工学电磁场与电磁波第讲无耗平面波导电平面波.pptx

Field and Wave Electromagnetic电磁场与电磁波电磁场与电磁波2010.5.72作业情况作业情况1班：人班：人2班：人班：人合计：人合计：人情况情况:3Review1.Maxwells Equations2.Electromagnetic Boundary Conditions The integral formThe differential form SignificanceFaradays law(电磁感应定律电磁感应定律)Amperes circuital law(全电流定律全电流定律)Gausss law(高斯定理高斯定理)No isolated magnetic charge(磁通连续磁通连续性原理性原理)43.Potential Functions4.Wave Equations and Their Solutions55.Time-Harmonic Fields 相量的模相量的模正弦量的幅值正弦量的幅值初位相初位相复角复角频率是已知频率是已知？频率频率相量乘以相量乘以 e ej j t t，再取实部，再取实部6Chapter8PlaneElectromagneticWaves4.Plane Waves in Lossy Media3.Polarization of Plane Waves5.Group Velocity6.Flow of Electromagnetic Power and the Poynting Vector1.Plane Waves in Lossless Media2.Transverse Electromagnetic Waves11.Oblique Incidence at a Plane Dielectric Boundary7.Normal Incidence at a Plane Conducting Boundary8.Oblique Incidence at a Plane Conducting Boundary9.Normal Incidence at a Plane Dielectric Boundary10.Normal Incidence at Multiple Dielectric Interfaces7Main topic Plane Electromagnetic Waves1.Plane Waves in Lossless Media1.1 transverse electromagnetic waves8振振动动状状态态的的传传播播叫叫做做波波动动，它它是是非非常常重重要要的的一一种种物物质质运运动动形形式式。我我们们和和周周围围环环境境的的联联系系大大都都是是以以波波动动的的形形式式进进行行的的。当当你你看看书书看看电电视视看看周周围围的的一一切切时时，信信息息就就以以光光波波的的形形式式进进入入你你的的眼眼睛睛；当当你你沉沉醉醉于于春春江江花花月月夜夜的的动动人人意意境境时时，优优美美的的旋旋律律就就以以声声波波的的形形式式进进入入你你的的耳耳朵朵；割割麦麦季季节节，当当你你漫漫步步在在乡乡间间小小道道上上时时，偶偶尔尔一一阵阵风风吹吹过过，你你将将看看到到广广袤袤的的麦麦海海立立刻刻就就起起了了金金黄黄色色的的麦麦浪浪，似似乎乎一一直直要要推推进进到到天天地地相相连连的的地地平平线线处处，而而麦麦子子仍仍在在地地里里。当当你你将将一一枚枚小小石石子子投投入入静静静静的的池池塘塘时时，你你将将看看到到以以小小石石子子投投入入点点为为中中心心，产产生生了了一一圈圈又又一一圈圈的的水水波波，它它们们不不断断向向外外扩扩展展，直直到到抵抵达达池池塘塘边边为为止止。如如果果水水面面上上正正好好有有一一片片树树叶叶，你你将将看看到到树树叶叶随随水水波波上上下下翻翻动动，前前后后摆摆动动，但但树树叶叶和和石石子子投投人人点点的的距距离离保保持持不不变变。世世界界充充满满了了波波，波波的的两两种种主主要要类类型型就就是是机机械械波波和和电电磁磁波波，光光波波是是电电磁磁波波，它它的的传传播播不不需需要要介介质质；声声波波、麦浪和水波都是麦浪和水波都是机械波机械波，它们的传播，它们的传播需要需要介质。介质。&1&1、波动、波动9我我们们描描述述波波动动时时，我我们们必必须须注注意意区区分分波波动动的的两两个个方方面面，这这就就是是振振动动的的传传播播(波波动动)和和介介质质中中质质点点相相对对其其平平衡衡位位置置的的振振动动，介介质质中中各各质质点点并并不不随随波波前前进进。根根据据波波的的传传播播方方向向和和介介质质中中质质点点位位移移的的方方向向(即即振振动动方方向向)间间的的关关系系，可可以以把把波波分分成成横横波波和和纵纵波波，横横波波就就是是介介质质中中质质点点位位移移方方向向与与传传播播方方向向垂垂直直的的波波，纵纵波波就就是是介介质质中中质质点点位位移移方方向向与与传传播播方方向向平平行行的的波波，如如图图所所示示。光光波波是是一一种种横横波波，声声波波是是一一种种纵纵波波，水水波波则则是是横横波波和纵波的组合。和纵波的组合。10当当波波源源所所产产生生的的扰扰动动在在介介质质中中沿沿各各个个方方向向传传播播时时，在在任任一一时时刻刻由由相相位位相相同同的的各各点点所所构构成成的的一一个个曲曲面面，称称为为波波面面（等等相相位位面面）。波波的的传传播播方方向沿波面的向沿波面的法线方向法线方向。任任一一时时刻刻由由扰扰动动所所传传播播到到的的各各点点所所构构成成的的波波面面，称称为为波波前前，在在波波前前上上各各点点的的振振动动相相位位就就等等于于波波源源开开始始振振动动时时的的相相位位。因因此此波波前前是是波波面面中中最最前面前面的一个。任一时刻的波面有无限多个，但波前只有一个。的一个。任一时刻的波面有无限多个，但波前只有一个。在在各各向向同同性性的的介介质质中中，当当波波源源的的大大小小和和形形状状可可以以忽忽略略即即看看成成点点波波源源时时，扰扰动动从从点点波波源源向向各各个个方方向向传传播播出出去去。波波前前是是球球面面而而波波线线是是与与其其波波前前垂垂直直的的许许多多通通过过球球心心的的法法线线。我我们们把把波波前前为为球球面面的的波波叫叫做做球球面面波波，由由点点源源产产生生；波波前前为为圆圆柱柱面面的的波波叫叫做做柱柱面面波波，由由无无限限长长的的线线源源产产生生；波波前前为平面的波叫做为平面的波叫做平面波平面波，由无限大的，由无限大的面源面源产生。产生。1112&2&2、行波与驻波行波与驻波Ex 001z1=02=O波波节节波波腹腹t1=0Ex(z,t)zO行波：电磁波向行波：电磁波向正正 z 方向传播。方向传播。空间各点空间各点合成波的合成波的相位相同相位相同，同时同时达达到最到最大大或最或最小小。平面波在空间没有移平面波在空间没有移动，因此称为动，因此称为驻波驻波。振振动动频频率率、振振幅幅和和传传播播速速度度相相同同而而传传播播方方向向相相反反的的两两列列波波叠叠加加时时，就就产产生生驻驻波波。