Biomedical Engineering Reference
In-Depth Information
dielectric permittivity with the help ofthe Drude formula
ω
2
p
ω
2
p
i
γ
ω
ε
ω
=
−
2
)
+
(
)
1
2
)
,
(9.14)
ω
+
γ
ω
+
γ
(
2
(
2
where
is the collision frequency.
Theeffectofafinitesizeofananowireistakenintoaccountbythe
renormalization of
ω
p
is the plasma frequency and
γ
A
v
R
,where
γ
γ
=
γ
∞
+
γ
∞
is the collision
frequency for bulk a material,
v
F
is the Fermi velocity, and
A
is a
normalizationcoe
cientthatdependsonthematerial,seeRef.[11].
As expected, an increase of the collision frequency
,
γ
leads to
a fast degradation of the Fano resonance, as seen in Fig. 9.12.
Nevertheless, for a cylinder in contrast to a sphere, it is possible to
observe pronounced Fano resonance at the nanoscale with weakly
dissipated metals, for example in nanowires with the radius of 30-
40nm.Asanexample,inFig.9.13,weshowtheresultofcalculations
Figure 9.12
Fano resonance in the backscattering cross-section caused by
the dipole-quadrupole interference for a nanowire with the size parameter
q
=
0.3.
