Biomedical Engineering Reference
In-Depth Information
4.4.2
The Analysis of the Results Obtained and Graphical
Illustrations
The process of the spontaneous decay of chiral molecules placed
near a cluster of two chiral spherical particles is very complicated,
and for clarity, we will present graphical illustrations only for the
mostinterestingcaseofachiralmoleculeplacedinthegapbetween
chiral particles on the symmetry axis (the z-axis, see Fig. 4.15). In
this case,
1
θ
0
=
0and
2
θ
0
=
π
; the expressions for the coe
cients
s
A
(0)
mn
,
s
B
(0)
mn
,
s
C
(0)
mn
,and
s
D
(0)
1, 2) become simpler (see
Appendix4.B),andnonzerocoe
cientsareonly
s
C
mn
and
s
D
mn
with
m
mn
(where
s
=
=
−
1; therefore, the lower limit of the summation over
q
in
(4.55), (4.56), and (4.58) must beequal to 1.
For simplicity, we will consider the radiative decay rate of
spontaneousemissiononlyforchiralmoleculeswithequalCartesian
projectionoftheelectricdipolemoment(
d
0
={
d
0
,
d
0
,
d
0
}
)andwith
equal Cartesian projection of the magnetic dipole moment (
m
0
0, 1,
=
{
m
0
,
m
0
,
m
0
}
).
Figure 4.16a shows the radiative decay rate of spontaneous
emission of a chiral molecule located in the gap between two
nonchiral dielectric spherical particles near the surface of the first
sphere as the function of the parameter
k
0
a
for different values of
the distance
l
/
(2
a
) between particles. One can see that for large
distances between the spheres, the decay rate behavior is similar
to a decay rate in the case of a single sphere. However, for a small
gapbetweenthenanoparticles,onecanobservesubstantialchanges
inspectra.Themostinterestingfeatureisthatnowthemaximumof
thedecayrateappearsforsmallersizeofnanoparticles(orforlarger
wavelength).
More interesting effects arise in the case of a cluster of chiral
dielectricparticles.Figure4.16bshowsthedependenciesanalogous
to those shown in Fig. 4.16a, but for chiral particles. As it is seen
in Fig. 4.16b, the nonzero chirality leads to the redistribution of
the maxima of the spontaneous emission decay rate and to the
appearance of new high-
Q
resonances in comparison with the case
of a nonchiral cluster. A more important observation is that for
chiralparticles,onecanobservethedifferencebetweentheradiative
decayratesofspontaneousemissionfor“right”and“left”molecules.
