Biomedical Engineering Reference
In-Depth Information
Figure 4.10
The dependence of the coe
cient
α
1
(see (4.39)) as the
function of permittivity (
ε
) and permeability (
μ
). (a)
χ
=
0. (b)
χ
=
0.1.
The particle is placed in vacuum,
k
0
a
=
0.1.
is shown. From this figure, it is seen that TM modes in a nonchiral
nanoparticle(seeFig.4.10a)haveelectricdipoleplasmonresonance
at
ε
≈−
2, nearly independent on permeability.
Atthesametime,anychirality(evensmall)ofananoparticle(see
Fig. 4.10b) leads to a radical change in the shape of the resonance
line, which becomes dependent in a nontrivial way on both the
permittivity and permeability of the material of the nanoparticle.
Below, we will see that these “hybrid” chiral-plasmon modes in the
nanoparticleprovidetheeffectiveinterferencebetweenradiationof
electric and magnetic dipole moments of the chiral molecule.
In practice, the orientation of the molecule can be arbitrary
with respect to the nanoparticle surface. Therefore in such cases,
one should average (4.45) over the orientations of the electric
and magnetic dipole moments. For spiral molecules with collinear
electric and magnetic dipole moments (i.e., for those with
m
0
=
ξ
d
0
), the averaging leads to the following expression:
2
2
γ
rad
γ
0
=
1
+
2
|
α
EE
−
i
ξα
EH
|
2
|
α
HE
−
i
ξα
HH
|
r
0
1
+ |
ξ
|
2
+
r
0
1
+ |
ξ
|
2
.
(4.48)
As a rule, the magnetic dipole moment of the molecule is much
smaller than the electric dipole moment
ξ<<
1. The chirality
parameter is also usually small (
χ<<
1) (see, however, [25]). So,
the second term in (4.48) corresponding to the induced electric
dipole moment is usually greater than the term corresponding to
the induced magnetic dipole moment [the third term in (4.48)].
