Energy in Electromagnetic Waves

Energy in Electromagnetic Waves tài liệu, giáo án, bài giảng , luận văn, luận án, đồ án, bài tập lớn về tất cả các lĩnh...

VNU Journal of Science, Mathematics - Physics 26 (2010) 115-120 115 The dependence of the nonlinear absorption coefficient of strong electromagnetic waves caused by electrons confined in rectangular quantum wires on the temperature of the system Hoang Dinh Trien*, Bui Thi Thu Giang, Nguyen Quang Bau Faculty of Physics, Hanoi University of Science, Vietnam National University 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam Received 23 December 2009 Abstract. The nonlinear absorption of a strong electromagnetic wave caused by confined electrons in cylindrical quantum wires is theoretically studied by using the quantum kinetic equation for electrons. The problem is considered in the case electron-acoustic phonon scattering. Analytic expressions for the dependence of the nonlinear absorption coefficient of a strong electromagnetic wave by confined electrons in rectangular quantum wires on the temperature T are obtained. The analytic expressions are numerically calculated and discussed for GaAs/GaAsAl rectangular quantum wires. Keywords: rectangular quantum wire, nonlinear absorption, electron- phonon scattering. 1. Introduction It is well known that in one dimensional systems, the motion of electrons is restricted in two dimensions, so that they can flow freely in one dimension. The confinement of electron in these systems has changed the electron mobility remarkably. This has resulted in a number of new phenomena, which concern a reduction of sample dimensions. These effects differ from those in bulk semiconductors, for example, electron-phonon interaction and scattering rates [1, 2] and the linear and nonlinear (dc) electrical conductivity [3, 4]. The problem of optical properties in bulk semiconductors, as well as low dimensional systems has also been investigated [5-10]. However, in those articles, the linear absorption of a weak electromagnetic wave has been considered in normal bulk semiconductors [5], in two dimensional systems [6-7] and in quantum wire [8]; the nonlinear absorption of a strong electromagnetic wave (EMW) has been considered in the normal bulk semiconductors [9], in quantum wells [10] and in cylindrical quantum wire [11], but in rectangular quantum wire (RQW), the nonlinear absorption of a strong EMW is still open for studying. In this paper, we use the quantum kinetic quation for electrons to theoretically study the dependence of the nonlinear absorption coefficient of a strong EMW by confined electrons in RQW on the temperature T of the system. The problem is considered in two cases: electron-optical phonon scattering and electron-acoustic phonon scattering. Numerical calculations are carried out with a specific GaAs/GaAsAl quantum wires to ______ * Corresponding author. Tel.: +84913005279 E-mail: hoangtrien@gmail.com H.D. Trien et al. / VNU Journal of Science, Mathematics - Physics 26 (2010) 115-120 116 show the dependence of the nonlinear absorption coefficient Energy in Electromagnetic Waves Energy in Electromagnetic Waves Bởi: OpenStaxCollege Anyone who has used a microwave oven knows there is energy in electromagnetic waves Sometimes this energy is obvious, such as in the warmth of the summer sun Other times it is subtle, such as the unfelt energy of gamma rays, which can destroy living cells Electromagnetic waves can bring energy into a system by virtue of their electric and magnetic fields These fields can exert forces and move charges in the system and, thus, work on them If the frequency of the electromagnetic wave is the same as the natural frequencies of the system (such as microwaves at the resonant frequency of water molecules), the transfer of energy is much more efficient Connections: Waves and Particles The behavior of electromagnetic radiation clearly exhibits wave characteristics But we shall find in later modules that at high frequencies, electromagnetic radiation also exhibits particle characteristics These particle characteristics will be used to explain more of the properties of the electromagnetic spectrum and to introduce