Biomedical Engineering Reference
In-Depth Information
projection of the magnetic dipole moment (
m
0
={
m
0
,
m
0
,
m
0
}
). In
this special case, the integrand expression (4.30) can be written as
follows:
U
(
h
)
2
2
h
2
k
0
β
h
−
k
0
α
h
|
d
0
|
2
=
−
k
0
δ
h
Re
d
0
m
0
.
(4.33)
Here, as before, we will call the molecules with parallel
d
0
and
m
0
(
d
0
and
m
0
havethesamesigns)“right”molecules,andthemolecules
with antiparallel
d
0
and
m
0
(
d
0
and
m
0
have the opposite signs) we
will call “left” molecules.
In Fig. 4.6, the dependence of the spontaneous decay rate of a
chiralmoleculeonitsdistancetotheinterfaceisshown.Asitfollows
from the figure, there is a difference between the decay rates of
“right” and “left” molecule enantiomers. In this case, the difference
is biggest for chiral metamaterial with
2
2
h
2
k
0
α
h
−
k
0
β
h
|
m
0
|
8
h
2
2
+
−
+
−
0(MNG-
metamaterial)(seeFig.4.6c)andforchiralmetamaterialwith
ε>
0and
μ<
ε<
0
μ<
and
0 (DNG-metamaterial) (see Fig. 4.6d). In the case of a
chiraldielectric,thisdifferenceissmaller(seeFig.4.6a).Forametal
with chiral properties, the curves for “left” and “right” molecules
have almost no difference (see Fig. 4.6b). This is due to a rather
large imaginary part of the wavenumbers in this case. In addition,
fromFig.4.6,itfollowsthattheasymptoticrelation(4.31)describes
well the nonradiative part of the total rate of spontaneous decay
for small values of
k
0
z
0
and for different values of permittivity and
permeability.
Figure 4.7 shows the ratio of the spontaneous decay rate of a
“left”moleculeandthespontaneousdecayrateofa“right”molecule
(
γ
L
/γ
R
) and, vice versa, the ratio of the spontaneous radiation rate
of a “right” molecule and the spontaneous radiation rate of a “left”
molecule (
γ
R
/γ
L
), as a function of permittivity and permeability of
the chiral half-space. From this figure, it follows that for certain
values
ε
and
μ
,theradiationratesofthe“right”and“left”molecules
differby10-15times.Itisseenthatachiralmetamaterialwith
−
1
<
ε<
0and
μ
≈−
1 (DNG-metamaterial) will increase radiation of
“left” molecule and suppress radiation of “right” molecules. At the
same time, a chiral metamaterial with
ε>
0and
μ
≈−
1(MNG-
metamaterial) and also a metamaterial with
ε<
−
1and
μ
≈−
1
