Surface magneto-plasmons in magnetic multilayers - Walther ...

Section 2.3
Reflectivity of surface plasmons 13
is equated with Eq. (2.22) what yields
θSPP = arcsin
1
ε ′(0)
ε (1) ε ′(2)
ε (1) . (2.25)
+ ε ′(2)
The imaginary part of the dielectric function ε ′′(1) describes the damping of light when
travelling through the metal. It depends on the thickness of the metal layer and it
is called radiation damping [34]. The radiation damping decrease exponentially with
the film thickness and therefore when assuming a thin film ε ′′(1) can be neglected.
With this assumption for a gold layer the resonance occurs at θSPP = 43.6 ◦ .
Since at resonance, surface plasmons are excited, there must be an attenuation of the
intensity of the totally reflected light in the prism. That is why the prism coupler is
also known as Attenuated Total Reflection coupler or short ATR coupler.
2.3 Reflectivity of surface plasmons
As mentioned in Sect. 2.2.1, the excitation of surface plasmons leads to a reduction
of the intensity of the reflected light. To calculate the angle dependency of the re-
flectivity of surface plasmons excited by an ATR device only the Fresnel equations
for p-polarised light with the wave vectors kx (Eq. (2.22)) and k (i)
z (Eq. (2.14)) are
needed [35].
Here, r p
ij
r p
ij
k(i) z /ε
= (i) − k (j)
z /ε (j)
k (i)
z /ε (i) + k (j)
z /ε (j)
and t p
ij = 1 + rp ij . (2.26)
is the reflection coefficient at an interface between media i and j, tp
ij
is the
transmission coefficient through medium j. The index i in tij says that the light
comes from medium i. For the sake of completeness the reflection and transmission
coefficients for s-polarised waves are
r s ij = k(i) z − k (j)
z
k (i)
z + k (j)
z
and t s ij = 2k(i) z
k (i)
z + k (j) . (2.27)
z