of 5
Supporting information: Functional plasmonic
nano-circuits with low insertion and propagation
losses
Arian Kriesch,
,
,
Stanley P. Burgos,
Daniel Ploss,
Hannes Pfeifer,
Harry A.
Atwater,
and Ulf Peschel
Institute of Optics, Information and Photonics, Erlangen Graduate School in Advanced Optical
Technologies, Friedrich-Alexander-University Erlangen-Nuremberg (FAU) and Max Planck
Institute for the Science of Light, 91058 Erlangen, Germany, and Kavli Nanoscience Institute,
California Institute of Technology, Pasadena, California 91125, USA
E-mail: arian.kriesch@mpl.mpg.de
Optical setup for far-field char-
acterization
The nano-circuits were positioned with 5 nm xyz
precision with a piezo scanning system (Physik In-
strumente, PI) and optically characterized with a
custom-made optical setup (1) that follows the de-
sign published by Banzer et al.
1
3D-piezo stage
Nano antenna
NPBS
Objective NA=1.3
Ref. diode
Super Continuum
Light Source
IR cam
Polarizer
1
Polarizer
2
Lens (total mag. = 150x)
Spectral Filter
Fourier optics
5 μm
Figure 1: The experimental setup to probe the po-
larization dependent spectral emission of a nano-
plasmonic circuit in real and Fourier space for
a broad spectral range
λ
=
1200 nm to 1850 nm.
Inset: The emission from the antenna through
crossed polarizers.
The collimated beam from a supercontin-
To whom correspondence should be addressed
University of Erlangen
Caltech
uum light source is spectrally filtered by a pro-
grammed acousto-optic tunable filter (operated
at
λ
=
1200
1850 nm) (NKT Koheras, SuperK
Extreme) and is subsequently directed through a
polarization filter (1) and a non-polarizing beam
splitter (NPBS), that directs 50 % of the power to
a reference diode (InGaAs). The main beam is
focused with a high NA objective (NA
=
0
.
9 from
air and NA
=
1
.
3 immersion, from substrate) that
was carefully characterized to preserve the polar-
ization properties of the laser beam. The diameter
of the collimated beam was carefully measured
(
FWHM
=
1
.
6 mm) with an InGaAs camera and
the effective numeric aperture of the experimental
focal spot was determined for all subsequent eval-
uation steps. The focus of the objective is adjusted
on the investigated excitation nano-antenna.
At the same time, the objective images the com-
plete nano-circuit, including the emission from the
other antennas. The collimated beam, carrying
the image, is polarization filtered (polarizer 2) and
passes imaging optics to form a real image on an
InGaAs NIR CCD camera (Xenics XS, 320 x 256
pixels). The setup features a variable magnifica-
tion factor (150x, 300x) and an additional, switch-
able focusing unit to allow for Fourier plane imag-
ing.
By adjusting the polarization filter (2) perpen-
dicular to polarization filter (1), the reflection of
1
the incident beam is mostly cancelled in the im-
age (1 : 5000
1 : 10000 extinction ratio) and the
emission from the monitor antennas of the circuit,
which are 90
turned with respect to the excitation
antenna, can be measured with exceptionally high
aspect ratio and dynamic range. However, con-
version of field components in the highly focused
beam into the perpendicular polarization causes a
characteristic four-lobe-pattern that remains intact
even when the incident beam is focused on an an-
tenna with no fabrication errors (1 inset). This
four-lobe pattern is visible in all measurements at
the position of the incoupling antenna (Fig. 7d,e,f
of the letter).
The absolute transmission of the nano-circuits
was determined by normalization with the known
reflectivity of the sample substrate. The spot inten-
sity of the monitor antennas (Fig. 7b of the letter,
green circles) was integrated. For each measure-
ment picture for a certain wavelength and circuit,
a reference image was taken, featuring the pure re-
flection of the four-lobe pattern on the substrate.
