1 Nanoplasmonics: From Present into Future
27
20 40
60
80
x ( n m )
20
40
60
80
y ( n m )
0
20
40
60
100
100
I/I 0
20 40
60
80
100
x (n m )
20
40
60
0
200
400
600
80
y ( n m )
I/I 0
100
Excitation:
3.13 eV
x-polarization
Excitation:
3.13 eV
y-polarization
(a)
( b )
Fig. 1.8 Spatial distributions of local field intensity I relative to the external intensity I 0 for an
individual CCA cluster of N = 1500 silver nanospheres in water (ε d = 2.0) for the frequency
ω = 3.13 eV. The polarizations of the excitation radiation is x (a) and y (b), as indicated in the
panels. The projection of the cluster nanospheres to the xy plane is also shown. Adapted from
Ref. [157]
the surface of the silver nanospheres at a relatively high frequency ω = 3.13 eV
corresponding to vacuum wavelength λ = 390 nm in the far blue end of the visible
spectrum. We can clearly see that the local intensity is highly non-uniform, exhibiting
pronounced singular hot spots. These hot spots are localized at the minimum scale
of the system (on the order of the radius of the nanospheres). The local intensity in
the hot spots is greatly enhanced (by a factor of up to ∼600) as one would expect
from an estimate I /I 0 ∼ Q 2 —cf. Fig. 1.2.
This hot spotting is nothing else as random nanofocusing. It is similar in this
respect to the formation of speckles in the wave optics, as we have discussed above in
conjunction with Fig. 1.5. However, reflecting the properties of the corresponding SP
eigenmodes, there is no characteristic wavelength that limits this hot spot singularity
by defining the characteristic size L s of the speckles, which is also a characteristic
separation between them—see Eq. (1.31).
Another property of the local fields of a great significance is the dramatic dependence of the intensity distribution on the polarization: the local distributions or the
x-polarization (Fig. 1.8a) and y-polarization (panel b) are completely different. An
experimental observation of this effect has been obtained in Ref. [118] already at a
very early stage of the development of nanoplasmonics.
Note that the SP eigenmode geometry is also strongly dependent on its frequency—
see Fig. 1.5. However, in externally-excited local fields, this frequency dependence
is obscured by the resonance broadening due to the losses, as is evident from the
expression for the resonant part of the Green’s function
We will present below spectral and statistical properties of the local fields using
a model of random planar composite (RPC). A specific RPC system used in the
computation is shown in Fig. 1.9a. To improve numerical accuracy, we smooth the
unit-step characteristic function Θ(r) with a Gaussian filter with a radius of 1 grid
step: this dramatically improves numerical accuracy of a grid method that we use to
solve the eigenproblem. Such a smoothing is clearly seen in Fig. 1.9a.
27
20 40
60
80
x ( n m )
20
40
60
80
y ( n m )
0
20
40
60
100
100
I/I 0
20 40
60
80
100
x (n m )
20
40
60
0
200
400
600
80
y ( n m )
I/I 0
100
Excitation:
3.13 eV
x-polarization
Excitation:
3.13 eV
y-polarization
(a)
( b )
Fig. 1.8 Spatial distributions of local field intensity I relative to the external intensity I 0 for an
individual CCA cluster of N = 1500 silver nanospheres in water (ε d = 2.0) for the frequency
ω = 3.13 eV. The polarizations of the excitation radiation is x (a) and y (b), as indicated in the
panels. The projection of the cluster nanospheres to the xy plane is also shown. Adapted from
Ref. [157]
the surface of the silver nanospheres at a relatively high frequency ω = 3.13 eV
corresponding to vacuum wavelength λ = 390 nm in the far blue end of the visible
spectrum. We can clearly see that the local intensity is highly non-uniform, exhibiting
pronounced singular hot spots. These hot spots are localized at the minimum scale
of the system (on the order of the radius of the nanospheres). The local intensity in
the hot spots is greatly enhanced (by a factor of up to ∼600) as one would expect
from an estimate I /I 0 ∼ Q 2 —cf. Fig. 1.2.
This hot spotting is nothing else as random nanofocusing. It is similar in this
respect to the formation of speckles in the wave optics, as we have discussed above in
conjunction with Fig. 1.5. However, reflecting the properties of the corresponding SP
eigenmodes, there is no characteristic wavelength that limits this hot spot singularity
by defining the characteristic size L s of the speckles, which is also a characteristic
separation between them—see Eq. (1.31).
Another property of the local fields of a great significance is the dramatic dependence of the intensity distribution on the polarization: the local distributions or the
x-polarization (Fig. 1.8a) and y-polarization (panel b) are completely different. An
experimental observation of this effect has been obtained in Ref. [118] already at a
very early stage of the development of nanoplasmonics.
Note that the SP eigenmode geometry is also strongly dependent on its frequency—
see Fig. 1.5. However, in externally-excited local fields, this frequency dependence
is obscured by the resonance broadening due to the losses, as is evident from the
expression for the resonant part of the Green’s function
We will present below spectral and statistical properties of the local fields using
a model of random planar composite (RPC). A specific RPC system used in the
computation is shown in Fig. 1.9a. To improve numerical accuracy, we smooth the
unit-step characteristic function Θ(r) with a Gaussian filter with a radius of 1 grid
step: this dramatically improves numerical accuracy of a grid method that we use to
solve the eigenproblem. Such a smoothing is clearly seen in Fig. 1.9a.