ECE 222B, Winter 2010
Homework Set 3: Due Tuesday, February 2nd.
1. A plane wave in medium 1 is incident on an interface (at z=0) with medium
2 with an angle of incidence
θ
i
. (See Figure 52 in Balanis for the geometry
of the problem). The permittivity and permeability is
ε
1
and
μ
0
in region
1, and
ε
2
and
μ
0
in region 2. Both permittivities are real (ideal media).
The incident wave is
circularly
polarized and the incident electric field can
be written as
→
E
i
(
x, z
) =
E
A
(
b
x
0
+
j
b
y
) exp
h

j
→
β
i
·
→
r
i
,
where
E
A
is a constant and
b
x
0
= cos
θ
i
b
x

sin
θ
i
b
z.
If the wave is incident upon the surface at the Brewster angle, what is the
fraction of power transmitted?
2. (15 points) Assume that you are given an idealized plasma such that the
effective permittivity is
²
=
²
0
"
1

ω
2
p
ω
2
#
where
ω
p
is a constant called the plasma frequency. You may assume that
μ
=
μ
0
.
(a) Assume that you are given a TEM wave propagating in the z direction
such that
~
E
=
E
0
exp [

jβz
] ˆ
x
. Express
β
as a function of
ω
.
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 '09
 Polarization, Speed of light, group velocity, phase velocity

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