38
DOC.
53
AUGUST
1907
But
if
k
0
(more
precisely,
dk
^
0),
the
curve
for
x
=
l
possesses
no
zero
points.
Here
we
obtain
curves
of the
kind
indicated.
x
=
0
to
x
=
I
In this
case one
does
not
obtain
a
possible
if
one
replaces
the
curves
left
of
the abscissas
t0
or
t1
by
the abscissa
axes; thus,
in the
case
where the
oscillatory
process
starts at
x
=
0
at
time
t0,
the
second
curve
does
not
represent
the
process
in
x
=
l.
Hence, in this
case,
therefore,
your
group
velocity
cannot be
interpreted
as a
signal
velocity. Simply,
the
parts
of the
first
curve
to the left
of
t0
have
here
an
influence
on
the
part
of the
second
curve
to
the
right
of
t1.
It
is
also
possible
to construct
a process
from which
a signal
velocity
can
be
inferred
in
the
case
of
an
absorbing
medium.
One need
only
construct
a wave
train that exhibits
a
plane
moving
in
the direction of
the
propagation
of
light
in which
the
amplitude
of
the
light
vector
is permanently
zero.
We
set[3]
aq 
egßt
_ axŦV
+
jwyo(/t

nx)
_
egß't

a'x
+
jwyco(r

n'x)
a
ß
co n are
real
and
positive.
If
a)
and ß
are given,
the
differential
equations
for the
dispersion
yield
a
and
n.
If
we
introduce the
complex
dielectric
constant
e'
used in
Drude's
textbook,
and
set sje'te
=
ty(co),
dispersion
theory
yields[4]
*!(*) 
jß)
=
'ja
+ con (1)
For there
to
exist
a
plane propagating
with
velocity
4
in which
the
amplitude
is
permanently equal
to
zero,
the
two
components
of
a
must
possess
the
same
amplitude
and
the
same
phase
for
x

O
f.
This
yields
ßf

ß
=
(a'

a)

O
co'

co
=
(co'n'

(on)E
(2)