Biomedical Engineering Reference
In-Depth Information
Thus, the interference between the electric and the magnetic fields
is possible onlyif the following twoconditions take place.
1. In the system under consideration, a chiral-plasmon resonance
must be present, that is, the condition (4.47) must be satisfied.
Under this condition, the contribution of a magnetic radiation
increases.
2. Electric dipole moment induced in the nanoparticle should be
zero,thatis,thefollowingconditionmustbesatisfied[see(4.48)]
α
EE
−
i
ξα
EH
=
0.
(4.49)
The solution of the system of Eqs. (4.47) and (4.49) determines
values of permittivity and permeability of the nanoparticle, which
correspond to minimal values of the radiative decay rate of a chiral
molecule. It means that the interference between the electric dipole
and magnetic dipole radiation becomes maximal and destructive if
2
d
0
d
0
+
2
m
0
m
0
+
μ
→−
ε
→−
m
0
,
d
0
.
(4.50)
χ
χ
2
2
From (4.50), it follows that by changing the sign of
m
0
, that
is, when the chirality of the molecule is changed, the resonant
permeability
μ
χ<<
1,
m
0
<<
d
0
)andap-
proximatelyequalsto
−
2.Onthecontrary,theresonantpermittivity
ε
mayhavedifferentsignsformoleculeswithdifferentchirality.This
means that both the nanoparticles with simultaneously negative
ε
and
μ
(DNG-metamaterials), and nanoparticles with negative
μ
and
positive
ε
(MNG-metamaterials)aresuitablefortheeffectivecontrol
of radiation ofchiral molecules.
One should note that all the results obtained [including (4.50)]
are valid for any values of the chirality parameter and the relation
between electric and magnetic dipole moments, not only for the
small ones. For a larger chirality parameter (see, e.g., [25]), one can
expect even more pronounced effects.
Figure 4.11 shows the radiative decay rate of spontaneous
emission of a chiral molecule located near the DNG chiral spherical
nanoparticles as a function of the permittivity for a fixed value of
permeability. As it is well seen in the figure, for molecules that
differ only in the orientation of the magnetic dipole moment of the
transition (for the “left” and the “right” molecules), the radiative
varies only slightly (
