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1
7.2
For a plane wave traveling in free space upwards towards the boundary at z=0 with medium 2,
calculate and plot the TE and TM reflection and transmission coefficients for the four cases given below.
Case1
:
ε
r
2
=4,
μ
r
2
=1
Case 2
:
ε
r
2
=1
μ
r
2
=4
Case 3
:
ε
r
2
=4
μ
r
2
=4
Case 4
:
ε
r
2
=0.3
μ
r
2
=1
a) First make these plots versus k
y
, given that the incident propagation constant is k
0
, In other words the x
axis of your plots shows k
y
/k
0
, and of course this quantity goes from 0 to 1.
b) Then repeat the plots versus angle of incidence.
c) If you see extreme behavior in the reflection coefficient such as it being 1 or 0, explain it.
(If you need to assume a frequency to do these calculations, assume 1GHz)
In MathCAD form
ZTM
mj
,
eta
m
kzm
,
km
m
⋅
:=
ZTE
,
eta
m
km
m
kzm
,
⋅
:=
kzm
,
km
m
()
2
ky
j
2
−
:=
km
m
k0
ep
m
mu
m
⋅
⋅
:=
eta
m
eta0
mu
m
ep
m
⋅
:=
mu
m
Material
m2
,
:=
ep
m
Material
m1
,
:=
m14
..
:=
Material
4
1
4
0.3
1
4
4
1
⎛
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎠
:=
I used the math options to change the starting
array point to 1 from the default of zero
I will do all the other materials in one shot by defining
ZTM0
j
eta0
kz0
j
k0
⋅
:=
ZTE0
j
eta0
k0
kz0
j
⋅
:=
kz0
j
k0
2
ky
j
2
−
:=
ky
j
jk0
⋅
1000
:=
j
1 999
..
:=
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 Spring '09
 diaz

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