Quasi-analytically, the reflectivity of a silica-to-air
interface was calculated by developing a focused
Gaussian beam with the correct NA into plane
waves, taking into account the crossed second po-
larization filter.
Possible fluctuations of the probe laser between
the main and the reference measurement are elim-
inated with the reference diode (1). This method
of absolute normalization eliminates sources for
additional measurement errors and cancels disper-
sion and loss of the optical setup.
Leakage microscopy
The guided mode of the waveguides does intrin-
sically not emit into the far-field. However, ev-
ery waveguide has slight imperfections. Utiliz-
ing the high dynamic range of the optial far-field
setup, it is possible to image the plasmonic nano-
circuit with leakage-microscopy. Highly overex-
posed (
>
300
×
saturation intensity) images of a
circuit, featuring a directional coupler (ODC) in
a direct overlay with an SEM of the same structure
show beating patterns inside the waveguides and
the coupler.
However, for this high exposure, even the ref-
x in μ
m
z in μ
m
0
10
20
30
40
0
10
20
30
40
0
0.5
1
Emitted intensity in vert. pol.
SEM
a
b
leakage emission
Figure 2: Leakage microscopy of the emission
from a nanocircuit with a directional coupler in
the configuration with crossed polarizers (5000
suppression
10000). Highly (
>
300
×
satura-
tion intensity) overexposed, this real-plane image
shows strongly saturated emission from the inci-
dent (top) and monitor (left, right) antennas.
2
erence antenna (compare to Fig. 7b, blue) shows
some emission. The slight scattering at the lower
edge of the circuit metal pad indicates that slight
residual bend loss is due to the conversion into pla-
nar SPPs. These subsequently propagate along the
metal surface, are scattered out at the lower edge
and detected with very high efficiency due to their
polarization being parallel to the emission polar-
ization of the monitor antennas.
Near Field Optical Scanning Mi-
croscope
The near field scanning optical microscopy
(NSOM) measurements (Fig. 4b) were taken with
a custom made setup for polarization-adjusted
coupling into the optical antennas, based on a
modified commercial fiber aperture NSOM sys-
tem (Nanonics MV 4000).
With tapping, phase-controlled AFM feedback,
a Ø
270 nm Au/Cr coated, FIB processed fiber
aperture tip was raster-scanned across the area
around the antenna (10
×
10 μm) with 40 nm lateral
scan resolution. The near-field, collected from the
structure and converted into a propagating mode
of an optical fiber, was detected with a high sensi-
tivity, highly amplified InGaAs diode detector.
To reveal the guided mode inside the connected
waveguide the scanned intensity is displayed with
log-scale and saturation at the beam position was
accepted. The plane of scanning is leveled 320
nm above the upper metal boundary due to the
cladding spin-on glass (SOG) layer, which in the
topography channel of the NSOM still showed
smoothed variations of height within
z
20 nm
that are caused by the underlying
z
220 nm to-
pography of the metal structures. In this measure-
ment already little maladjustment of the laser fo-
cus leads to slight diffraction artifacts towards the
metal surface. To ensure precise adjustment, dur-
ing the scan also the reflected light from the an-
tenna was collected through the excitation optical
pathway and monitored to quantify the distortion
of the reflected signal by the scanning NSOM tip.
Additional measurements showed low additional
loss from waveguide bends with at least
R
=
3 μm
bend radius (Fig. S2b), which coincides well with
the far-field circuit characterization that indicated
these bends to be applicable with negligible ad-
ditional loss compared to the straight waveguide
propagation loss.
Fitting the circuit transmission
with a lossy Fabry-Pérot model
Based on the lumped network circuit model
2
(Fig.
