16
M. I. Stockman
nonperturbative nonlinear process is the predicted plasmon soliton [143] where
strong local optical fields in a plasmonic waveguide cause a significant redistribution of the conduction-electron density.
• There are also relevant strongly-nonlinear processes in non-plasmonic materials
that are based on nanolocalized fields and are very similar to those in plasmonics. Among them are near-field enhanced electron acceleration from dielectric
nanospheres with intense few-cycle laser fields [144]. Another such a process is
a strong optical-field electron emission from tungsten nanotips controlled with an
attosecond precision [145].
• Finally, a recently predicted phenomenon of metallization of dielectrics by strong
optical fields [146, 147] belongs to a new class of highly-nonlinear phenomena
where strong optical fields bring a dielectric nanofilm into a plasmonic metal-like
state.
1.3 Nanolocalized Surface Plasmons (SPs) and Their Hot Spots
1.3.1 SPs as Eigenmodes
Assuming that a nanoplasmonic system is small enough, R ∪ λ, R l s , we employ
the so-called quasistatic approximation where the Maxwell equations reduce to the
continuity equation for electrostatic potential ϕ(r),
∂
∂r
ε(r)
∂
∂r
ϕ(r) = 0.
(1.20)
The systems permittivity (dielectric function) varying in space is expressed as
ε(r) = ε m (ω)Θ(r) + ε d [1 − Θ(r)].
(1.21)
Here Θ(r) is the so-called characteristic function of the nanosystem, which is equal
to 1 when r belongs to the metal and 0 otherwise. We solve this equation following
the spectral theory developed in Refs. [29, 78, 148].
Consider a nanosystem excited by an external field with potential ϕ 0 (r) at an
optical frequency ω. This potential is created by external charges and, therefore,
satisfies the Laplace equation within the system,
∂ 2
∂r 2 ϕ 0 (r) = 0.
(1.22)
We present the field potential as
ϕ(r) = ϕ 0 (r) + ϕ 1 (r),
(1.23)
M. I. Stockman
nonperturbative nonlinear process is the predicted plasmon soliton [143] where
strong local optical fields in a plasmonic waveguide cause a significant redistribution of the conduction-electron density.
• There are also relevant strongly-nonlinear processes in non-plasmonic materials
that are based on nanolocalized fields and are very similar to those in plasmonics. Among them are near-field enhanced electron acceleration from dielectric
nanospheres with intense few-cycle laser fields [144]. Another such a process is
a strong optical-field electron emission from tungsten nanotips controlled with an
attosecond precision [145].
• Finally, a recently predicted phenomenon of metallization of dielectrics by strong
optical fields [146, 147] belongs to a new class of highly-nonlinear phenomena
where strong optical fields bring a dielectric nanofilm into a plasmonic metal-like
state.
1.3 Nanolocalized Surface Plasmons (SPs) and Their Hot Spots
1.3.1 SPs as Eigenmodes
Assuming that a nanoplasmonic system is small enough, R ∪ λ, R l s , we employ
the so-called quasistatic approximation where the Maxwell equations reduce to the
continuity equation for electrostatic potential ϕ(r),
∂
∂r
ε(r)
∂
∂r
ϕ(r) = 0.
(1.20)
The systems permittivity (dielectric function) varying in space is expressed as
ε(r) = ε m (ω)Θ(r) + ε d [1 − Θ(r)].
(1.21)
Here Θ(r) is the so-called characteristic function of the nanosystem, which is equal
to 1 when r belongs to the metal and 0 otherwise. We solve this equation following
the spectral theory developed in Refs. [29, 78, 148].
Consider a nanosystem excited by an external field with potential ϕ 0 (r) at an
optical frequency ω. This potential is created by external charges and, therefore,
satisfies the Laplace equation within the system,
∂ 2
∂r 2 ϕ 0 (r) = 0.
(1.22)
We present the field potential as
ϕ(r) = ϕ 0 (r) + ϕ 1 (r),
(1.23)