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ELECTRODYNAMICS
PROBLEM SET 9
due April 13
th
, before class
I. REFLECTION WITH DISPERSION
A plane wave of frequency
ω
is incident normally from vacuum on a semiinﬁnite slab of material with a complex
n
(
ω
).
a) Show that the ratio of reﬂected power to incident power is
R
=
±
±
±
±
1

n
(
ω
)
1 +
n
(
ω
)
±
±
±
±
2
.
(1)
II. ANISOTROPIC MEDIUM
Plane waves propagate in a homogeneous, nonpermeable (
μ
= 1) but anisotropic dielectric medium. The dielectric
is characterized by a tensor
±
ij
such that
D
i
=
±
ij
E
j
.
±
ij
is symmetric so it can be diagonalized by choosing an
appropriate orthogonal coordinate system.
.
a) Show that plane waves with frequency
ω
and wave vector
k
must satisfy
k
×
(
k
×
E
) +
ω
2
c
2
D
= 0
.
(2)
b) Show that for a given wave vector
k
=
k
n
there are two distinct modes of propagation with diﬀerent phase
velocities
v
=
ω/k
which satisfy the
Fresnel equation
:
3
X
i
=1
n
2
i
v
2

v
2
i
= 0
,
(3)
where
v
i
=
c/
√
±
i
and
n
i
is the i
th
component of
k
/

k

.
III. ORDERS OF MAGNITUDE
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This note was uploaded on 12/29/2011 for the course PHYSICS 606 taught by Professor Bedaque during the Spring '11 term at Maryland.
 Spring '11
 Bedaque
 Power, Work

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