Biomedical Engineering Reference
In-Depth Information
Figure 4.5
The solution of the dispersion equation (4.23) at
χ
=
0.1.
(a)
μ
=
1; (b)
μ
=−
1. The crosses show the asymptoti
c solutio
n
(4
.24). The c
ircles correspond to the solution of the equation
ε
k
0
−
q
2
+
k
0
εμ
−
q
2
=
0. The points show the numerical solution of Eq. (4.23).
The relative rate of spontaneous emission of a chiral molecule
near a chiral (or any other) material body can be defined from
the classical point of view as the ratio of the power lost by the
moleculetodrivetheelectromagneticfieldandtheanalogouspower
of the molecule in free unboundedspace.
The total rate of doing work by the fields in a finite volume
V
is
[73]:
2
Re
V
dV
j
E
(
r
)
·
E
(
r
)
+
j
∗
H
(
r
)
·
H
(
r
)
,
1
P
=
(4.25)
Here,
E
=
E
0
+
E
sc
and
H
=
H
0
+
H
sc
are the total electric and
magnetic fields near the chiral molecule. Densities of the external
currents in this case are defined by the molecular dipole moments:
j
E
j
H
d
0
−
i
m
0
=−
ω
δ
−
i
(
r
r
0
),
(4.26)
where
δ
(
r
−
r
0
)istheDiracdeltafunction;
r
0
istheradiusvectorof
the position of achiral molecule.
The power
P
0
, which is radiated by the dipole sources in the
empty space, is
3
|
2
.
ck
0
2
P
0
=
d
0
|
+ |
m
0
|
(4.27)
Substituting currents (4.26) into the power (4.25) and normalizing
the resulting expression to the power lost by the chiral molecule in
