12 Plasmonics with a Twist: Taming Optical Tornadoes on the Nanoscale
437
where ω is the light angular frequency, ω p =
ne 2 /λ 0 m is the plasma frequency,
and the effects of interband transitions and quantum size effects for particles much
smaller than the carrier mean free path are neglected. Accordingly, the energy density
of a harmonic field propagating through a non-magnetic, dispersive and absorptive
medium characterized by the Drude permittivity can be written as [37, 51, 52]:
W = λ 0 /4 · (λ r + 2ωλ i /α ) · |E|
2
+ μ 0 /4 · |H|
2
.
(12.4)
The energy conservation law in this case reflects the rate of the energy change within
the metal volume V due to leakage across its surface γ as well as due to volume
dissipation:
−
V
˙
W dV =
γ
Sdγ +
1
2
V
ωλ 0 λ i |E|
2 dV .
(12.5)
One rarely-discussed yet important consequence of Eqs. 12.4–12.5 is that while a
plasmonic nanostructure may provide light concentration in the volume below the
diffraction limit in the host medium, the effective mode volume–which accounts for
the portion of the electric field energy stored inside the metal–can in principle exceed
this limit [37]. Furthermore, the energy dissipation rate grows with the increase of
the imaginary part of permittivity, and also with the amount of energy stored in the
electric rather than magnetic field. Typically, for electromagnetic fields confined in
the vicinity of sub-wavelength plasmonic nanostructures, magnetic energy is just a
tiny portion of the electric energy. This results in the fast energy dissipation and low
degree of temporal coherence of localized SP modes [53]. Typical approaches to
alleviate or compensate for dissipation losses include loss compensation with gain
[4, 54, 55]–which however may require high pump rates and complicates local heat
management in sub-wavelength plasmonic components–and the search for new materials with high charge carriers mobility yet reduced dissipative losses [56–59]. In the
following, I will discuss an alternative approach to reducing the dissipative losses by
modifying the pattern of the nanoscale powerflow through plasmonic nanostructures.
12.3 How can a Particle Absorb more than the Light Incident
on it?
The above question was famously posed and answered by Craig Bohren [23] to
explain the physics of the strong energy concentration on metal nanoparticles by
studying the modification of the optical powerflow in the electromagnetic field due
to the presence of a single nanoparticle. The Poynting vector field lines—which
otherwise would have been parallel lines along the propagation direction of the plane
wave–become drastically distorted in the vicinity of the particle at the frequencies
corresponding to the real parts of the particle eigenmodes frequencies [23, 60, 61].
This effect is illustrated in Fig. 12.4a, which shows the optical powerflow behavior
437
where ω is the light angular frequency, ω p =
ne 2 /λ 0 m is the plasma frequency,
and the effects of interband transitions and quantum size effects for particles much
smaller than the carrier mean free path are neglected. Accordingly, the energy density
of a harmonic field propagating through a non-magnetic, dispersive and absorptive
medium characterized by the Drude permittivity can be written as [37, 51, 52]:
W = λ 0 /4 · (λ r + 2ωλ i /α ) · |E|
2
+ μ 0 /4 · |H|
2
.
(12.4)
The energy conservation law in this case reflects the rate of the energy change within
the metal volume V due to leakage across its surface γ as well as due to volume
dissipation:
−
V
˙
W dV =
γ
Sdγ +
1
2
V
ωλ 0 λ i |E|
2 dV .
(12.5)
One rarely-discussed yet important consequence of Eqs. 12.4–12.5 is that while a
plasmonic nanostructure may provide light concentration in the volume below the
diffraction limit in the host medium, the effective mode volume–which accounts for
the portion of the electric field energy stored inside the metal–can in principle exceed
this limit [37]. Furthermore, the energy dissipation rate grows with the increase of
the imaginary part of permittivity, and also with the amount of energy stored in the
electric rather than magnetic field. Typically, for electromagnetic fields confined in
the vicinity of sub-wavelength plasmonic nanostructures, magnetic energy is just a
tiny portion of the electric energy. This results in the fast energy dissipation and low
degree of temporal coherence of localized SP modes [53]. Typical approaches to
alleviate or compensate for dissipation losses include loss compensation with gain
[4, 54, 55]–which however may require high pump rates and complicates local heat
management in sub-wavelength plasmonic components–and the search for new materials with high charge carriers mobility yet reduced dissipative losses [56–59]. In the
following, I will discuss an alternative approach to reducing the dissipative losses by
modifying the pattern of the nanoscale powerflow through plasmonic nanostructures.
12.3 How can a Particle Absorb more than the Light Incident
on it?
The above question was famously posed and answered by Craig Bohren [23] to
explain the physics of the strong energy concentration on metal nanoparticles by
studying the modification of the optical powerflow in the electromagnetic field due
to the presence of a single nanoparticle. The Poynting vector field lines—which
otherwise would have been parallel lines along the propagation direction of the plane
wave–become drastically distorted in the vicinity of the particle at the frequencies
corresponding to the real parts of the particle eigenmodes frequencies [23, 60, 61].
This effect is illustrated in Fig. 12.4a, which shows the optical powerflow behavior