the formal study of modern physics Another startling discovery of modern physics is that particles, such as electrons and protons, exhibit wave characteristics This simultaneous sharing of wave and particle properties for all submicroscopic entities is one of the great symmetries in nature 1/10 Energy in Electromagnetic Waves Energy carried by a wave is proportional to its amplitude squared With electromagnetic waves, larger E-fields and B-fields exert larger forces and can more work But there is energy in an electromagnetic wave, whether it is absorbed or not Once created, the fields carry energy away from a source If absorbed, the field strengths are diminished and anything left travels on Clearly, the larger the strength of the electric and magnetic fields, the more work they can and the greater the energy the electromagnetic wave carries A wave’s energy is proportional to its amplitude squared (E2 or B2) This is true for waves on guitar strings, for water waves, and for sound waves, where amplitude is proportional to pressure In electromagnetic waves, the amplitude is the maximum field strength of the electric and magnetic fields (See [link].) Thus the energy carried and the intensity I of an electromagnetic wave is proportional to E2 and B2 In fact, for a continuous sinusoidal electromagnetic wave, the average intensity Iave is given by Iave = cε0E20 , where c is the speed of light, ε0 is the permittivity of free space, and E0 is the maximum electric field strength; intensity, as always, is power per unit area (here in W/m2) The average intensity of an electromagnetic wave Iave can also be expressed in terms of the magnetic field strength by using the relationship B = E / c, and the fact that ε0 = / μ0c2, where μ0 is the permeability of free space Algebraic manipulation produces the relationship Iave = cB20 2μ0 , where B0 is the maximum magnetic field strength One more expression for Iave in terms of both electric and magnetic field strengths is useful Substituting the fact that c ⋅ B0 = E0, the previous expression becomes Iave = E0B0 2μ0 Whichever of the three preceding equations is most convenient can be used, since they are really just different versions of the same principle: Energy in a wave is related to amplitude squared Furthermore, since these equations are based on the assumption that 2/10 Energy in Electromagnetic Waves the electromagnetic waves are sinusoidal, peak intensity is twice the average; that is, I0 = 2Iave Calculate Microwave Intensities and Fields On its highest power setting, a certain microwave oven projects 1.00 kW of microwaves onto a 30.0 by 40.0 cm area (a) What is the intensity in W/m2? (b) Calculate the peak electric field strength E0 in these waves (c) What is the peak magnetic field strength B0 ? Strategy In part (a), we can find intensity from its definition as power per unit area Once the intensity is known, we can use the equations below to find the field strengths asked for in parts (b) and (c) Solution for (a) Entering the given power into the definition of intensity, and noting the area is 0.300 by 0.400 m, yields I= P A = 1.00 kW 0.300 m × 0.400 m Here I = Iave, so that Iave = 1000 W 0.120 m2 = 8.33 × 103 W/m2 Note that the peak intensity is twice the average: I0 = 2Iave = 1.67 × 104 W / m2 Solution for (b) To find E0, we can rearrange the first equation given above for Iave to give E0 = 2Iave 1/2 cε0 ( ) Entering known values gives 3/10 Energy in Electromagnetic Waves E0 2(8.33 × 103 W/m2) = √ = 2.51 × 103 V/m (3.00 × 108 m/s)(8.85 × 10 – 12 C2 / N ⋅ m2) Solution for (c) Perhaps the easiest way to find magnetic field strength, now that the electric field strength is known, is to use the relationship given by B0 = E0 c Entering known values gives B0 = = 2.51 × 103 V/m 3.0 × 108 m/s 8.35 × 10 − T Discussion As before, a relatively strong electric field is accompanied by a ...BEHAVIOUR OF ELECTROMAGNETIC WAVES IN DIFFERENT MEDIA AND STRUCTURES Edited by Ali Akdagli Behaviour of Electromagnetic Waves in Different Media and Structures Edited by Ali Akdagli 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 Lipović Technical Editor Teodora Smiljanic Cover Designer Jan Hyrat Image