Biomedical Engineering Reference
In-Depth Information
not consider the nonradiative channel of the spontaneous decay. A
detailed investigationof this case is performed in [44].
4.3.2
Analysis of the Results obtained and Graphical
Illustrations
In a very important case of a chiral nanoparticle, that is, a particle
having a size much smaller than the wavelength of the radiation,
the expression (4.43) can be expanded in a series over the small
parameter
k
0
a
→
0. Taking into account only the main terms of
theexpansion,wefindthefollowingexpressionforthespontaneous
emission relative radiative decay rate [42]:
⎧
⎨
⎩
⎫
⎬
⎭
m
0
)
2
+
α
i
α
EE
r
0
EH
r
0
·
−
−
·
−
d
0
(3
n
(
n
d
0
)
d
0
)
(3
n
(
n
m
0
)
γ
1
rad
γ
0
=
d
0
)
,
2
2
2
+
α
i
α
|
d
0
|
+ |
m
0
|
HH
r
0
HE
r
0
+
m
0
(3
n
(
n
·
m
0
)
−
m
0
)
+
(3
n
(
n
·
d
0
)
−
(4.45)
where electromagnetic polarizabilities of a chiral spherical particle
in the uniform field have the form:
α
EE
=
a
3
(
ε
−
1)(
μ
+
2)
+
2
εμχ
2
2
,
(
ε
+
2)(
μ
+
2)
−
4
εμχ
2
α
HH
=
a
3
(
ε
+
2)(
μ
−
1)
+
2
εμχ
2
,
(
ε
+
2)(
μ
+
2)
−
4
εμχ
εμχ
3
i
a
3
α
EH
=−
α
HE
=
2
;
(4.46)
(
ε
+
2)(
μ
+
2)
−
4
εμχ
n
is the unit vector directed from the center of the particle to the
molecule position.
The vanishing of the denominator (4.46) determines the values
of
, which correspond to excitation of the chiral-plasmon
resonances in chiral spherical nanoparticle:
(
ε
and
μ
2
. (4.47)
In a special case of a nonchiral material (
χ
=
0), one can obtain
two independent equations from (4.47):
ε
+
2
=
0and
μ
+
2
=
0,
which correspond to the dipole plasmon resonances in a nonchiral
spherical nanoparticle [43].
InFig.4.10,thestructureofplasmonicresonancesforaspherical
nanoparticle without chirality and with the chirality factor
ε
+
2)(
μ
+
2)
=
4
εμχ
χ
=
0.1
