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

Section 2.3
Reflectivity of surface plasmons 15
of all reflected and transmitted light paths.
When E is the electric field of the incident wave, one part of it is reflected at the
interface 01 which yields a term (Er01) and the other part is transmitted giving a
term (Et01e iα ). With
e ik′
k = k ′ + ik ′′
describes a phase shift and e ik′′
⇒ e iα ≡ e ikd = e ik′ d + e ik ′′ d
(2.30)
a damping of the light when propagating through
medium 1. The transmitted part is now reflected at the interface 12 (Et01e iα r12e iα ). As
only the reflected part is of interest, the transmitted part through 12 is omitted. Now,
repeating the above procedure shows that the nth transmitted light wave through 10
is E0t01e iα (r12e iα r10e iα ) n t10. Using
E p′ can be calculated, to
r p
ij = −rp ji and t p
ij = 1 + rp ij , (2.31)
E p′ = E p r p
01 + E p t p
01e iα r p
12e iα t p
10
∞
n=0
r p
12e iα r p
10e iα
= E p r p
01 + E p (1 + r p
01)e iα r p
12e iα (1 − r p
01)
=
Ep (r p
01 + r p
12e2iα )
1 + r p
01r p
12e2iα Substituting Eq. (2.32) into Eq. (2.29) gives
R p
=
2
r p
01 + r p
12e2ikz1d 1 + r p
01r p
12e2ikz1d ∞
n=0
r p
12e iα r10e iα
(2.32)
(2.33)
(2.34)
2
. (2.35)
Equation (2.35) is the reflectivity of an ATR coupler consisting of a single metal layer
in contact with the prism on one side and air on the other. Note that for Eq. (2.35)
the prism is assumed to be semi-infinite.
Since kx is continuous throughout all the interfaces (see Eq. (2.12)) only the evanescent
part k (i)
z is damped phase shifted when propagating through the metal film.
For light with λ = 650 nm and a silver layer with thickness dAg = 50 nm the reflectivity