Biomedical Engineering Reference
In-Depth Information
Notethattheanalyticbranchesofthesquareroots
k
J
−
q
2
and
k
0
−
q
2
in (4.A.1) and (4.A.2) are defined in the same way as in
(4.22) and ensure proper directions of energy flows.
More information about the properties of the vector cylindrical
harmonics can befound, forexample, in [69].
4.A.2 Electromagnetic Field of a Chiral Molecule in
Cylindrical Coordinates
The expressions for the electric and magnetic fields of a chiral
molecule placed at the point
z
0
(
z
0
>
0) of the Cartesian z axis in
vacuum havethe following forms:
,
H
0
=
,
E
(
+
0
,
z
>
z
0
E
(
−
0
,
z
<
z
0
H
(
+
0
,
z
>
z
0
H
(
−
0
,
z
<
z
0
E
0
=
(4.A.3)
where
∞
1
dq
C
(
±
)
,
E
(
±
)
n
(
±
)
D
(
±
)
m
(
±
)
=
nq
σ
+
0
nq
σ
nq
σ
nq
σ
n
=
0
σ
=
e
,
o
0
∞
1
dq
D
(
±
)
. (4.A.4)
H
(
±
)
n
(
±
)
σ
+
C
(
±
)
m
(
±
)
=−
i
0
nq
σ
nq
nq
σ
nq
σ
σ
=
n
=
0
e
,
o
0
The coe
cients of the expansion in (4.A.4) havethe following form:
id
0
z
k
0
k
0
−
q
2
+
δ
n
1
k
0
im
0
y
k
0
k
0
−
q
2
C
(
±
)
=
δ
n
0
q
±
d
0
x
−
nqe
exp
∓
i
k
0
−
q
2
z
0
,
±
d
0
y
+
exp
∓
i
k
0
−
q
2
z
0
,
im
0
x
k
0
k
0
−
q
2
C
(
±
)
=
δ
n
1
k
0
nqo
