7 Ultrafast and Nonlinear Plasmon Dynamics
269
7.3.6 Nonlinear Optical Antennas
As discussed above, particles and rough surfaces can provide large field enhancements, but with the increasing interest in plasmonic applications such as imaging,
sensing, cloaking, or harvesting, a need for controllable and reproducible linear and
nonlinear responses has developed. Recent advances in chemical synthetic methods allow the production of crystalline metal nanostructures with a wide range of
shapes and sizes with nanometer-scale structural control. Single-crystal nanoparticles and nanowires often exhibit strong plasmonic resonances due to their low defect
density and well-defined shape. Additionally, lithographic techniques, focused ion
beam milling, and template stripping now provide a means to generate arrays of
nanoparticles and other more complex structures such as coupled nanowires and
bowtie antennas, which have a large field enhancement in the nanogap region. For
an antenna, the SHG polarization is again given by
P
(2)
(2ω) = χ
(2)
(−2ω; ω, ω)L
2
(ω)L(2ω)E
2
,
(7.36)
where the nonlinear response is given by the material susceptibility. The local field
factor L now describes enhancements due to antenna resonances in addition to
localized plasmon resonances, and so depends sensitively on geometrical and environmental properties and the coupling of plasmonic modes.
Similar to radio-frequency antennas, antenna resonances for plasmonic antennas
such as rods occur when the length of the antenna is equivalent to an integer multiple
of half the wavelength. However, the wavelength is modified from the free-space
wavelength by the SPP dispersion on the surface of the metal [56]. The precise resonant behavior of the antenna depends sensitively on geometrical details such as
diameter, cross-section, and shape, as well as roughness. For such simple antennas, the spectral dependence of the antenna resonances is often approximated by
Lorentzian lineshapes,
L(ω) ◦
l
A l
ω l − ω + iΓ l
,
(7.37)
where ω l are the resonance frequencies, Γ l is the damping of the antenna, and A l the
relative strength of the resonance.
The local field correction arising from optical antenna resonances can provide an
enhanced nonlinear response, up to several orders of magnitude, arising from the
enhancement of the linear electric field. However, the spectral dependence of the
local field enhancement can lead to a shift in the emission spectrum, as represented
in Fig. 7.15, and therefore also an apparent spectral shift in the nonlinear response.
The nonlinear response may also not be accurately predicted by the linear far-field response, due to the different near-field spectral density of states distribution compared
to the far-field [57].
For non-degenerate wavemixing processes, coupled antennas can be designed
such that several input frequency components are simultaneously enhanced [58, 59].
269
7.3.6 Nonlinear Optical Antennas
As discussed above, particles and rough surfaces can provide large field enhancements, but with the increasing interest in plasmonic applications such as imaging,
sensing, cloaking, or harvesting, a need for controllable and reproducible linear and
nonlinear responses has developed. Recent advances in chemical synthetic methods allow the production of crystalline metal nanostructures with a wide range of
shapes and sizes with nanometer-scale structural control. Single-crystal nanoparticles and nanowires often exhibit strong plasmonic resonances due to their low defect
density and well-defined shape. Additionally, lithographic techniques, focused ion
beam milling, and template stripping now provide a means to generate arrays of
nanoparticles and other more complex structures such as coupled nanowires and
bowtie antennas, which have a large field enhancement in the nanogap region. For
an antenna, the SHG polarization is again given by
P
(2)
(2ω) = χ
(2)
(−2ω; ω, ω)L
2
(ω)L(2ω)E
2
,
(7.36)
where the nonlinear response is given by the material susceptibility. The local field
factor L now describes enhancements due to antenna resonances in addition to
localized plasmon resonances, and so depends sensitively on geometrical and environmental properties and the coupling of plasmonic modes.
Similar to radio-frequency antennas, antenna resonances for plasmonic antennas
such as rods occur when the length of the antenna is equivalent to an integer multiple
of half the wavelength. However, the wavelength is modified from the free-space
wavelength by the SPP dispersion on the surface of the metal [56]. The precise resonant behavior of the antenna depends sensitively on geometrical details such as
diameter, cross-section, and shape, as well as roughness. For such simple antennas, the spectral dependence of the antenna resonances is often approximated by
Lorentzian lineshapes,
L(ω) ◦
l
A l
ω l − ω + iΓ l
,
(7.37)
where ω l are the resonance frequencies, Γ l is the damping of the antenna, and A l the
relative strength of the resonance.
The local field correction arising from optical antenna resonances can provide an
enhanced nonlinear response, up to several orders of magnitude, arising from the
enhancement of the linear electric field. However, the spectral dependence of the
local field enhancement can lead to a shift in the emission spectrum, as represented
in Fig. 7.15, and therefore also an apparent spectral shift in the nonlinear response.
The nonlinear response may also not be accurately predicted by the linear far-field response, due to the different near-field spectral density of states distribution compared
to the far-field [57].
For non-degenerate wavemixing processes, coupled antennas can be designed
such that several input frequency components are simultaneously enhanced [58, 59].