驻驻波波形形成成时时，空空间间各各处处的的介介质质点点或或物物理理量量只只在在原原位位置置附附近近做做振振动动，波波停停驻驻不不前前，而而没没有有行行波波的的感感觉觉，所所以以称称为为驻驻波波。形形成成驻驻波波时时，各各处处介介质质质质点点或或物物理理量量以以不不同同的的振振幅幅振振动动。振振幅幅最最大大处处叫叫波波腹腹，振振幅幅最最小小处处即即看看上上去去静静止止不不动动处处叫叫波节波节。相邻两个波节或波腹之间的距离是。相邻两个波节或波腹之间的距离是半个波长半个波长。驻波也是一种波的驻波也是一种波的干涉现象干涉现象，但是一种特殊的干涉现象，但是一种特殊的干涉现象131.1.等相位面：等相位面：在某一时刻，空间具有相同相位的点构成的面称为等相位面。在某一时刻，空间具有相同相位的点构成的面称为等相位面。等相位面又称为波阵面。等相位面又称为波阵面。2.2.球面波：球面波：等相位面是球面的电磁波称为球面波等相位面是球面的电磁波称为球面波。3.3.平面波：平面波：等相位面是平面的电磁波称为平面电磁波。等相位面是平面的电磁波称为平面电磁波。4.4.均匀平面波：均匀平面波：任任意意时时刻刻，如如果果在在平平面面等等相相位位面面上上，每每一一点点的的电电场场强强度度均均相相同同，这种电磁波称为均匀平面波。，这种电磁波称为均匀平面波。&3&3、平面电磁波的基本概念、平面电磁波的基本概念14上式中上式中 t 称为称为时间相位时间相位。kz 称为称为空间相位空间相位。空间空间相位相等的点组成的曲面称为相位相等的点组成的曲面称为波面波面。由上式可见，由上式可见，的平面为波面。因此，的平面为波面。因此，这种电磁波称为这种电磁波称为平面波平面波。因因Ex(z)与与 x,y 无关，在无关，在 的的波波面面上上，各各点点场场强强振振幅幅相相等等。因因此此，这这种种平平面面波又称为波又称为均匀均匀平面波。平面波。z15时间相位时间相位 t 变化变化 2 所经历的时间称为所经历的时间称为周期周期(T)。空间相位空间相位 kz 变化变化 2 所经过的距离称为所经过的距离称为波长波长()。频率频率描述电磁波的相位随描述电磁波的相位随时间时间的变化特性的变化特性。k 表示表示单位长度单位长度内的相位变化，因此称为内的相位变化，因此称为相位常数相位常数。波长波长描述电磁波的相位随描述电磁波的相位随空间空间的变化特性的变化特性。一秒内一秒内相位相位变化变化 2 的次数称为的次数称为频率频率(f)。161.Plane Waves in Lossless MediaIn this and future chapters we focus our attention on wave behavior in the sinusoidal steady state(时时谐谐、稳稳态态),using phasors(相相量量)to great advantage.The source-free(无无源源)wave equation for free space(自自由由空空间间)becomes a homogeneous vector Helmholtzs equation(齐齐次次的的亥亥姆姆霍兹矢量方程霍兹矢量方程):Where k0 is the free-space wavenumber(自由空间波数自由空间波数)In Cartesian coordinates,the above equation is equivalent to three scalar Helmholtzs equations,one each in the components Ex,Ey,and Ez.Writing it for the component Ex,we have17Consider a uniform plane wave(均均匀匀平平面面波波)characterized by a uniform Ex(uniform magnitude and constant phase振振幅幅均均匀匀相相位位恒恒定定)over plane surfaces perpendicular(垂直垂直)to z;that is,Equation simplifies to The solution is readily seen to beWhere E0+and E0-are arbitrary(and,in general,complex)constants that must be determined by boundary conditions(边边界界条件确定的任意常数条件确定的任意常数).18复习：复习：二阶二阶常系数常系数线性线性常微分常微分齐次齐次方程的解方程的解19Using cos t as the reference and assuming E0+to be a real constant(zero reference phase at z=0),we haveAt t=0,it is a cosine curve with an amplitude E0+.At successive times the curve effectively travels in the positive z direction.We have,then,a traveling wave(行行波波).If we fix our attention on a particular point(a point of a particular phase恒定相位的点恒定相位的点)on the wave,we setFrom which we obtain the velocity of propagation of an equiphase front等等相相位位面面(the phase velocity相相速速度度)in free space 20Wavenumber波数波数 k0 bears a definite relation to the wavelength.Which measures the number of wavelengths in a complete cycle一一个个周周期内所含的波长数期内所含的波长数,hence its name.An inverse relation of equation is The above two equations are valid without the subscript 0 if the medium is a lossless material such as a perfect dielectric,instead of free space.在无耗介质中，去掉脚标在无耗介质中，去掉脚标0 0后上式仍然有效。后上式仍然有效。It is obvious without replotting that the second phasor term on the right side of that equation,represents a cosinusoidal wave traveling in the z direction with the same velocity c.