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
e2=-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
0.8
[ Z 3 cos( kd )  jZ 2 sin( kd )]
Z3  Z2
Z 2 cos( kd )  jZ 3 sin( kd )
"
REFLECTANCE
SURFACE PLASMONS
This approach can be applied in slab
structures to analyze electromagnetic wave
reflection and transmission
Gold layer
0.6
Surface layer n=2.25
0.4
30
10
50
ANGLE (degrees)
90
70
The resonance angle is very sensitive
to a surface layer on the gold
semi-infinite medium
Z2
Z1
Z3"
d=0
d=5nm
d=10nm
0.0
slab
semi-infinite medium
Surface layer thickness
0.2
Impedance transformation reduces
the number of interfaces by one
Substrate
The Maryland Optics Group
Z3
PLASMON RESONANCE WITH GOLD
n=1.5
1.0
n2 - air or dielectric surface wave (plasmon)
semi-infinite medium
ngold

Z1
semi-infinite medium
Z3"
Z Z

Z Z
"
3
"
3
'
1
'
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( )
'
0.0
35
39
43
ANGLE (degrees)
47
SURFACE PLASMONS
The Maryland Optics Group
• 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
e2=-15.73-j0.968
The Maryland Optics Group
PLASMON EXCITED IN TIR GEOMETRY
surface wave (plasmon)
n2 - air or dielectric
ngold

E
n1 - substrate
The Maryland Optics Group
PLASMON RESONANCE WITH GOLD
n=1.5
1.0
REFLECTANCE
0.8
Surface layer thickness
d=0
d=5nm
d=10nm
0.6
Surface layer n=2.25
0.4
0.2
0.0
10
30
50
ANGLE (degrees)
70
90
The Maryland Optics Group
PLASMON RESONANCE WITH GOLD
n=1.5
1.0
REFLECTANCE
0.8
0.6
Surface layer thickness
d=0
d=5nm
d=10nm
Surface layer n=2.25
0.4
0.2
0.0
35
39
43
ANGLE (degrees)
47
The Maryland Optics Group
IMPEDANCE TRANSFORMATION
If a transmission line of characteristic impedance Z0
and of length d is terminated in a load impedance ZL,
then the impedance observed at the beginning of the line,
at location z= -d relative to a load at z=0 is
[Z L cos(kd)  jZ 0 sin( kd)]
Z in  Z 0
Z 0 cos(kd)  jZ L sin( kd)
This approach can be applied in slab structures to analyze
electromagnetic wave reflection and transmission
The Maryland Optics Group
Kretschman total internal reflection geometry for plasmon excitation
Dielectric (absorber) layer
Gold layer
Substrate
The Maryland Optics Group
surface wave (plasmon)
n2 - air or dielectric
ngold

n1 - substrate