Biomedical Engineering Reference
In-Depth Information
Distribution of the Poynting vector for nondissipative plasmonic
nanoparticle and small
q
=
0.02 at the points corresponding to
the symmetrical quadrupole resonance and forward and backward
scattering are shown in Fig. 9.7. We observe dramatic modifications
of the vortex structures in the near field.
9.5 Scaling of Fano Resonances in Plasmonic
Nanostructures
Although a majority of plasmonic structures with Fano resonances
suffer from scaling, there exists an important exception for the
structures with the cylindrical symmetry. For such structures, all
surface plasmon resonances at small values of the size parameter
q
→
ε
=−
1. This, in principle,
permits the creation of Fano resonances with extreme nano-size in
the visible regime, see Fig. 9.9. Here,
a
i
denotes the corresponding
amplitude of the electric scattering coe
cients within the Mie
theory for the cylinder [20-22]. Here, a bar is used to distinguish
these scattering amplitudes for spheres and cylinders. In the
cylindrical nanowire, the surface plasmons are excited in the case
of the perpendicular polarization,
E
⊥
z
(TE-mode), and, thus
are not excited with
E
||
z
(TM-mode) [20]. For the case of TE-mode
and normal incidence, the scattering e
ciency
Q
sca
is given by the
expression
0 start from the same value
∞
2
q
2
.
Q
sca
=
|
a
|
(9.9)
=−∞
=
Inthisdefinitionof
q
kR
,
R
isthephysicalradiusofthenanowire.
The scattering amplitudes
a
(electric) are defined by the well-
known formulas [3, 20]. However, it is convenient to write these
formulas by separating the real and imaginary parts
+
i
a
=
,
(9.10)
where the functions
and
are given by:
=
nJ
(
nq
)
J
(
q
)
−
J
(
nq
)
J
(
q
),
nJ
(
nq
)
N
(
q
)
J
(
nq
)
N
(
q
),
=
−
(9.11)
