Chemistry Reference
In-Depth Information
magnetic field vector are always vertical to each other and the magnetic field is
moved by a phase shift of
π
/2 or 90
°
in comparison to the electric field.
Consequently, nodes of the electric field coincide with antinodes of the
magnetic field, and vice versa. Several physical and chemical effects of electro-
magnetic radiation are correlated with the antinodes of the electric field [2].
Crests and troughs of the propagating wave travel with a velocity
c
/cos
α
in
the
+
x
-direction parallel to the surface plane. They have a distance
λ
2 cos
α
hc
0
E
1
2cos
α
a
parallel
(2.12b)
At normal incidence, Equation 2.11 is reduced to
E
int
2
E
0
sin
k
0
z
φ
cos
k
0
ct
(2.13)
This equation describes the most familiar standing wave with a period
a
vertical
of
λ
/2.
The radiation intensity is dependent on the Poynting vector,
S
, which is
proportional to the cross-product of the electric and magnetic field strength. In
order to determine this quantity within the electromagnetic field of a plane
wave, the electric field strength has to be squared at any point in space and
temporally averaged. A general formula for the intensity can be derived [9] by
assuming a reflectivity
R
<
100% for the substrate in accord with Equation 1.76.
In front of a flat substrate, the intensity
I
int
is given by
p
R
α
I
int
α
;
z
I
0
1
R
α
2
cos 2
π
z
=
a
vertical
φα
(2.14)
where
I
0
is a measure for the intensity of the
primary
beam, which is supposed
to be constant in time and space. The argument of the cosine is the phase
difference of the incoming and reflected waves, including two components: a
travel distance
2
π
z/a
vertical
and a phase shift
φ
depending on
α
. This phase
shift [9] only occurs in the region of total reflection and is determined by
"
#
2
arccos 2
α
α
crit
φα
1
(2.15)
It falls from
π
to 0 if
α
is changed from 0 to
α
crit
but is continuously zero for
α
>
α
crit
.
The intensity,
I
int
, given by Equation 2.14 is dependent on
α
and
z
but
independent of
x
and
y
. Nodes and antinodes can be characterized by a
minimum or by a maximum of the intensity, respectively:
p
R
α
I
min
;
max
I
0
1
R
α
2
(2.16)
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