WAVE PROPAGATION Edited by Andrey Petrin Wave Propagation Edited by Andrey Petrin 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 Ana Nikolic Technical Editor Teodora Smiljanic Cover Designer Martina Sirotic Image Copyright Sebastian Kaulitzki, 2010. Used under license from Shutterstock.com First published March, 2011 Printed in India A free online edition of this book is available at www.intechopen.com Additional hard copies can be obtained from orders@intechweb.org Wave Propagation, Edited by Andrey Petrin p. cm. ISBN 978-953-307-275-3 free online editions of InTech Books and Journals can be found at www.intechopen.com Part 1 Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Preface IX Wave Propagation in Metamaterials, Micro/nanostructures 1 Wave Propagation Inside a Cylindrical, Left Handed, Chiral World 3 Pierre Hillion Microwave Sensor Using Metamaterials 13 Ming Huang and Jingjing Yang Electromagnetic Waves in Crystals with Metallized Boundaries 37 V.I. Alshits, V.N. Lyubimov, and A. Radowicz Electromagnetic Waves Propagation Characteristics in Superconducting Photonic Crystals 75 Arafa H Aly Electromagnetic Wave Propagation in Two-Dimensional Photonic Crystals 83 Oleg L. Berman, Vladimir S. Boyko, Roman Ya. Kezerashvili and Yurii E. Lozovik Terahertz Electromagnetic Waves from Semiconductor Epitaxial Layer Structures: Small Energy Phenomena with a Large Amount of Information 105 Hideo Takeuchi Wave Propagation in Dielectric Medium Thin Film Medium 131 E. I. Ugwu The Electrodynamic Properties of Structures with Thin Superconducting Film in Mixed State 151 Mariya Golovkina Contents Contents VI Light Wave Propagation and Nanofocusing 171 Detection and Characterization of Nano-Defects Located on Micro-Structured Substrates by Means of Light Scattering 173 Pablo Albella, Francisco González, Fernando Moreno, José María Saiz and Gorden Videen Nanofocusing of Surface Plasmons at the Apex of Metallic Tips and at the Sharp Metallic Wedges. Importance of Electric Field Singularity 193 Andrey Petrin Radiative Transfer Theory for Layered Random Media 213 Saba Mudaliar Antennas and Waveguides 239 Metamaterial Waveguides and Antennas 241 Alexey A. Basharin, Nikolay P. Balabukha, Vladimir N. Semenenko and Nikolay L. Menshikh On the Electrodinamics of Space-Time Periodic Mediums in a Waveguide of Arbitrary Cross Section 267 Eduard A. Gevorkyan The Analysis of Hybrid Reflector Antennas and Diffraction Antenna Arrays on the Basis of Surfaces with a Circular Profile 285 Oleg Ponomarev Wave Propagation in Plasmas 309 Electromagnetic Waves in Plasma 311 Takayuki Umeda Propagation of Electromagnetic Waves in and around Plasmas 331 Osamu Sakai Electromagnetic Waves Absorption and No Reflection Phenomena 353 Electromagnetic Wave Absorption Properties of RE-Fe Nanocomposites 355 Ying Liu, LiXian Lian and Jinwen Ye Part 2 Chapter 9 Chapter 10 Chapter 11 Part 3 Chapter 12 Chapter 13 Chapter 14 Part 4 Chapter 15 Chapter 16 Part 5 Chapter 17 Contents VII Electromagnetic Wave Absorption Properties of Nanoscaled ZnO 379 Yue Zhang, Yunhua Huang and Huifeng Li Composite Electromagnetic Wave Absorber Made of Soft Magnetic Material Particle and Metal Particle Dispersed in Polystyrene Resin 397 Kenji Sakai, Norizumi Asano, Yoichi Wada, Yang Guan, Yuuki Sato and Shinzo Yoshikado No-Reflection Phenomena for Chiral Media 415 Yasuhiro Tamayama, Toshihiro Nakanishi, Kazuhiko Sugiyama, and Masao Kitano Nonlinear Phenomena and Electromagnetic Wave Generation 433 Manipulating the Electromagnetic Wave with a Magnetic Field 435 Shiyang Liu, Zhifang Lin and S. T. Chui The Nonlinear Absorption of a Strong Electromagnetic Wave in Low-dimensional Systems 461 