以以相相同同速速度度c c沿沿-z-z方方向向传传播的余弦波。播的余弦波。21The associated magnetic field H can be found from 与与E E相伴的磁场相伴的磁场H HWhich leads to Thus Hy+is the only nonzero component of H;andWe have introduced a new quantity,0,which is called the intrinsic impedance of the free space自由空间的本征阻抗自由空间的本征阻抗.22Because 0 is a real number实实数数,Hy+(z)is in phase with Ex+(z)相相位位相相同同,and we can write the instantaneous瞬时值瞬时值 expression for H asHence,for a uniform planewave均均匀匀平平面面波波 the ratio of the magnitudes of E and H is the intrinsic impedance of the medium振振幅幅之之比比等等于于媒媒质质的的本本征征阻阻抗抗.We also note the H is perpencicular to E and that both are normal to the direction of propagation.电场电场 磁场磁场 传播方向两两垂直传播方向两两垂直zHyExEHan2324EHan2526Example.The electric field intensity of a uniform plane wave in free space is given by ,Determine:(1)The phase velocity of propagation:(2)The phase constant (rad/m)(3)The wave frequency(4)The intrinsic impedance(5)The wavelength 27Summary1.Plane Waves in Lossless Media281.1 transverse electromagnetic wavesWe have seen that a uniform plane wave均均匀匀平平面面波波 characterized by E=axEx,propagating in the+z-direction has associated with it a magnetic field H=ayHy.Thus E and H are perpendicular垂垂直直 to each other,and both are transverse to横横向向 the direction of propagation.It is a case of a transverse electromagnetic(TEM)wave横电磁波横电磁波.The phasor electric field intensity for a uniform plane wave propagating in the+z-direction is沿沿+z+z方向传播的均匀平面波方向传播的均匀平面波where E0 is a constant vector常常矢矢量量.A more general form is 更更一一般般的形式的形式29zyxdanP0E0P(x,y,z)RIt can be easily proved by direct substitution that this expression satisfies the homogeneous Helmholtzs equation 满满足足齐齐次次亥亥姆姆霍霍兹兹方方程程,provided thatIf we define a wavenumber vector波数矢量波数矢量/传播矢量传播矢量 asand a radius vector from the origin从从原原点点出发的径向矢量出发的径向矢量then30where an is a unit vector in the direction of propagation.沿沿传传播播方方向的单位矢量向的单位矢量zyxdanP0E0P(x,y,z)RThe geometrical relations of an,and R are illustrated in Figure,from which we see thatis the equation of a plane normal to an,the direction of propagation.an R=Constant is a plane of constant phase and uniform amplitude for the wave.是一个相位恒定和振幅均匀的平面是一个相位恒定和振幅均匀的平面In a charge-free region,E=0.As a result,31thenWhich requiresThus the plane-wave solution implies that E0 is transverse to the direction of propagation.E E0 0垂直与传播方向垂直与传播方向The magnetic field associated with E(R)may be obtained as 相伴的磁场相伴的磁场32Where is the intrinsic impedance(wave impedance)of the medium.媒媒质的本征阻抗质的本征阻抗/波阻抗波阻抗EHanIt is now clear that a uniform plane wave propagting in an arbitrary direction,an,is a TEM wave with E H and that both E and H are normal to an.沿任意方向传播的均匀平面波是横电磁沿任意方向传播的均匀平面波是横电磁(TEM)(TEM)波波The electric field associated with H(R)may be obtained as33Summary1.Plane Waves in Lossless Media341.1 transverse electromagnetic waves35homeworkThank you!Bye-bye!Thank you!Bye-bye!答疑安排答疑安排时间：周四时间：周四下午下午15：0018：00地点：地点：1301，1311P.8-4;8-5;