1 Introduction to Laser Micro-to-Nano Manufacturing
13
Fig. 1.6 Diagram of localized surface plasmon resonances (LSPRs) (Reprinted with permission
from [71]. Copyright 2019. Hindawi Publishing Corporation)
conduction electron cloud with respect to the metal lattice and leads to a localized
restoring field within the particle. The periodical shift of the electrons and change
of the restoring field create coherent, resonant oscillations of the electron gas related
to the exciting electromagnetic field. This phenomenon is called localized surface
plasmon resonances (LSPRs) (Fig. 1.6).
Quasistatic Approximation can be used to describe LSPs in nanoparticles whose
sizes are significant small compare with the wavelength of the exciting light [24].
Therefore exciting light can be regarded as a homogeneous field and the retardation
over the particle volume can be neglected. Consider a homogeneous, isotropic sphere
located at the origin in a uniform, static, homogeneous electric field E 0 , surrounding
by an idea non-absorbing, isotropic medium with dielectric constant ε m . Here we
define the polarizability α via p = ε 0 ε m aE 0 , where p is the dipole moment at the
particle. By casting the Laplace equation, the complex polarizability is given by
α= 4πa
3 ε(ω) − ε m
ε(ω) + 2ε m
(1.2.5)
where a and ε(ω) are the diameter and the dielectric function of the sphere of the
sphere, respectively. The distribution of the electric field can be expressed as
E in =
3ε m
ε(ω) + 2ε m
E 0
(1.2.6)
E out = E 0 +
3n(n · p) − p
4πε 0 ε m
1
r 3
(1.2.7)
where r is the position vector point from the center of the sphere to the outside, n is
the unit vector. The corresponding cross sections for scattering and absorption C sca
and C abs are given by
13
Fig. 1.6 Diagram of localized surface plasmon resonances (LSPRs) (Reprinted with permission
from [71]. Copyright 2019. Hindawi Publishing Corporation)
conduction electron cloud with respect to the metal lattice and leads to a localized
restoring field within the particle. The periodical shift of the electrons and change
of the restoring field create coherent, resonant oscillations of the electron gas related
to the exciting electromagnetic field. This phenomenon is called localized surface
plasmon resonances (LSPRs) (Fig. 1.6).
Quasistatic Approximation can be used to describe LSPs in nanoparticles whose
sizes are significant small compare with the wavelength of the exciting light [24].
Therefore exciting light can be regarded as a homogeneous field and the retardation
over the particle volume can be neglected. Consider a homogeneous, isotropic sphere
located at the origin in a uniform, static, homogeneous electric field E 0 , surrounding
by an idea non-absorbing, isotropic medium with dielectric constant ε m . Here we
define the polarizability α via p = ε 0 ε m aE 0 , where p is the dipole moment at the
particle. By casting the Laplace equation, the complex polarizability is given by
α= 4πa
3 ε(ω) − ε m
ε(ω) + 2ε m
(1.2.5)
where a and ε(ω) are the diameter and the dielectric function of the sphere of the
sphere, respectively. The distribution of the electric field can be expressed as
E in =
3ε m
ε(ω) + 2ε m
E 0
(1.2.6)
E out = E 0 +
3n(n · p) − p
4πε 0 ε m
1
r 3
(1.2.7)
where r is the position vector point from the center of the sphere to the outside, n is
the unit vector. The corresponding cross sections for scattering and absorption C sca
and C abs are given by