Nguyen Quang Bau and Hoang Dinh Trien Electromagnetic Waves Generated by Line Current Pulses 483 Andrei B. Utkin Radar Investigations 509 A Statistical Theory of the Electromagnetic Field Polarization Parameters at the Scattering by Distributed Radar Objects 511 Victor Tatarinov and Sergey Tatarinov Radar Meteor Detection: Concept, Data Acquisition and Online Triggering 537 Eric V. C. Leite, Gustavo de O. e Alves, José M. de Seixas, Fernando Marroquim, Cristina S. Vianna and Helio Takai Electromagnetic Waves Propagating Around Buildings 553 Mayumi Matsunaga and Toshiaki Matsunaga Chapter 18 Chapter 19 Chapter 20 Part 6 Chapter 21 Chapter 22 Chapter 23 Part 7 Chapter 24 Chapter 25 Chapter 26 Pref ac e In the recent decades, there has been a growing interest in telecommunication and wave propagation in complex systems, micro- and nanotechnology. The advances in these engineering directions give rise to new applications and new types of materi- als with unique electromagnetic and mechanical properties. This book is devoted to the modern methods in electrodynamics which have been developed to describe wave propagation in these modern materials, systems and nanodevices. The book collects original and innovative research studies of the experienced and ac- tively working scientists in the fi eld of wave propagation which produced new meth- ods in this area of research and obtained new and important results. Every chapter of this book is the result of the authors achieved in the particular fi eld of research. The themes of the studies are varied from investigation on modern ap- plications such as metamaterials, photonic crystals and nanofocusing of light to the traditional engineering applications of electrodynamics such as antennas, waveguides and radar investigations. The book contains 26 chapters on the following themes: - Wave Propagation in Metamaterials, Micro/nanostructures; - Light Wave Propagation and Nanofocusing; - Antennas and Waveguides; - Wave Propagation in Plasmas; - Electromagnetic Waves Absorption and No Refl ection Phenomena; - Nonlinear Phenomena and Electromagnetic Wave Generation; - Radar Investigations. It is necessary to emphasise that this book is not a textbook. It is important that the results combined in it are taken “from the desks of researchers“. Therefore, I am sure that in this book the interested and actively working readers (scientists, engineers and students) will fi nd many interesting results and new ideas. Andrey Petrin Joint Institute for High Temperatures of Russian Academy of Science, Russia a_petrin@mail.ru [...]... the exponential factor from (10 ), (18 ) and using (12 a), we get at once from (13 ) in terms of Eθ ≅ E1 with kr2+kz2 = k12 Er = −ikzE1/k1, Eθ = E1, Ez = krE1/k1 (19 a) Substituting (18 ) into (1a), taking into account (19 a) and using (12 a) give Br = ckzE1/ω, Bθ = ick1E1/ω, Bz = ickrE1/ω and, with (19 a,b) substituted into the Post constitutive relations (3), we get (19 b) 7 Wave Propagation Inside a Cylindrical,... (3), we get (19 b) 7 Wave Propagation Inside a Cylindrical, Left Handed, Chiral World Dr = −ikzD1†E1, Hr = −kzH1†E1, Dθ = −k1D1†E1, Dz = −krD1†E1, Hθ = −ik1H1†E1, D1† = |ε|/k1 − cξ/ω Hz = −ikr H1†E1, H1† = c/ω|μ| − ξ/k1 (19 c) (19 d) Similarly, with k22−ω2n2 = −αωk2, kr2+kz2 = k22 , Eθ ≅ E2 , we get from (13 and (12 a) Er = ikzE2/k2, Eθ = E2, Bθ = −ick2E2/ω, Br = ckzE2/ω, Ez = − krE2/k2 Bz = ickrE2/ω (20a)... S1,θ(r,z,t) = c/8π(EzHr* −ErHz*)(r,z,t) = −ckrkz H1†/4πk1 J0(krr) J1(krr) |E1]2 ( 21) S1,z(r,z,t) = c/8π(ErHθ* −EθHr*)(r,z,t) = ckz H1†/4π J12(krr) |E1]2 Now, according to (11 ) and (17 ): ξ/k1 = -2ξ[ω|α| (1+ γ)] -1 = -c(ξ /|ξ| ω|μ|) (1+ γ) -1 (22) so that since according to (19 d), H1†= c/ω|μ| − ξ/k1, we get H1†= c/ω|μ| [1+ ξ/ |ξ| (1+ γ) -1] (22a) and H1† > 0 whatever the sign of ξ/|ξ| is So for kz > 0 (resp kz < 0) the... into account (1a) 1/ c ∂t ∂zBr 1/ c ∂t ∂rBz = (∂r2 +1/ r∂ r 1/ r2 + ∂z2)Eθ 1/ c2 ∂t2Bθ = 1/ c∂t∂rEz − 1/ c∂t∂zEr so that Eq.