Hon Tat Hui
Revision of Plane Wave Propagation
NUS/ECE
EE4101
1
Revision of Plane Wave Propagation
1
Plane Waves in Lossless Media
In a source free lossless medium,
.
0
=
=
=
σ
ρ
J
0
0
=
⋅
∇
=
⋅
∇
∂
∂
=
×
∇
∂
∂
=
×
∇
H
E
E
H
H

E
μ
ε
ε
μ
t
t
Maxwell’s equations:
See animation “Plane Wave Viewer”
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Hon Tat Hui
Revision of Plane Wave Propagation
NUS/ECE
EE4101
2
Take the curl of the first equation and make use of the
second and the third equations, we have:
E
H
E
2
2
2
t
t
∂
∂
=
×
∇
∂
∂
=
∇
με
μ
(
)
E
E
E
2
:
Note
∇
−
⋅
∇
∇
=
×
∇
×
∇
This is called the
wave equation
:
0
2
2
2
=
∂
∂
−
∇
E
E
t
με
A similar equation for
H
can be obtained:
0
2
2
2
=
∂
∂
−
∇
H
H
t
με
Hon Tat Hui
Revision of Plane Wave Propagation
NUS/ECE
EE4101
3
In free space, the wave equation for
E
is:
0
2
2
0
0
2
=
∂
∂
−
∇
E
E
t
ε
μ
where
2
0
0
1
c
=
ε
μ
c
being the speed of light in free space (~ 3
×
10
8
(m/s)).
Hence the speed of light can be derived from Maxwell’s
equation.
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