8平面波垂直入射(10-2).doc
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9. Normal Incidence to a Plane Boundary
A. Normal incidence to a plane between two dissipated media
The plane interface between two dissipated media is assumed to coincide with the coordinate plane .
The space is divided by the interface into two regions: region 1 () in which the medium parameters are , and region 2 () in which the medium parameters are .
The incident and the reflected waves in region 1 are, respectively, given by
and
where and are, respectively, the intrinsic impedance and the wave
number of the medium in region 1,
and
, ,
In region 2, there exists the transmitted wave only,
where and are, respectively, the intrinsic impedance and the wave
number of the medium in region 2,
and
The reflection coefficient and the transmission coefficient at the plane interface () are, respectively, defined by
and
In region 1, the wave is the sum of the incident wave and the reflected wave, given by
The electric field and the magnetic field boundary conditions at the interface plane are given by
These boundary conditions are solved for the reflection coefficient as follows.
then
then
then
then
finally
These boundary conditions can also be solved for the transmission coefficient as follows.
then
then
then
finally
It is inferred from
and
that
The combined wave of the incident and the reflected waves in region 1 must be a standing wave, and the standing-wave ratio is defined by
Since
then
and
therefore
Since the magnitude of the reflection coefficient is less than or equal to one
then the standing wave ratio should be
It is noted that
for pure traveling wave, no reflected wave exists, and ;
for pure standing wave, full reflection has made, and ;
for common standing wave, and ;
the smaller the standing wave ratio or the magnitude of the reflection coefficient is, the larger the traveling-wave part will be, and vice versa.
Conversely, it follows from
that
or
hence
Problem 2-8
A uniform plane wave traveling in +z direction with electric f
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