ELECTROMAGNETIC WAVESPROPAGATIONIN COMPLEXMATTER  EditedbyAhmedA.Kishk              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 Non Commercial Share Alike Attribution 3.0 license, which permits to copy, distribute, transmit, and adapt the work in any medium, so long as the original work is properly cited. After this work has been published by InTech, authors have the right to republish it, in whole or part, in any publication of which they are the author, and to make other personal use of the work. Any republication, 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 of the use of any materials, instructions, methods or ideas contained in the book. Publishing Process Manager Iva Lipovic Technical Editor Teodora Smiljanic Cover Designer Jan Hyrat Image Copyright Leigh Prather, 2010. Used under license from Shutterstock.com First published June, 2011 Printed in Croatia A free online edition of this book is available at www.intechopen.com Additional hard copies can be obtained from orders@intechweb.org Electromagnetic Waves Propagation in Complex Matter, Edited by Ahmed A. Kishk p. cm. ISBN 978-953-307-445-0 free online editions of InTech Books and Journals can be found at www.intechopen.com   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. Terechov and 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 VI Contents 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 Smyk and Marek Tudruj   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k eeps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ar bitrarily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 cry stal axi s, 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solu tions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 yi elds 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cry stal.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 X Preface energy flux through the surface of a sphere with a point dipole pl aced 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integ ral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ju stified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som e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us edinthetherapyofvariousdiseases.Forasmall, on the average,permissiblelev el 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ele ctric‐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 ceno sphere 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.  [...]... 1 ˜ ˜ −G0 ˜ 1 ˜ −(ε 0 ε) G1 , M = ψ0 ˜ ˜ −G0 ( μ 0 μ ) 1 G1 ⎞ ⎛ 2 k1 k3 k − k2 k 1 k 2 0 1 ⎝ 1 2 − k2 k k ⎠ , ˜ k1 k2 k2 G1 = 2 3 0 iω k1 k3 k 2 k 3 k2 − k2 3 0 where (13 ) (14 ) √ k0 ≡ ω ε 0 εμ0 μ, k2 = k2 + k2 + k2 x y z (15 ) By considering the inverse Fourier transformation ˜ M 1 = F 1 [ M 1 ˜ J = F 1 [J], ], ˜ U = F− 1 [ U ] (16 ) and using the property of convolution: ˜ 1 ˜ F 1 [M J] = M 1. .. k x 0 (10 ) The solution of the problem is reduced to determination of the system of the linear algebraic ˜ equations relative to Fourier-components of the fields, where U is defined by means of inverse 6 Electromagnetic Waves Propagation in Complex Matter Electromagnetic Waves 4 ˜ 1 matrix M : ˜ 1 ˜ ˜ U = M J (11 ) By introducing new function according to ˜ ψ0 = 1 , k2 − k2 0 (12 ) we define the inverse... 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 ... Weiglhofer, 19 90; 19 93) The problems, however, are mostly analyzed in spectral domain in terms of Fourier transform, due to the 4 2 Electromagnetic Waves Propagation in Complex Matter Electromagnetic Waves difficulty of finding the expansion of the dyadic Green’s functions in terms of vector wave functions for anisotropic media It shows the necessity of better characterizing the anisotropic media and producing... 1 ˜ F 1 [M J] = M 1 ∗ J, (17 ) where symbol "∗" denotes the convolution on coordinates x, y, z, it is possible to get the solution of the Maxwell equations (4) as: U = M 1 ∗ J, (18 ) where ⎛ M− 1 = −(ε 0 ε) 1 G1 −G0 or E H = −G0 ψ0 , (μ0 μ ) 1 G1 ∂ + k2 0 ∂x 2 − 1 ⎜ ∂2 ⎜ G1 = iω ⎝ ∂x∂y 2 (iε 0 εω ) 1 (∇∇ + k2 )(j ∗ ψ0 ) 0 −∇ × (j ∗ ψ0 ) 2 ∂2 ∂x∂z ∂2 ∂y∂z ⎞ ⎟ ⎟ ⎠ (19 ) (ε 0 ε) 1 ∇ρ ∗ ψ0 − iμ0 μωψ0 ∗ j ,... Fourier transform is widely applied (Chen, 19 83; Kong, 19 86; Ren, 19 93; Uzunoglu et al., 19 85) The radiation field of a dipole in a anisotropic medium is considered in greater detail and devised by (Bunkin, 19 57; Clemmow, 19 63a;b; Kogelnik & Motz, 19 63) It is shown (Clemmow, 19 63a;b) that each such field is related by a simple scaling procedure to a corresponding vacuum field The vacuum field is expressed... equation in cylindrical coordinates for a gyroelectric medium (Ren, 19 93) continued that work for spherical coordinates in a similar procedure and obtained spherical wave functions and dyadic Green’s functions in gyroelectric media The dyadic Green’s functions for various kinds of anisotropic media with different structures have been studied by many authors (Barkeshli, 19 93; Cottis, 19 95; Lee & Kong, 19 83;... Professor Department of Electrical and Computer Engineering   Tier 1 Canada Research Chair,   Canada        XIII Part 1 Solutions of Maxwell's Equations in Complex Matter 0 1 The Generalized Solutions of a System of Maxwell’s Equations for the Uniaxial Anisotropic Media Seil Sautbekov Eurasian National University Kazakhstan 1 Introduction Media with anisotropic properties are widely used in modern radio... 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. ... media are obtained Due to the fundamental solutions, general exact expression of an electromagnetic field in boundless uniaxial crystal is obtained in the vector type by the method of generalized functions The results 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 In particular, . Media 4 Electromagnetic Waves matrix ˜ M 1 : ˜ U = ˜ M 1 ˜ J. (11 ) By introducing new function according to ˜ ψ 0 = 1 k 2 0 −k 2 , (12 ) we define the inverse matrix: ˜ M 1 = ˜ ψ 0  −( ε 0 ε) 1 ˜ G 1 − ˜ G 0 − ˜ G 0 (μ 0 μ) 1 ˜ G 1  ,. k 2 z . (15 ) By considering the inverse Fourier transformation M 1 = F 1 [ ˜ M 1 ], J = F 1 [ ˜ J ], U = F 1 [ ˜ U ] (16 ) and using the property of convolution: F 1 [ ˜ M 1 ˜ J ]=M 1 ∗J, (17 ) where. matrix: ˜ M 1 = ˜ ψ 0  −( ε 0 ε) 1 ˜ G 1 − ˜ G 0 − ˜ G 0 (μ 0 μ) 1 ˜ G 1  , (13 ) where ˜ G 1 = 1 iω ⎛ ⎝ k 2 1 −k 2 0 k 1 k 2 k 1 k 3 k 1 k 2 k 2 2 −k 2 0 k 2 k 3 k 1 k 3 k 2 k 3 k 2 3 −k 2 0 ⎞ ⎠ , (14 ) k 0 ≡ ω √ ε 0 εμ 0 μ,