7a) the nano-circuit was treated as a Fabry-Pérot
resonator to determine waveguide and antenna
properties in one iterative least-square fit over the
independent variables wavelength and waveguide
length. The fitted model is based on the transmis-
sion of a Fabry-Pérot resonator with loss in the res-
onator and at the mirrors, which has length
L
and
a characteristic wave number
k
T
FPR
=
T
ant
1
+
Γ
sin
2
(
kL
)
,
where
T
ant
represents the efficiency of the anten-
nas to couple the focused laser beam into the FPR
cavity, respectively out of it. The antennas are as-
sumed to experience Lorentzian broadening due to
plasmonic loss:
T
ant
=
T
max
ant
1
+
(
λ
λ
0
γ
)
2
.
Γ
determines the inverse line width that can be
expressed in terms of the reflectivity
R
=
R
in
=
R
out
of the resonator mirrors, which is caused by
imperfect impedance matching between the opti-
cal antennas and the waveguides
Γ
=
4
Re
α
L
(
1
Re
α
L
)
2
.
The antenna efficiency curve and the antenna
loss curve are caused by the same loss mecha-
nism. Hence, the reflectivity of the antenna res-
onator mirrors can be described as
R
=
1
T
ant
A
ant
=
1
T
max
ant
+
A
max
ant
1
+
(
λ
λ
0
γ
)
2
where, according to the applied model,
A
ant
rep-
resents the absorption inside the antenna with
A
=
3
1
T
R
. With an iterative fit of this model to the
experimental circuit transmission values, the spec-
tral propagation length
L
0
, the effective index of
the guided mode (
n
eff
=
k
λ
0
/
(
2
π
)
), the antenna
efficiency
T
max
ant
, the central wavelength
λ
0
and an-
tenna linewidth FWHM
=
2
γ
are determined as
free parameters. There may be additional sources
for loss, which we are not able to systematically
determine.
We can however determine an upper bound for
the loss
A
1
T
min
R
, which effectively makes
T
ant
(
λ
)
a lower bound for the spectral transmission
efficiency of the antennas to convert light from
the far field into the waveguide and vice versa.
Error propagation was applied to all determined
free variables
T
max
ant
,
γ
,
λ
0
,
L
0
,
n
eff
, based on the er-
ror bounds from the iterative fit over several mea-
surements and different fabricated structures. The
determined values for the standard deviation
σ
, as
indicated in Fig. 2b, 5a and 5b therefore include
statistical errors of fabrication and measurement.
Fitting the optical directional
coupler transmission model
The directional couplers are well described with
coupled mode theory. The coupling length
L
c
for
periodic full transfer of the power from one waveg-
uide to the other was determined by fitting this
model to experimental data over a variation of the
parallel length of the couplers
L
=
0
,
3
,
6
,
9
,
12 μm.
The system is well described as a weakly cou-
pled system of two harmonic oscillators, exchang-
ing energy proportional to the coupling constant
κ
.
The intensity out of the waveguides bar and cross
after an ODC of length
L
is given by
I
bar
=
cos
2
(
κ
L
)
and
I
cross
=
sin
2
(
κ
L
)
and the coupling length can be expressed as
L
c
=
π
/
2
κ
. We used the ratio of the integrated
emission from both spots of the monitor antennas
(Fig. 7b green, compare Fig. 7 d,e,f))
I
cross
/
I
bar
as it is intrinsically more robust to measurement
error and even slight maladjustments of the excit-
ing laser beam. However,
I
cross
/
I
bar
=
tan
2
(
κ
L
)
diverges and is unsuitable for iterative least-square
fitting. A more suitable approach was chosen by
0
2
4
6
8
10
12
−0.5
0
0.5
1
1.5
2
Length of the coupler
L
Coupling phase
φ
Figure 3: The experimental coupling ratio of 8
nano-circuits with directional couplers of varied
straight length
L
(all
w
=
50 nm) is converted to
the periodic coupling phase (red dots) and is iter-
atively fitted with coupled mode theory. Fit result
(blue curve) and 90% confidence intervals (blue
shaded).
fitting the non-diverging coupling phase, which is
as well periodic with full coupling lengths:
φ
(
L
) =
arctan
(
I
cross
I
bar
)
=
[
π
L
L
bend
2
L
c
]
π
mod
π
2
This expression allows for a fit over a variation
of the length of the coupler
L
.
