246
M. B. Raschke et al.
5
0
1 0
1 5
2 0
2 5
3 0
Wavevector (m
-1 x 10
6 )
ω sp =
ω p
1+ε
ω =
ω p
ε ∞
∞
0.1
0.2
0.3
0.4
ω / ω
p
Experimental
Drude
Drude (no damping)
Light
Fig. 7.4 Dispersion relation of surface plasmon polariton for the case of an ideal (undamped) Drude
metal (red), and Au as an example of a real metal assuming both pure free electron Drude damping
(green), and additional interband damping from experimental values (blue) [9, 10]. The frequency
is normalized with respect to the plasma frequency ω p
direction. The characteristic length l ∞,i is defined as the distance from the surface
where |E(z)/E(z = 0)| = 1/e. For medium i with complex dielectric function
ε i = ε ∼
i + iε ∼∼
i , l ∞,i is given by
l ∞,i =
1
k ∞,i
=
λ 0
2π
ε ∼
1 + ε 2
ε 2
i
1/2
.
(7.11)
The penetration depth into the metal is related to the skin depth (the 1/e penetration
depth of the optical field into the metal) δ = c/κω, with κ the imaginary part of
refractive index N = n + iκ. For gold, δ ∝ 22 − 25 nm throughout the mid IR
to visible spectral range (0.1–2 eV) [10]. The weak frequency dependence in that
regime is due to the near linear dependence of 1/κ with ω.
The SPP is sensitive to a wide range of which affect surface modifications, including charge, contact to dielectrics, adsorbates, etc. which affect the surface dispersion
relation through the modification of the dielectric function. This is closely related
to the size and shape dependence of local SPPs in confined geometries (Mie and
Rayleigh resonances) as discussed in the following section.
7.1.9 Localized SPP in Small Metal Particles
Localized SPPs are non-propagating modes that can be excited in structurally inhomogeneous environments of dimensions comparable to or smaller than the optical
wavelength, i.e. where the translational invariance of the medium is lost on the length
scale of the SPP wavelength. With R defining a characteristic structural dimension
the parameter 1/R plays a role analogous to the parallel SPP wavevector for the case
M. B. Raschke et al.
5
0
1 0
1 5
2 0
2 5
3 0
Wavevector (m
-1 x 10
6 )
ω sp =
ω p
1+ε
ω =
ω p
ε ∞
∞
0.1
0.2
0.3
0.4
ω / ω
p
Experimental
Drude
Drude (no damping)
Light
Fig. 7.4 Dispersion relation of surface plasmon polariton for the case of an ideal (undamped) Drude
metal (red), and Au as an example of a real metal assuming both pure free electron Drude damping
(green), and additional interband damping from experimental values (blue) [9, 10]. The frequency
is normalized with respect to the plasma frequency ω p
direction. The characteristic length l ∞,i is defined as the distance from the surface
where |E(z)/E(z = 0)| = 1/e. For medium i with complex dielectric function
ε i = ε ∼
i + iε ∼∼
i , l ∞,i is given by
l ∞,i =
1
k ∞,i
=
λ 0
2π
ε ∼
1 + ε 2
ε 2
i
1/2
.
(7.11)
The penetration depth into the metal is related to the skin depth (the 1/e penetration
depth of the optical field into the metal) δ = c/κω, with κ the imaginary part of
refractive index N = n + iκ. For gold, δ ∝ 22 − 25 nm throughout the mid IR
to visible spectral range (0.1–2 eV) [10]. The weak frequency dependence in that
regime is due to the near linear dependence of 1/κ with ω.
The SPP is sensitive to a wide range of which affect surface modifications, including charge, contact to dielectrics, adsorbates, etc. which affect the surface dispersion
relation through the modification of the dielectric function. This is closely related
to the size and shape dependence of local SPPs in confined geometries (Mie and
Rayleigh resonances) as discussed in the following section.
7.1.9 Localized SPP in Small Metal Particles
Localized SPPs are non-propagating modes that can be excited in structurally inhomogeneous environments of dimensions comparable to or smaller than the optical
wavelength, i.e. where the translational invariance of the medium is lost on the length
scale of the SPP wavelength. With R defining a characteristic structural dimension
the parameter 1/R plays a role analogous to the parallel SPP wavevector for the case