12.3 Surface Plasmon Enhanced GaN-Based LED
271
properties such as high electromagnetic field strength and DOS (density of state).
Figure 12.15a shows the distribution of electromagnetic fields and charges. Considering the properties of the SPP at the metal-dielectric interface, to simplify the
problem we assume that the dielectric substrate with ideal plane shows no light
absorption, and the metal with ideal plane is thick enough that the interaction of
the plasmons at the upper and lower interfaces is negligible. Then, the electric field
intensity of the SPP propagating along the metal interface (z = 0) in x direction can
be expressed as
E S P (x, z) = E 0 exp(ik S P x − k z |z|)
(12.2)
The following expression corresponds to the surface mode with wave vector of
propagating along the surface, its field strength decays exponentially in the direction
perpendicular to the interface.
k
2
z = k
2
S P −
ω
c
2
ε i
ε m
Dielectric metal
(12.3)
Generally, metal’s dielectric constant is greater than the dielectric’s dielectric
constant. The penetration depth of SPP’s electric field in the metal is smaller than
that in the dielectric. Figure 12.15b shows the penetration depth of the SPP. The
dispersion relationship of the SPP is expressed as follow:
k
2
S P =
ω
c
2 ε i ε m
ε i + ε m
(12.4)
where E i , E m is the dielectric constant of dielectric the metal, ω / c is the light’s wave
vector. Figure 12.17c shows the dispersion curve of the SPP and photons in the
dielectric. Since the SPP’s wave vector is always larger than the photon’s wave
vector, the SPP at the ideal interface cannot radiate photons, which means SPP can’t
Fig. 12.15 The SPP at the metal-dielectric interface combine the properties of surface charge and
electromagnetic field, a the distribution of surface electromagnetic field and charge, b penetration
depth of the interface’s evanescent field in the metal and dielectric, c dispersion relationship of the
SPP
271
properties such as high electromagnetic field strength and DOS (density of state).
Figure 12.15a shows the distribution of electromagnetic fields and charges. Considering the properties of the SPP at the metal-dielectric interface, to simplify the
problem we assume that the dielectric substrate with ideal plane shows no light
absorption, and the metal with ideal plane is thick enough that the interaction of
the plasmons at the upper and lower interfaces is negligible. Then, the electric field
intensity of the SPP propagating along the metal interface (z = 0) in x direction can
be expressed as
E S P (x, z) = E 0 exp(ik S P x − k z |z|)
(12.2)
The following expression corresponds to the surface mode with wave vector of
propagating along the surface, its field strength decays exponentially in the direction
perpendicular to the interface.
k
2
z = k
2
S P −
ω
c
2
ε i
ε m
Dielectric metal
(12.3)
Generally, metal’s dielectric constant is greater than the dielectric’s dielectric
constant. The penetration depth of SPP’s electric field in the metal is smaller than
that in the dielectric. Figure 12.15b shows the penetration depth of the SPP. The
dispersion relationship of the SPP is expressed as follow:
k
2
S P =
ω
c
2 ε i ε m
ε i + ε m
(12.4)
where E i , E m is the dielectric constant of dielectric the metal, ω / c is the light’s wave
vector. Figure 12.17c shows the dispersion curve of the SPP and photons in the
dielectric. Since the SPP’s wave vector is always larger than the photon’s wave
vector, the SPP at the ideal interface cannot radiate photons, which means SPP can’t
Fig. 12.15 The SPP at the metal-dielectric interface combine the properties of surface charge and
electromagnetic field, a the distribution of surface electromagnetic field and charge, b penetration
depth of the interface’s evanescent field in the metal and dielectric, c dispersion relationship of the
SPP