Surface Plasmon Polaritons (SPPs) - Introduction and basic properties

Derivation of SPP dispersion
Derivation of SPP dispersion
E
H
t
c ∂
∂
= 1
curl ε
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
∂
=
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
×
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
∂
∂
∂
z
x
t
y
z
y
x
E
E
c
H 0
1
0
0
ε
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
−
=
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
∂
∂
−
z
x
y
x
y
z
E
E
c
H
H
0
0
ω
ε
Maxwell eq.:
z-component:
Diel.:
Metal:
zm
m
y
x
E
c
H
k
ω
ε
−
=
+
zd
d
y
x
E
c
H
k
ω
ε
−
=
+
x-component:
Diel.:
Metal: ym
zm
ym
z
H
k
H +
=
∂
−
yd
zd
yd
z
H
k
H −
=
∂
−
x
m
y
zm
E
c
H
k
ω
ε
−
=
+
x
d
y
zd
E
c
H
k
ω
ε
+
=
+
( )
t
z
k
x
k
i zd
x
e
ω
−
+
( )
t
z
k
x
k
i zm
x
e
ω
−
−
Diel.:
Metal: