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C:\User\Teaching\505506\S11\HW01'sol.doc
PHY 506
Classical Electrodynamics II
Spring 2011
Homework 1 with solutions
Problem 1.1
(to be graded of 25 points). A monochromatic, plane EM wave is normally incident from
free space on a uniform slab of a material with electric permittivity
and magnetic permeability
, with
slab thickness
d
comparable with the wavelength.
(i) Calculate the power transmission coefficient
F
, i.e. the fraction of the incident power, which
is transmitted through the slab.
(ii) Assuming that
and
are frequencyindependent and positive, analyze in detail the
frequency dependence of
F
. In particular, how does function
F
(
) depend on the film thickness
d
and
the wave impedance
Z
= (
/
)
1/2
of its material?
Solutions
:
(i) Since the wave may be partly reflected from the second
interface (see Fig. on the right), we should look for the solution in
the form of five traveling waves:
.
for
,
,
0
for
,
,
0
for
,
)
(
0
0
0
0
0
z
d
e
T
d
z
e
R
Te
z
e
R
e
e
E
E
d
z
ik
ikz
ikz
z
ik
z
ik
t
i
The four unknown (complex) coefficients
R
,
R
0
,
T
, and
T
0
, participating in these expressions may
be found by plugging them into four boundary conditions which express the continuity of the electric
field
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 Spring '08
 Stephens,P
 Work, free space, power transmission

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