Biomedical Engineering Reference
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associated with very weak scattering. The fascinating property of
such structures is related to the coexistence of the Fano resonance
and topological optics effects, where the characteristic size of
vortices is well beyond the diffraction limit. This property can be
found, for example, for weakly dissipative plasmonic nanoparticles
in the framework of the Mie theory. In this chapter, we demonstrate
that the limitation
q
1 for the pronounced Fano resonances
can be overtaken for the cylindrical plasmonic structures, which
exhibit a Fano resonance at the nanoscale,
q
≈
<<
1. Important
peculiarities of the far-field scattering and near-field Poynting flux
are presented for this novel type of “nano-Fano resonance.” We
believe that our results provide an insightful mechanism for the
manipulationofFanoresonancesattheextremenanoscale,andalso
open an unprecedented way for controlling vortices in topological
optics.
9.2 Fano Resonance and its Mechanical Analogue
The fascinating phenomenon of Fano resonance refers to the
interference of a broad and narrow spectral radiation [1, 2]. In
the case of light scattering by small plasmonic particles, the dipole
Rayleigh scattering plays a role of a broad spectral radiation and
the surface plasmon resonance (e.g., quadrupole or higher-order
resonance) plays a role of a narrow spectral line interacting with
thebroadradiation.Intheframeworkofthewell-knownMietheory
[3, 4], such a Fano resonance manifests itself in the differential
scattering e
ciency cross-sections. In terms of the interference
of electrical or magnetic scattering amplitudes (namely,
a
or
b
within the Mie theory), it looks like an overlap of broad and narrow
spectral lines, for example, broad dipole and narrow quadrupole
lines (see Fig. 9.1). Within the Mie theory, the scattering amplitudes
are defined by the well-knownformulas:
(
a
)
(
b
)
a
=
,
b
=
,
(9.1)
(
a
)
(
a
)
(
b
)
(
b
)
+
i
+
i
where the functions
are combinations of the spherical
Bessel and Neumann functions, see details in Ref. [5]. The
and
