电磁场与电磁波第20讲坡印亭矢量

(a) No dispersion无色散: (c) Anomalous dispersion异常色散: du p du p 0 (u pincreasing with ） 0 (u p与无关，即 是的线性函数） d d ug >u p u p =ug (b) Normal dispersion正常色散:
c (1 j )
2 up (m/s) f
=
1
f (1 j ) () 2 u p 2 (m) f f


1 f
(m); for good conductors: =
1


2
9
An information-bearing载信息 signal normally has a small spread of frequencies频带 (side-bands) around a high carrier frequency. Such a signal comprises a “group” of frequencies频率群 and forms, a wave packet波包. A group velocity群速度 is the velocity of propagation of the wave-packet envelope波包包络 (of a group of frequencies).
2
(m/s)
The phase velocity up in a good conductor is
2 up (m/s) f
8
2 1 1 2 up c up (m/s) 1 (m/s) u p k0 0 0 8 f
1 ˆ E ( R) H ( R) or E ( R) an H ( R) (V/m) j
3
2. Plane Waves in Lossy Media
2 E kc E 0
2
c j ' j '' kc c j
y
E
linear polarization:相位相同或相反
circular polarization: 振幅相同，相位差900
y
y
E
x
x
x
elliptically polarized: 振幅不同，相位不同 y
E
y
E
y
x
x
x
5
ˆ ˆ E ( z ) E0 (ax ja y )e j z ; ˆ Ei ( x, z ) a y 10e j (6 x 8 z ) ; ˆ ˆ Ei ( y, z ) 5(a y az 3)e j 6(
kx k y kz k ˆ ˆ ˆ ˆ k ax kx ay k y az kz kan
2 2 2 2 2
ˆ ˆ ˆ R ax x ay y az z
1 1 ˆ H ( R) E ( R) or H ( R) an E ( R) (A/m), j
11
A relation between the group and phase velocities may be
1 d d 1 du p = ( ) 2 ug d d u p u p u p d ug up
du p 1 u p d
we see three possible cases:
t z constant
From which we obtain
dz 1 ug . dt /
In the limit that 0, we have the formula for computing the group velocity in a dispersive medium色散媒质中群速.
7
3. Group Velocity
The phase velocity up in a lossless material is
up c k0 0 0
The phase velocity up in a low-loss dielectrics is

1 1 up 1 8

We defined the phase velocity相速度, up , of a single-frequency plane wave as the velocity of propagation of an equiphase wavefront等相位 面传播的速度. For a plane waves in a lossless medium, the phase constant , , is a linear function of . As a consequence, the phase velocity is a constant that is independent of frequency与频率无关. However, in some case the phase constant is not a linear function of ; waves of different frequencies will propagate with different phase velocities不同的相速度. Inasmuch as all information-bearing signals consist of a band of frequencies许多频率分量, waves of the component frequencies travel with different phase velocities, causing a distortion 畸变 in the signal wave shape. The signal “disperses 色散” . The phenomenon of signal distortion caused by a dependence of the phase velocity on frequency is called dispersion色散媒质.
(m)
4
1. polarization of plane waves
ˆ Ex ( z, t ) ax Exm cos(t kz ) ˆ E y ( z, t ) a y E ym cos(t kz )
Ex ( z ) ax Exm e jkz ˆ ˆ E y ( z ) a y E ym e jkz e j
dz 0 up dt 0
10
The velocity of the envelope包络的传播速度 (the group velocity ug ) can be determined by setting the argument of the first cosine factor equal to a constant第一个余弦函数项的幅角为常数来确定:
E ( z, t ) E0 cos[(0 )t (0 ) z ] E0 cos[(0 )t (0 ) z ] 2E0 cos(t z ) cos(0t 0 z)
Since << 0, the expression represents a rapidly oscillating wave having an angular frequency 0 and an amplitude that varies slowly with an angular frequency .以角频率0快速振荡的波，其振幅随角 频率缓慢变化 The wave inside the envelope propagates 包 络 里 面 的 波 with a phase velocity found by setting 0t0z =Constant:
du p
d ug <u p
0 (u p decreasing with ）
12
Example 8-6 p378-379
13
14
4. Flow of Electromagnetic Power and the Poynting Vector 玻印亭矢量
Electromagnetic waves carry with携带 them electromagnetic power. Energy is transported through space to distant receiving points by electromagnetic waves电磁波. We will now derive a relation between the rate of such energy transfer and the electric and magnetic field intensities associated with a traveling electromagnetic wave所传送的 能量和电磁波中电场及磁场强度之间的比率关系. We begin with the curl equations The verification of the following identity of vector operations is straightforward矢量恒等式
3y z )
;
ˆ x 3cos 2 107 t ky az 3cos 2 107 t ky ˆ Ea 2
y
右旋圆极化；
right-hand circularly polarized wave
线极化； linear polarizaFra Baidu bibliotekion
0 z x
线极化； 左旋圆极化；
left-hand circularly polarized wave
6
Main topic
Plane Electromagnetic Waves
3. Group Velocity(群速)
4. Flow of Electromagnetic Power and the Poynting Vector (电磁功率流和坡印亭矢量)
1 ug d / d
(m/s).
This is the velocity of a point on the envelope of the wave packet波包 的包络上一个点的速度, and is identified as the velocity of the narrow-band signal窄频带信号的速度.
Field and Wave Electromagnetic
电磁场与电磁波
第20讲
作业情况
1班：人
合计：人 情况:
2
Review
1.1 transverse electromagnetic waves 横电磁波
jk R jkan R ˆ E(R) E0e =E0e (V/m) ˆ k R kan R kx x k y y kz z
-1
jkc j c (m )
j j c =j (
1/ 2 ) j (1 ) j j
Ex E0e z E0e z e j z
For a good conductor
f