12
A. Hu et al.
ε(ω) = 1 −
ω
2
p
ω(ω + jγ ω)
(1.2.2)
where ω p is the plasma frequency of the free electron gas, γ ~ 1/τ is the impact
frequency and τ is the characteristic impacting time.
Clearly the dielectric function of plasmonic material includes a complex form.
The real and imaginary components ε(ω) = ε r (ω) + ε i (ω) are given by
ε r (ω) = 1 −
ω
2
p τ
2
1 + ω 2 τ 2
(1.2.3)
ε i (ω) =
ω
2
p τ
2
ω
1 + ω 2 τ 2
(1.2.4)
where the imaginary components of the complex dielectric function implies the
attenuation of the lights inside the plasmon materials.
Note that this approximation is not adequate for high angle frequencies, where
interband transitions occur [67]. This phenomenon is considerable at visible optical
band for noble metals, where photons are efficient in inducing interband transitions
[24]. For some of the noble metals such as gold and silver, this effect even occurs
at an optical wavelength around 1 μm. The electrons from the filled band below the
Fermi surface are excited to higher bands, and ultimately leads to a consequence of
an increased damping.
By introducing the complex dielectric function of plasmon material, the interaction of plasmon materials with light can be generally described through classical electromagnetic field theory based on macroscopic Maxwell’s equations. This theory is
valid even when the spatial scale of the plasmon material is down to several nanometers, though quantum mechanics should be taking into account at sub-nanometer
scale reign. In this chapter we limit our description within the realms of the classical
theory. However, we have to be open mind for unexpected phenomena with the strong
dependence of the properties on frequency and material characteristics.
Surface plasmons can be divided into two categories, i.e., localized surface plasmons (LSPs) and surface plasmon polaritons (SPPs). LSPs are non-propagating excitations of the conduction electrons of plasmonic structures by the light [68]. For metal
or some certain kind of semiconductor nanoparticles with dimensions smaller than
the incident light wavelength, LSPs can be excited by direct optical excitation. On
the other hand, SPPs are electromagnetic excitations propagating at the interface and
evanescently confined in the perpendicular direction [69, 70]. With the wavevector
matching, SPPs can also be excited and propagated along a metallic nanowire that
served as a subwavelength plasmonic waveguide, which is discussed in the next
section.
Here, let us consider a small, isolated metal particle with its size comparable to
the penetration depth of the incident electromagnetic field into the metal. Therefore
the external electromagnetic field can penetrate into the particle and shift the free
A. Hu et al.
ε(ω) = 1 −
ω
2
p
ω(ω + jγ ω)
(1.2.2)
where ω p is the plasma frequency of the free electron gas, γ ~ 1/τ is the impact
frequency and τ is the characteristic impacting time.
Clearly the dielectric function of plasmonic material includes a complex form.
The real and imaginary components ε(ω) = ε r (ω) + ε i (ω) are given by
ε r (ω) = 1 −
ω
2
p τ
2
1 + ω 2 τ 2
(1.2.3)
ε i (ω) =
ω
2
p τ
2
ω
1 + ω 2 τ 2
(1.2.4)
where the imaginary components of the complex dielectric function implies the
attenuation of the lights inside the plasmon materials.
Note that this approximation is not adequate for high angle frequencies, where
interband transitions occur [67]. This phenomenon is considerable at visible optical
band for noble metals, where photons are efficient in inducing interband transitions
[24]. For some of the noble metals such as gold and silver, this effect even occurs
at an optical wavelength around 1 μm. The electrons from the filled band below the
Fermi surface are excited to higher bands, and ultimately leads to a consequence of
an increased damping.
By introducing the complex dielectric function of plasmon material, the interaction of plasmon materials with light can be generally described through classical electromagnetic field theory based on macroscopic Maxwell’s equations. This theory is
valid even when the spatial scale of the plasmon material is down to several nanometers, though quantum mechanics should be taking into account at sub-nanometer
scale reign. In this chapter we limit our description within the realms of the classical
theory. However, we have to be open mind for unexpected phenomena with the strong
dependence of the properties on frequency and material characteristics.
Surface plasmons can be divided into two categories, i.e., localized surface plasmons (LSPs) and surface plasmon polaritons (SPPs). LSPs are non-propagating excitations of the conduction electrons of plasmonic structures by the light [68]. For metal
or some certain kind of semiconductor nanoparticles with dimensions smaller than
the incident light wavelength, LSPs can be excited by direct optical excitation. On
the other hand, SPPs are electromagnetic excitations propagating at the interface and
evanescently confined in the perpendicular direction [69, 70]. With the wavevector
matching, SPPs can also be excited and propagated along a metallic nanowire that
served as a subwavelength plasmonic waveguide, which is discussed in the next
section.
Here, let us consider a small, isolated metal particle with its size comparable to
the penetration depth of the incident electromagnetic field into the metal. Therefore
the external electromagnetic field can penetrate into the particle and shift the free