Copyright Ivanagott, 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 Behaviour of Electromagnetic Waves in Different Media and Structures, Edited by Ali Akdagli p. cm. ISBN 978-953-307-302-6 Contents Preface IX Chapter 1 Electric and Magnetic Characterization of Materials 1 Leonardo Sandrolini, Ugo Reggiani and Marcello Artioli Chapter 2 Features of Electromagnetic Waves Scattering by Surface Fractal Structures 17 O. Yu. Semchuk and M. Willander Chapter 3 Electromagnetic Wave Scattering from Material Objects Using Hybrid Methods 27 Adam Kusiek, Rafal Lech and Jerzy Mazur Chapter 4 The Eigen Theory of Electromagnetic Waves in Complex Media 53 Shaohua Guo Chapter 5 Electromagnetic Waves in Cavity Design 77 Hyoung Suk Kim Chapter 6 Wide-band Rock and Ore Samples Complex Permittivity Measurement 101 Sixin Liu, Junjun Wu, Lili Zhang and Hang Dong Chapter 7 Detection of Delamination in Wall Paintings by Ground Penetrating Radar 121 Wanfu Wang Chapter 8 Interaction of Electromagnetic Radiation with Substance 141 Andrey N. Volobuev Chapter 9 Ultrafast Electromagnetic Waves Emitted from Semiconductor 161 YiMing Zhu and SongLin Zhuang VI Contents Chapter 10 Electromagnetic Wave Propagation in Ionospheric Plasma 189 Ali Yeşil and İbrahim Ünal Chapter 11 Exposing to EMF 213 Mahmoud Moghavvemi, Farhang Alijani, Hossein Ameri Mahabadi and Maryam Ashayer Soltani Chapter 12 Low Frequency Electromagnetic Waves Observation During Magnetotail Reconnection Event 237 X. H. Wei, J. B. Cao and G. C. Zhou Chapter 13 Solitary Electromagnetic Behaviour of Electromagnetic Waves in Different Media and Structures 18 increase the degree of a surface calibration the picture becomes complicated; the greatest intensity of a scattering wave is observed in a mirror direction; there are other direction in which the bursts of intensity are observed. 2. Fractal model for two-dimensional rough surfaces At theoretical research of processes of electromagnetic waves scattering selfsimilar heterogeneous objects (by rough surfaces) is a necessity to use the mathematical models of dispersive objects. As a basic dispersive object we will choose a rough surface. As is generally known, she is described by the function () zx,yof rejections z of points of M of surface from a supporting plane (x,y) (fig.1) and requires the direct task of relief to the surface. Fig. 1. Schematic image of rough surface There are different modifications of Weierstrass–Mandelbrot function in the modern models of rough surface are used. For a design a rough surface we is used the Weierstrass limited to the stripe function [3,4] () 1 (3) 01 22 ,sincossin, NM Dn n w nm nm mm zxy c q Kq x y MM − − ==   ππ  =++ϕ       (1) where c w is a constant which ensures that W(x, y) has a unit perturbation amplitude; q(q> 1) is the fundamental spatial frequency; D (2 < D< 3) is the fractal dimension; K is the Features of Electromagnetic Waves Scattering by Surface Fractal Structures 19 fundamental wave number; N and M are number of tones, and nm ϕ is a phase term that has a uniform distribution over the interval [,]−π π . The above function is a combination of both deterministic periodic and random structures. This function is anisotropic in the two directions if M and N are not too large. It has a large derivative and is self similar. It is a multi-scale surface that has same roughness down to some fine scales. Since natural surfaces are generally neither purely random nor purely periodic and often anisotropic, the above proposed function is a good candidate for modeling natural surfaces. The phases nm ϕ can be chosen determinedly or casually, receiving accordingly determine or stochastic function () ,zxy. We further shall consider nm ϕ as casual values, which in regular distributed on a piece ;−π π     . With each particular choice of numerical meanings all NM× phases nm ϕ (for example, with the help of the generator of random numbers) we receive particular (with the beforehand chosen meanings of parameters w c , ,,, ,qKDNM) realization of function () ,zxy. The every possible realizations of function () ,zxy form ensemble of surfaces. A deviation of points of a rough surface from a basic plane proportional w c , therefore this parameter is connected to height of inequalities of a structure of a surface. Further it is found to set a rough surface, specifying root-mean-square height of its structure σ , which is determined by such grade: 2 ,hσ≡ (2) where () ,hzxy= , 1 01 ( ) 2 NM nm nm d π − == −π ϕ = π ∏∏  - averaging on ensemble of surfaces. The connection between w c and σ can be established, directly calculating integrals: () () () () () 1 2 1 2 23 1 2 23 01 1 ,. 