This preview shows pages 1–3. Sign up to view the full content.
Homework 8 solutions
8.1 Omega beta diagram for the PPP
n1
3
..
:=
a
0.01
:=
c3
1
0
8
⋅
:=
omegacutoff
n
π
n
⋅
a
c
⋅
:=
omegacutoff
2
π
⋅
0
1.5
10
10
×
31
0
10
×
4.5
10
10
×
⎛
⎜
⎜
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎟
⎟
⎠
=
i
1
1000
..
:=
f
i
100 10
9
⋅
i
1000
⋅
:=
omega
i
f
i
2
⋅π
⋅
:=
k0
i
omega
i
c
:=
kz
in
,
omega
i
c
1
omegacutoff
n
omega
i
⎛
⎜
⎝
⎞
⎟
⎠
2
−
⋅
:=
kz
,
Re kz
,
()
iI
mk
z
,
⋅
−
:=
making sure that
k is beta  j alpha
01
.
10
11
2
.
10
11
3
.
10
11
4
.
10
11
5
.
10
11
6
.
10
11
7
.
10
11
1000
500
0
500
1000
1500
2000
2500
Re kz
i1
,
Re kz
i2
,
Re kz
i3
,
Im kz
,
Im kz
,
Im kz
,
k0
i
95 10
9
⋅
191 10
9
⋅
omega
i
I have highlighted the first two cutoff omegas where the propagation constant comes out of being
j alpha to become purely real.
You also see how as frequency goes up kz approaches k0
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document only plot real angles
slope
n
kx
n
Re knz
n
()
0.0000001
+
⎛
⎜
⎝
⎞
⎟
⎠
⎛
⎜
⎝
⎞
⎟
⎠
:=
Then the ray representing the wave travels with the slope:
z
p
p
a
1000
⋅
:=
p
0
1000
..
:=
I will now make a dummy plotting variable along the zaxis of
propagation
knz
n
k0
0
2
kx
n
2
−
:=
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 04/22/2009 for the course EEE 341 taught by Professor Diaz during the Spring '09 term at ASU.
 Spring '09
 diaz

Click to edit the document details