electromagnetic wave in a heterogeneous medium is constructed using the generalized wave equation and the Dirichlet theorem. Twelve conditions at the interfaces of adjacent media are obtained and justified without using a surface charge and surface current in explicit form. The conditions are fulfilled automatically in each section of the heterogeneous medium and are conjugate, which make it possible to use through‐ counting schemes for calculations. The effect of concentration of ʺmedium‐frequencyʺ waves with a length of the order of hundreds of meters at the fractures and wedges of domains of size 1‐3 μm is established. Numerical calculations of the total electromagnetic energy on the wedges of domains are obtained. It is shown that the energy density in the region of wedges is maximum and in some cases may exert an influence on the motion, sinks, and the source of dislocations and vacancies and, in the final run, improve the near‐surface layer of glass due to the ʺmicromagnetoplasticʺ effect. The results of these calculations are of special importance for medicine, in particular, when microwaves are used in the therapy of various diseases. For a small,
on the average, permissible level of electromagnetic irradiation, the concentration of electromagnetic energy in internal angular structures of a human body (cells, membranes, neurons, interlacements of vessels, etc) is possible. A consistent physicomathematical model of interaction of nonstationary electric and thermal fields
in a layered medium with allowance for mass transfer is constructed. The model is based on the methods of thermodynamics and on the equations of an electromagnetic field and is formulated without explicit separation of the charge carriers and the charge of an electric double layer. The relations for the electric‐field strength and the temperature are obtained, which take into account the equality of the total currents and the energy fluxes, to describe the electric and thermal phenomena in layered media where the thickness of the electric double layer is small compared to the dimensions of the object under study. The heating of an electrochemical cell with allowance for the influence of the electric double layer at the metal‐electrolyte interface
is numerically modeled. The calculation results are in satisfactory agreement with experimental data.
Chapter 3 demonstrates the fabrication process, structure and magnetic properties of metal (alloy) coated cenosphere composites by heterogeneous precipitation thermal reduction method to form metal‐coated core‐shell structural composites. These composites can be applied for advanced functional materials such as electromagnetic wave absorbing materials.
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Preface XI
In chapter 4, a novel approach based on a periodic distribution of planar or quasi‐ planar chiral particles is proposed for the design of artificial chiral media. The metal particles are replaced by dielectric ones, so that a high contrast between the permittivity of the new dielectric particles and the host medium is achieved. This approach would allow the design of materials with lower losses and more simply scalable in frequency. Both approaches are presented by dealing with the aspects of design and realization of different “basic cells”. Numerical analysis in time and frequency‐domain using commercial software program are used to treat the propagation. Characterization of the media and their propagation properties are verified experimentally.
Soil is a complex, potentially heterogeneous, lossy, and dispersive material. Propaga‐ tion and scattering of electromagnetic waves in soil is, hence, more challenging than air or other less complex media. Chapter 5 explains the fundamentals of modeling electromagnetic wave propagation and scattering in soil by solving Maxwell’s equa‐ tions using a finite difference time domain (FDTD) model. The chapter explains how the lossy and dispersive soil medium (in both dry and water‐saturated conditions), two different types of transmitting antennae (a monopole and a dipole), and required absorbing boundary conditions can be modeled. A sample problem is simulated to demonstrate the scattering effects of a dielectric anomaly in soil. Thereafter, the details about preparation and conduct of an experimental simulation are discussed. The pre‐ cautions necessary to perform a repeatable experiment is explained in detail as well. The results of the numerically simulated example is compared and validated against experimental data.
In Chapter 6, Einstein field equations (EFE) are extended to explain electromagnetism
by charge distributions in like manner, which should not be confused with the Ein‐ stein‐Maxwell equations, in which electromagnetic fields energy contents were added onto those as attributed to the presence of matter, to account for gravitational motions. This chapter is substituting the term ʺelectric chargeʺ for energy, and electromag‐ netism for gravity, i.e., a geometrization of the electromagnetic force. Einstein field equations describe one space‐time, but in this chapter two are proposed: one for ʺpar‐ ticlesʺ and the other for ʺwaves;ʺ to wit, there are two gravitational constants. The gravitational motions in a ʺcombined space‐time 4‐manifoldʺ are unified. Also, the reader finds that the chapter proves that electromagnetic fields as produced by charg‐
es, in analogy with gravitational fields as produced by energies, cause space‐time cur‐ vatures, not because of the energy contents of the fields but because of the Coulomb potential of the charges. As a result, a special constant of proportionality between an electromagnetic energy‐momentum tensor and Einstein tensor are derived.
In chapter 7, a ray tracing approach based on the Jacobi‐Hamiltonian theory is used as rays are defined by their characteristic vector and the slowness (inverse of phase veloc‐ ity) vector along the ray. Both are functions of the integration variable and of the initial conditions (launching point and direction). The characteristic vector satisfies the Ham‐
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ilton differential equations. The Hamiltonian function describes the wave propagation
in the considered medium. Rays trajectories are functions of the unique integration pa‐ rameter. Hamilton‐Jacobi theory guarantees that there is always a domain of represen‐ tation in which solutions are monodrome functions. Here, the wave fronts are mono‐ drome function of the ray launching angle. Amplitude is computed through paraxial rays. Caustics arise when the ray field folds. These events are carefully accounted so that proper phase shifts can be applied to the field.
In chapter 8, an overview of the whole process to compute electromagnetic field levels based on the high frequency technique modified equivalent current approximation is presented. Moreover, three new fast algorithms are briefly described to solve the visibility problem. Those are used to complete a modified equivalent current approximation. They can also be helpful in other disciplines of engineering.
In chapter 9, the field theory on electrodynamics and derive of the Maxwell equation and the Lorenz force are introduced. The multiconductor transmission‐line (MCTL) equations for the TEM mode are developed. Solutions of the MCTL equations for a normal mode without coupling to the common and antenna modes are provided as well as a solution of one antenna system for emission and absorption of radiation. A three‐conductor transmission‐line system and the symmetrization for the decoupling
of the normal mode from the common and antenna modes are discussed.
A fundamental and accurate technique to compute the propagation constant of waves
in a lossy rectangular waveguide is proposed in chapter 10. The formulation is based
on matching the fields to the constitutive properties of the material at the boundary. The electromagnetic fields are used in conjunction of the concept of surface impedance
to derive transcendental equations, whose roots give values for the wavenumbers in the transverse directions of the waveguide axis for different transverse electric and transverse magnetic modes. The new boundary‐matching method is validated by comparing the attenuation of the dominant mode with the transmition coefficients measurement, as well as that obtained from the power‐loss method. The attenuation curve plotted using the new method matches with the power‐loss method at a reason‐ able range of frequencies above the cutoff. There are, however, two regions where both curves are found to differ significantly. At frequencies below the cutoff, the pow‐ er‐loss method diverges to infinity with a singularity at cutoff frequency. The new method, however, shows that the signal increases to a highly attenuating mode as the frequencies drop below the cutoff. Such result agrees very closely with the measure‐ ment result, therefore, verifying the validity of the new method. At frequencies above
100 GHz, the attenuation obtained using the new method increases beyond that pre‐ dicted by the power‐loss method. At frequency above the millimeter wavelengths, the field in a lossy waveguide can no longer be approximated to those of the lossless case. The additional loss predicted by the new boundary‐matching method is attributed to the presence of the longitudinal electric field component in hybrid modes.