IMPEDANCE METHODS FOR ANALYZING SURFACE PLASMONS
Quirino Balzano, Igor Smolyaninov, and Christopher C. Davis
Department of Electrical and Computer Engineering
●Classical solutions to Maxwell’s
equations at the interface between a
dielectric and a metal
●A metal is a dense electron-hole plasma
●A metal has a complex dielectric
constant with a large negative part.
●For example, for gold at 632.8nm
ε 2=-15.73-j0.968
Kretschman total internal reflection
geometry for plasmon excitation
Dielectric (absorber) layer
IMPEDANCE TRANSFORMATION
Plasmon resonances in gold
revealed by an impedance
analysis
If a slab structure is modeled as a series of
transmission lines then the impedance
observed at the first interface, at location z= d relative to a final interface at z=0 is
PLASMON RESONANCE WITH GOLD
n=1.5
1.0
Z3 = Z2
"
[ Z 3 cos(kd ) + jZ 2 sin(kd )]
Z 2 cos(kd ) + jZ 3 sin(kd )
This approach can be applied in slab
structures to analyze electromagnetic wave
reflection and transmission
0.8
REFLECTANCE
SURFACE PLASMONS
Gold layer
slab
semi-infinite medium
semi-infinite medium
Z2
Z1
Z3"
Surface layer thickness
d=0
d=5nm
d=10nm
0.6
Surface layer n=2.25
0.4
0.2
Impedance transformation reduces
the number of interfaces by one
Substrate
The Maryland Optics Group
0.0
10
30
50
ANGLE (degrees)
70
90
The resonance angle is very sensitive
to a surface layer on the gold
Z3
PLASMON RESONANCE WITH GOLD
n=1.5
1.0
n2 - air or dielectric surface wave (plasmon)
semi-infinite medium
ngold
θ
Z1
semi-infinite medium
Z3"
Z 3" − Z 1'
ρ= "
Z 3 + Z 1'
E
REFLECTANCE
0.8
0.6
Surface layer thickness
d=0
d=5nm
d=10nm
Surface layer n=2.25
0.4
0.2
n1 - substrate
For P(TM) waves
Z ' = Z cos(θ )
0.0
35
39
43
ANGLE (degrees)
47