28
M. I. Stockman
0
10
20
30
0
10
20
30
(a)
10
20
30
10
20
30
2000
4000
6000
20
30
|E(r)| 2
|E (0) | 2
———
(b)
ħω=1.55 eV
10
20
30
10
20
30
100
200
300
20
30
|E(r)| 2
|E (0) | 2
———
ħω=2.0 eV
(c)
x (nm)
x (n m )
x (n m )
y (n m )
y (n m )
y
(nm)
Fig. 1.9 a Geometry of nanostructured random planar composite (RPC): characteristic function
Θ(r) is displayed in the xz plane of the RPC. Axes unit is nm; thickness of the system in the y
direction (normal to its plane) is 2 nm. The fill factor is p = 0.5. Characteristic function Θ(r)
is smoothed by a Gaussian filter with a radius of 1 nm to improve numerical accuracy (shown in
the panel by the halftone density). b Local field intensity |E(r)|
2 in the plane of the nanostructure
displayed relative to the excitation field intensity |E (0) | 2 ; excitation frequency ω = 1.55 eV;
computed using Eq. (1.38). The metal is silver embedded in the dielectric with ε d = 2. c Same as
(b) but for ω = 2.0 eV. Adapted from data computed for Ref. [178]
In Fig. 1.9b, c, we display the spatial distribution of the local field intensity |E(r)|
2
in the plane of the nanostructure at the surface of the metal. These computations are
described in Ref. [178]. They are done for silver whose dielectric function is adopted
from Ref. [32]; the embedding dielectric has permittivity is set as ε d = 2.0. This
intensity is plotted relative to the excitation field intensity |E 0 | 2 ; thus the quantity
displayed is the enhancement factor of the local field intensity. Panel (b) shows the
intensity computed from Eq. (1.38). The maximum of the local intensity enhancement
of ≈6000 is in a reasonable agreement with the estimate ∼Q 2 ∼ 10 4 , where Q is
displayed in Fig. 1.2.
Dependence of the local fields on frequency is dramatic: cf. Figs. 1.9b, c. As
frequency increases from the near-IR (1.55 eV) to visible (2.0 eV), the distribution
becomes much more delocalized and its magnitude dramatically decreases, which
cannot be explained by some decrease of quality factor Q alone. Most importantly,
at all frequencies these near-field intensity distributions are dominated by the pronounced hots spots. These are manifestation of the hot spots of the SP eigenmodes—
see Fig. 1.7.
Generally, the intensity distribution of local field intensity in Fig. 1.9b, c is highly
singular: it consists of relatively narrow peaks (hot spots [158, 163]) separated by
regions of a low intensity. This is a typical distribution of intensity in plasmonic
nanosystems, which is a reflection of the inhomogeneous localization of the SP
eigenmodes.
M. I. Stockman
0
10
20
30
0
10
20
30
(a)
10
20
30
10
20
30
2000
4000
6000
20
30
|E(r)| 2
|E (0) | 2
———
(b)
ħω=1.55 eV
10
20
30
10
20
30
100
200
300
20
30
|E(r)| 2
|E (0) | 2
———
ħω=2.0 eV
(c)
x (nm)
x (n m )
x (n m )
y (n m )
y (n m )
y
(nm)
Fig. 1.9 a Geometry of nanostructured random planar composite (RPC): characteristic function
Θ(r) is displayed in the xz plane of the RPC. Axes unit is nm; thickness of the system in the y
direction (normal to its plane) is 2 nm. The fill factor is p = 0.5. Characteristic function Θ(r)
is smoothed by a Gaussian filter with a radius of 1 nm to improve numerical accuracy (shown in
the panel by the halftone density). b Local field intensity |E(r)|
2 in the plane of the nanostructure
displayed relative to the excitation field intensity |E (0) | 2 ; excitation frequency ω = 1.55 eV;
computed using Eq. (1.38). The metal is silver embedded in the dielectric with ε d = 2. c Same as
(b) but for ω = 2.0 eV. Adapted from data computed for Ref. [178]
In Fig. 1.9b, c, we display the spatial distribution of the local field intensity |E(r)|
2
in the plane of the nanostructure at the surface of the metal. These computations are
described in Ref. [178]. They are done for silver whose dielectric function is adopted
from Ref. [32]; the embedding dielectric has permittivity is set as ε d = 2.0. This
intensity is plotted relative to the excitation field intensity |E 0 | 2 ; thus the quantity
displayed is the enhancement factor of the local field intensity. Panel (b) shows the
intensity computed from Eq. (1.38). The maximum of the local intensity enhancement
of ≈6000 is in a reasonable agreement with the estimate ∼Q 2 ∼ 10 4 , where Q is
displayed in Fig. 1.2.
Dependence of the local fields on frequency is dramatic: cf. Figs. 1.9b, c. As
frequency increases from the near-IR (1.55 eV) to visible (2.0 eV), the distribution
becomes much more delocalized and its magnitude dramatically decreases, which
cannot be explained by some decrease of quality factor Q alone. Most importantly,
at all frequencies these near-field intensity distributions are dominated by the pronounced hots spots. These are manifestation of the hot spots of the SP eigenmodes—
see Fig. 1.7.
Generally, the intensity distribution of local field intensity in Fig. 1.9b, c is highly
singular: it consists of relatively narrow peaks (hot spots [158, 163]) separated by
regions of a low intensity. This is a typical distribution of intensity in plasmonic
nanosystems, which is a reflection of the inhomogeneous localization of the SP
eigenmodes.