(6b) becomes ∆1Eθ + 2iξ|μ|/c (∂r∂tΕz−∂z∂tΕr) = 0 (8b) Finally in (6c) , the first and third terms are according to (1a) 1/ c ∂t(∂r +1/ r)Bθ = (∂r2 +1/ r∂ r + ∂z2)Ez 1/ c2 ∂t2Bz = 1/ c(∂r +1/ r) ∂tEθ and, taking into account these two relations, we get ∆0 Ez − 2iξ|μ|/c (∂r +1/ r) ∂tEθ = 0 (8c)... electromagnetic fields, Science Vol 312 ,17 80 -17 82 Post E.J., (19 62) Formal Structure of Electromagnetism, North Holland, Amsterdam Sihvola A.A (2007), Metamaterials in electromagnetism Metamaterials Vol .1, 1- 11 12 Wave Propagation Veselago V (19 68), The electrodynamic of substances with simultaneously negative ε and μ, Sov.Phys.Usp Vol .10 509- 514 Ziolkowski R.W & Heyman E., (20 01) Wave propagation in media having... H2†/4π J12(krr) |E2]2 (23) Taking into account (11 ), (17 ), we have ξ/k2 = 2(ξ/ω |α| ) (1 γ) 1 = c(ξ/|ξ|ω|μ|) (1 γ) 1 (24) and, since according to (20d) H2† = c/ω|μ| + ξ/k2 , we get taking into account (24) H2† = c/ω|μ| [1+ ξ/|ξ| (1 γ) 1] (25) H2† is positive for ξ/|ξ| = 1 and for ξ/|ξ| = 1 with γ > 2 leading to the same conclusion as for the first mode while for ξ/|ξ| = 1 and 1 < γ < 2 Bessel waves propagate... located in the rectangular waveguide to form the microwave sensor The simulation model is shown in Fig 14 (a) The geometric parameters for the Ω-shaped particles are chosen as w = 0 .14 4 mm, h = 4.5 mm, d = 0 .1 mm, R1=1mm and R2 = 1. 4 mm (see Fig 14 (b)) The cross section of the rectangle waveguide is axb =15 mmx7.5mm The length is l =12 mm The incident wave is the fundamental TE10 mode propagates along the... −2i (ξ/|ε| |μ|) (1+ 2ξ2|μ|/|ε|)BrBθ* EθHr* = −2i (ξ/|ε| |μ|) (1+ 2ξ2|μ|/|ε|)BθBr* (A .15 ) Substituting (A .15 ) into (A .14 ) gives Sφ = (c/8π/|ε| |μ|) (1+ 2ξ2|μ|/|ε|) Im{ BrBθ* − BθBr*} (A .16 ) Now, according to (A.4), (A.8), (A .10 ) we have with B2 = |Br|2+|Bθ|2 E.D* = −2ξ2Β2/|ε|, BH* = − B2 (1/ |μ|+ 2ξ2/|ε|) (A .17 ) So, the energy density w = 1/ 8π (E.D* + BH* ) is w = 1/ 8π ( (1/ |μ|+ 4ξ2/|ε|) (A .18 ) The energy... =2ξ|μ|/c (11 ) Let us now substitute (10 ) into (8a,b,c) The Bessel functions with k2 = kr2 +kz2 satisfy the following relations with the exponential factor exp(iωt +ikzz) implicit ∆1J1(krr) = −(k2−ω2n2) J1(krr), ∂rJ0(krr) = −krJ1(krr), ∆0J0(krr) = −(k2−ω2n2) J0(krr) (∂r +1/ r) J1(krr) = krJ0(krr) (12 a) (12 a) then, using (12 a,b) we get the homogeneous system of equations on the amplitudes Er, Eθ, Ez 6 Wave Propagation. .. metamaterial particle The model of the waveguide filled with a single metamaterial particle is shown in Fig 11 (a) The metamaterial particle with the thickness of 0.44mm is located at the center of the WR -14 rectangular waveguide Since the topology structure of the particle influence the performance of the microwave sensor, the resonators with two different geometries are discussed, as shown in Fig 11 (b) and 11 (c) . D θ = −k 1 D 1 † E 1 , D z = −k r D 1 † E 1 , D 1 † = |ε|/k 1 − cξ/ω (19 c) H r = −k z H 1 † E 1 , H θ = −ik 1 H 1 † E 1 , H z = −ik r H 1 † E 1 , H 1 † = c/ω|μ| − ξ/k 1 (19 d) Similarly,. k 1 2 E r = −ik z E 1 /k 1 , E θ = E 1 , E z = k r E 1 /k 1 (19 a) Substituting (18 ) into (1a), taking into account (19 a) and using (12 a) give B r = ck z E 1 /ω, B θ = ick 1 E 1 /ω,. = ck z H 1 † /4π J 1 2 (k r r) |E 1 ] 2 ( 21) Now, according to (11 ) and (17 ): ξ/k 1 = -2ξ[ω|α| (1+ γ)] -1 = -c(ξ /|ξ| ω|μ|) (1+ γ) -1 (22) so that since according to (19 d), H 1 † = c/ω|μ|