2 21 ND NM nm w D nm Mq d zxy c q − π − − == −π   −  ϕ   σ= =    π  −      ∏∏  (3) So, the rough surface in our model is described by function from six parameters: w c (or ), ,,, ,qKDNM. The influence of different parameters on a kind of a surface can be Electromagnetic Wave Scattering from Material Objects Using HybridMethods 21 4.5 5 5.5 6 6.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 R 0 f [GHz] TE ξ =0 ° ξ=45 ° ξ=90 ° 4.5 5 5.5 6 6.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 R 0 f [GHz] ξ =0 ° ξ=45 ° ξ=90 ° TM Fig. 23. Power reflection coefficients of the fundamental space harmonics versus frequency for one-hundred-layered square lattice periodic arrays of metallic posts embedded in dielectric cylinders from Fig 22. Parameters of the structure: h = 19.5mm, d = 25mm, r 0 = 0.01h, r 1 = 0.09h, R = 0.19h, ψ 1,2 = 10 ◦ , ε r = 20 structures are identical but rotated by 90 ◦ with respect to each other. For the same plane wave illuminating both configurations, they produce stop bands which only slightly overlap. When half of the structure (i.e. 10 last or first arrays) are being rotated with respect to the other half one obtains the effect of stop band shifting. The stop bands, which are almost identical in width, can be shifted from one bandwidth to another. The case of 90 ◦ rotation of stacks is presented in Fig. 24(b). When only every other periodic array are being rotated the produced stop band is widening and in the case of 90 ◦ rotation it embraces both stop bands as can be seen in Fig. 24(c). 3.3.4 Tunneling effect An interesting effect of wave tunneling can be obtained in the structure under investigation. This effect, along with the "growing evanescent envelope" for field distributions, was previously observed in metamaterial medium (negative value of real permittivity and permeability) and a structure composed of a pair of only-epsilon-negative and only-mu-negative layers Alu & Engheta (2003). This effect was also discussed in Alu & Engheta (2005) for periodically layered stacks of frequency selective surfaces (FSS). It was shown in Alu & Engheta (2005) that a complete electromagnetic wave tunneling may be achieved through a pair of different stacked FSSs which are characterized by dual behaviors, even though each stack is completely alone opaque (operates in its stop band). Similar effect can be obtained for the structure composed of a pair of identical stacks of periodic arrays of cylindrical posts rotated by 90 ◦ with respect to each other. This effect can also be controlled by introducing a gap d between the stacks (see Fig. 25). The calculation of a total scattering matrix for a pair of such stacks boils down to cascading the scattering matrix of a stack calculated for TE wave excitation with the scattering matrix calculated for TM wave excitation. The tunneling effect has been obtained for the periodic structure described in Fig. 25. The stop bands are formed in the same frequency range for both TE and TM waves. Therefore, we obtain a pair of stacks with dual behavior both of which operate in their stop bands. In the equivalent circuit analogy one stack is represented by a periodical line loaded with capacitors, while the other one is loaded with inductances. 47 Electromagnetic Wave Scattering from Material Objects Using Hybrid Methods 22 Will-be-set-by-IN-TECH 5 5.5 6 6.5 7 7.5 8 8.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 f[GHz] 5 5.5 6 6.5 7 7.5 8 8.