emlab 1 plane wave reflection and transmission. emlab 2 reflection of uniform plane waves at normal...
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EMLAB
1
Plane wave reflection and transmission
EMLAB
2Reflection of uniform plane waves at normal incidence
EMLAB
3Boundary conditions
tritri HHHEEE , (at the interface, z =0)
EMLAB
4Reflection from perfect electric conductor
0,0 tritri HHHEEE (at the interface, z =0)
112
12
)0( 2
010 sin2)( 11ii
zjzjri EzjEee EEE
EMLAB
5Example
EMLAB
6
}Re{2
1})(Re{
2
1 *2*ininininr HEHES
EMLAB
7Wave reflection from multiple interfaces
ljZZ
ljZZZZ
L
Lin
tan
tan
0
00
1
1
in
in
lj
ljin
232
2232 tan
tan
EMLAB
8Example : radome
31
),3,2,1(2 mml
3232
2232 tan
tan
lj
ljin
0 2 4 6 8 10 12 14 16 180
0.2
0.4
0.6
0.8
1
Reflection
Transmission
EMLAB
9Example : anti-reflection coating
Calculate the refractive index and minimum thickness for the glass coating to provide total transmission from air to the glass at a free space wavelength of 570nm. refractive index of the glass is n3=1.45.
313312
nm][1194
)12( 2
ml
2.12
022
rn
(n: refractive index)
EMLAB
10Plane wave refraction at oblique incidence angles
EMLAB
11Plane of incidence
EMLAB
12
s-polarization (perpendicular) p-polarization (parallel)
If an EM wave approaches a surface obliquely, it is easier to decompose the field into two components, s-polarization and p-polarization.
EMLAB
13p-polarization (E-field parallel to the plane of incidence)
)cos,sinsin,cos(sin kk
11111 2),sin,0,(cos kk
,2
),sin,0,cos( 11111 kk
22222 2),sin,0,(cos kk
1111101 ,),cos,0,sin( EE
1111101 ,),cos,0,sin( EE
2222202 ,),cos,0,sin( EE
EMLAB
14E-field tangential component continuity
10110110 coscos TEREE
EMLAB
15
• phase matching condition (Snell’s law)
EMLAB
16H-field tangential component continuity
2
20
1
10
1
10
TEREE
)sin,0,(cos 1111 kk
101
10110 ˆ
ˆEy
EkH
)cos,0,sin( 11101 EE
EMLAB
17
2
10
1
10
1
10
TEREE
210110110 coscoscos TEREE TR1
2
cos
cos1
TR2
11
1122
12
2
1
1
22
1
1
2
coscos
cos2
coscos
2
cos
cos2
TT
1122
1122
2
1
1
2
2
1
1
2
2
1
1
2
coscos
coscos
coscoscoscos
2cos
cos
TR
EMLAB
18Reflection coefficient for parallel polarization
EMLAB
19Reflection coefficient for perpendicular polarization (s)
EMLAB
20Example
EMLAB
21
EMLAB
22
EMLAB
23Total reflection
EMLAB
24Optical fiber
EMLAB
25
TV antenna
TV signal transmitting antenna
TV signals are transmitted as EM wave with horizontal polarization.
Wave propagation
EMLAB
26Polarization of EM waves
Source current
Source current
EMLAB
27Reflection from ionosphere
EMLAB
28Reflection from ground and troposphere
EM waves undergo reflections and diffractions while propagat-ing toward receivers.
EMLAB
292-Ray Ground Reflection
• For d>> hr, ht,
– low angle of incidence allows the earth to act as a reflector– the reflected signal is 180 out of phase– Pr 1/d4
RT
ht hr
Phase shift!
d
EMLAB
30
Rcj
SRT
RcjR
cj
S
Rcj
RT eRGGR
e
R
eR
R
eGGH
1
44)(
121
21
4
222
2
2
2
2
1
4
2cos1
4
R
hhGGP
R
hkh
RGGP
R
hkhR
RGGPP
RTRTT
RTRTT
RTRTTR
EMLAB
31
4
1
R
2
1
R