L
bend
represents an
additional offset, which is caused by coupling that
already occurs in the bends where cross and bar
waveguides approach with a radius of
R
=
3 μm.
This bend-coupling is expressed in terms of an ex-
tra virtual length of the coupler and leads to sig-
nificant transfer of energy even in the case of zero
straight parallel length of the ODC (
L
=
0).
The investigated circuits with the lengths avail-
able already cycle through several full coupling
lengths. The ODCs with the most narrow fila-
ment (
w
=
50 nm) resulted in the best fits with least
statistical fabrication and measurement deviations
and the shortest coupling length, as displayed in
Fig. S3. In this case eight measurements on dif-
ferent fabricated circuits were combined. The re-
sulting fit is displayed with 90% prediction bands
and gave
L
c
=
2
.
46
±
0
.
04 μm coupling length and
4
L
bend
=
1
.
7
±
0
.
07 μm equivalent coupler length
of the bend. The indicated error margins take ac-
count for statistical errors, not potential systematic
errors that might not have been possible to deter-
mine with the applied methods.
Simulation with FDTD and par-
ticle swarm optimization (PSO)
The antennas, waveguides and couplers were sim-
ulated with a 2D and full 3D Finite Difference
Time Domain solver (Lumerical FDTD Solu-
tions). For design purposes, literature values from
Johnson and Christy
3
were used as material pa-
rameters. After first fabricated structures were ex-
perimentally characterized, the simulations were
repeated with the ellipsometrically determined di-
electric susceptibility of Au, which turned out to
be close to the initially used literature values in
the real part of the dielectric susceptibility, but de-
viated up to a factor of 1
.
5 in the imaginary part.
In the simulations, the antenna was excited with
a highly focused Gaussian beam with the same
beam properties as determined for the experiment
with the objectives in use (NA = 0.9 from air and
NA
=
1
.
3 from silica). Its emission directionality
and efficiency were analyzed in reverse configu-
ration, exciting the guided mode inside the SPP
gap waveguide with a mode solver and observing
the emission with appropriate frequency domain
ports. The more narrow resulting angular direc-
tivity of the such optimized antennas was experi-
mentally taken into account by adjusting the col-
limated beam diameter to slightly reduce the nu-
meric aperture and was characterized as described
in section 1.
The supplementary video shows the electric field
|
E
|
2
in time domain, as a focused beam (NA
=
0
.
9)
impinges the optimized geometry of a Yagi-Uda
nano-antenna and is converted into a guided mode,
propagating along the waveguide.
Instrumentation
All investigated nano-circuits were fabricated
with a lift-off patterning process as described
in the main article.
A 100 kV Leica EBPG-
5000+ system with pattern generator transferred
the nano-circuit designs to the resist. Standard
procedures for development, lift-off and standard
manufacturer-recipes were used for the applica-
tion, baking and curing under N
2
atmosphere of
the commercially available silsesquioxane spin-
on-glass (SOG) Filmtronics 400F. For cross-
sections, geometric characterization and fabrica-
tion optimization a Zeiss Dual Beam FIB sys-
tem and a FEI Nova-200 FIB system were used.
The laser for far-field and near-field measure-
ments was a NKT Photonics / Koheras SuperK
Extreme supercontinuum source with nominal
6 W output power and subsequent NKT Koheras
acousto-optical tunable filters (AOTFs) for tun-
able wavelength-selection. A sensitive InGaAs
NIR camera (Xenics CS, 320
×
256) pixels was
used for image acquisition of the light emitted
from the circuits.
References
(1) Banzer, P.; Peschel, U.; Quabis, S.; Leuchs, G.
Opt. Express
2010
,
18
, 10905–10923.
(2) Engheta, N.
Science
2007
,
317
, 1698–702.
(3) Johnson, P. B.; Christy, R. W.
Phys. Rev. B
1972
,
6
, 4370–4379.
5