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 R 0 f[GHz] h l plane wave H k E R 0 R 0 plane wave H k E plane wave H k E l h plane wave H k E a) b) c) Fig. 24. Power reflection coefficients of the fundamental space harmonics versus frequency for normal incidence of TE wave on a periodic structures; Parameters of the structures h = 20mm, l = h, r = 0.06h , R = 0.35h, ε r1 = 3, ε r2 = 2.5, number of sections 20. Fig. 25. Schematic 3-D representation 5 Electromagnetic Waves in Cavity Design Hyoung Suk Kim Kyungpook National University Korea 1. Introduction Understanding electromagnetic wave phenomena is very important to be able to design RF cavities such as for atmospheric microwave plasma torch, microwave vacuum oscillator/amplifier, and charged-particle accelerator. This chapter deals with some electromagnetic wave equations to show applications to develop the analytic design formula for the cavity. For the initial and crude design parameter, equivalent circuit approximation of radial line cavity has been used. The properties of resonator, resonant frequency, quality factor, and the parallel-electrodes gap distance have been considered as design parameters. The rectangular cavity is introduced for atmospheric microwave plasma torch as a rectangular example, which has uniform electromagnetic wave distribution to produce wide area plasma in atmospheric pressure environment. The annular cavity for klystrode is introduced for a microwave vacuum oscillator as a circular example, which adapted the grid structure and the electron beam as an annular shape which gives high efficiency compared with conventional klystrode. Some simulation result using the commercial software such as HFSS and MAGIC is also introduced for the comparison with the analytical results. 2. Equivalent circuit approximation of radial-line cavity Microwave circuits are built of resonators connected by waveguides and coaxial lines rather than of coils and condensers. Radiation losses are eliminated by the use of such closed elements and ohmic loss is reduced because of the large surface areas that are provided for the surface currents. Radio-frequency energy is stored in the resonator fields. The linear dimensions of the usual resonator are of the order of magnitude of the free-space wavelength corresponding to the frequency of excitation. A simple cavity completely enclosed by metallic walls can oscillate in any one of an infinite number of field configurations. The free oscillations are characterized by an infinite number of resonant frequencies corresponding to specific field patterns of modes of oscillation. Among these frequencies there is a smallest one, f c 00 λ = (1) , where the free-space wavelength is of the order of magnitude of the linear dimensions of the cavity, and the field pattern is unusually simple; for instance, there are no internal nodes in the electric field and only one surface node in the magnetic field. Behaviour of Electromagnetic Waves in Different Media and Structures 78 The oscillations of such a cavity are damped by energy lost to the walls in the form of heat. This heat comes from the currents circulating in the walls and is due to the finite conductivity of the metal of the walls. The total energy of the oscillations is the integral over the volume of the cavity of the energy density, () 22 00 1 2 v WEHdv εμ =+  (2) Hm 7 0 410 / μπ − =× and Fm 9 0 1 10 / 36 ε π − =× (3) , where E and H are the electric and magnetic field vectors, in volts/meter and ampere- turns/meter, respectively. The cavity has been assumed to be empty. The total energy W in a particular mode decreases exponentially in time according to the expression, t Q WWe 0 0 ω − = (4) , where f 00 2 ωπ = and Q is a quality factor of the mode which is defined by ener gy stored in the cavit y Q energy lost in one cycle 2( ) () π = . (5) The fields ... energy does it deliver on a 1.00-mm2 area? (a) 333 T 6/10 Energy in Electromagnetic Waves (b) 1.33×1019 W/m2 (c) 13.3 kJ Show that for a continuous sinusoidal electromagnetic wave, the peak intensity... assumption that 2/10 Energy in Electromagnetic Waves the electromagnetic waves are sinusoidal, peak intensity is twice the average; that is, I0 = 2Iave Calculate Microwave Intensities and Fields On... What power 8/10 Energy in Electromagnetic Waves is incident on the coil? (b) What average emf is induced in the coil over one-fourth of a cycle? (c) If the radio receiver has an inductance of 2.50