Biomedical Engineering Reference
In-Depth Information
Figure 9.4
Scattering e
ciencies versus permittivity. Forward-scattering
e
ciency vanishes along the blue curve given by the first equation of
Eq. (9.7). Red curve corresponds to the second equation of Eq. (9.7),
and it presents the back scattering e
ciency. Inset shows the region of
small
q
.
nanoparticles. The asymmetrical shapes in differential scattering
e
ciencies are shown in Fig. 9.5 in the vicinity of the quadrupole
resonance. Variation of the scattering diagrams from the forward
scattering to backward scattering is shown in the circular insets to
Fig. 9.5.
Now, we can illustrate the basic problem that arises with scaling
of the Fano resonance. Any real metal has a finite dissipation that
strongly influences the behavior of the differential scattering, see
Fig. 9.6. When the size parameter
q
becomes of the order of unity,
it is possible to observe the Fano resonance in the media with weak
dissipation. However, when
q
<<
1, it is impossible to observe
the Fano resonance even with weakly dissipating plasmonic media.
We notice that for weakly dissipating metals such as K, Na, and Al,
the minimum value of the dissipation parameter is about Im
ε
≈
0.14
−
0.18 near the plasmon resonance frequencies [11].
