Supporting Information:
Efficient Coupling between Dielectric-Loaded
Plasmonic and Silicon Photonic Waveguides
Ryan M. Briggs,
*,†
Jonathan Grandidier,
†
Stanley P. Burgos,
†
Eyal Feigenbaum,
†
and Harry A.
Atwater
†,‡
Thomas J. Watson Laboratories of Applied Physics, Kavli Nanoscience Institute, California
Institute of Technology, Pasadena, California 91125
*
To whom correspondence should be addressed, rbriggs@caltech.edu.
†
Thomas J. Watson Laboratories
of Applied Physics.
‡
Kavli Nanoscience Institute.
Waveguide coupling setup:
To couple light through grating-coupled silicon-on-insulator (SOI)
waveguides, and subsequently through dielect
ric-loaded surface plasmon polariton (DLSPP)
devices, we used a fiber-coupled New Focus 6428
Vidia Swept tunable diode laser source with
identical input/output lensed fiber focusers,
1
as shown in Fig. S1. The
pigtail focusers consist of
single-mode fibers integrated with aspheric
lens pairs designed for a 12.4-mm working distance
and a spot size of approximately
10 μm. Between the laser and the input focuser, an in-line
polarization controller was used to set the polar
ization at the input grating. From the output
fiber, light was coupled into either a calib
rated InGaAs power meter or a 10-MHz InGaAs
1
photoreceiver connected to a 500-MHz oscilloscope.
The laser wavelength was swept linearly at
a rate of 10 nm/s or slower for spectral meas
urements, resulting in sub-pm detector-limited
wavelength resolution when using the photoreceiver.
Figure S1.
Schematic of the fiber-coupling setup used
to couple light through SOI-waveguide-
coupled DLSPP devices.
The lensed fiber focusers were mounted to
rotation stages atop precision translation
stages, allowing the focusers to be positioned above
the SOI gratings and rotated eucentrically to
access a specific grating coupling angle,
θ
. Positive coupling angles could be achieved with the
configuration represented in Fig. S1, while nega
tive coupling angles were accessible by focusing
the input focuser onto the output grating, and vice
versa. The long working distance of the fiber
focusers allowed access to a relatively wide range of positive and negative coupling angles.
Based on the overall transmission through our waveguide test setup and the input laser power,
the grating-plus-taper loss is estimated to be 7
dB per coupler; however, we envision that with a
waveguide-coupled on-chip light source, the devi
ces we have developed could be realized
2
without free-space couplers. The insertion loss
for DLSPP waveguides would then be just the
SOI-DLSPP transition loss of approximately 1 dB.
Characterization of SOI waveguide modes:
We analyzed the modes supported by our SOI
waveguide geometry by investigating the res
ponse of a 400-μm diameter SOI ring resonator
patterned on the same sample as the DLSPP ring
devices. The ring was evanescently coupled to
a straight SOI waveguide across a 1-μm gap.
1,2
In addition, the ring diameter is large enough
that bending losses are negligible.
3
With a cross section identical to the SOI waveguides used
for coupling light into the DLSPP waveguides, th
e SOI ring device supports just the fundamental
transverse-electric (TE) and transverse-magnetic (TM) modes near
λ
= 1550 nm. By scanning
the input wavelength through the straight wavegui
de, we observe coupling to whispering-gallery
modes, as shown in Fig. S2. For di
ffraction-grating coupling angles of
θ
= +26° and -26.5°, we
see coupling to either TE or TM resonator mode
s, respectively, confirming that the gratings
allow for selective coupling to just one polariza
tion due to the different phase velocities of the
TE and TM modes. We can verify the identity
of the whispering-gallery modes based on their
free-spectral range, which is different for the two polarizations due to their unique group
velocities.
1
Selective coupling to a single polarization
proved useful for demonstrating that light
is transmitted through the DLSPP waveguides only for the TM polarization.
3
Figure S2.
(Top panel) TM-mode transmission spectru
m collected at a diffraction-grating
coupling angle of
θ
= -26.5° for a waveguide coupled to a 400-μm diameter SOI ring resonator
(shown in the optical micrograph). The inset shows a high-resolution wavelength scan at the
indicated resonance along with the loaded quality
factor obtained from a Lorentzian fit. The
lower panel shows the transmission spectrum for th
e same device but with the light selectively
coupled to the TE waveguide mode at a coupling angle of
θ
= +26°
As seen in the TM-mode transmission spectrum
in the top panel of
Fig. S2, obtained at a
coupling angle of
θ
= -26.5°, the extinction ratio for the SOI ring-resonator whispering-gallery
modes is largest near
λ
= 1550 nm, where the “magic-width” condition is satisfied.
4
The loaded
resonator quality factor for the resonance centered near
λ
= 1549.5 nm is 94,000. By accounting
for coupling loss, the intrinsic quality factor due to propagation loss,
Q
int
, can be determined.
2
4
The high-resolution transmission spectrum,
T
(
λ
), shown in the top inset
of Fig. S2, was fit to the
following form:
5
T
(
λ
)
=
(
a
−
t
)
2
+
(2
π
n
g
L
c
)
2
at
(
λ
−
λ
0
)
2
λ
0
4
(1
−
at
)
2
+
(2
π
n
g
L
c
)
2
at
(
λ
−
λ
0
)
2
λ
0
4
,
(S1)
which is derived from the general expression from Yariv
6
and is valid for small wavelength
deviations around a central wavelength,
λ
0
.
L
c
= 400
π
μm is the circumference of the SOI ring,
n
g
is the modal group index, and
a
and
t
account for attenuation due to propagation loss and
coupling, respectively. The round-trip frac
tional loss, independent of coupling, is
l
= -2 ln(
a
),
corresponding to an intrinsic quality factor of
Q
int
= 2
π
n
g
L
c
/(
λ
0
l
) = 126,000, where the group
index,
n
g
= 3.96, can be obtained from the free-spectral range,
Δ
λ
, by the relation
n
g
≈
λ
0
2
/(
Δ
λ
L
c
). The propagation loss is -2 ln(
a
)/
L
c
= 1.28 cm
-1
, or 5.5 dB/cm, which is more than
two orders of magnitude lower than the DLSPP-waveguide loss at
λ
= 1550 nm.
The TE-mode transmission spectrum for the same
device is shown in the lower panel of
Fig. S2. The TE-polarized waveguide mode was
accessed selectively using a coupling angle of
θ
= +26°. The TE whispering-gallery modes are di
stinguishable from the TM modes because of
their distinct free-spectral range,
Δ
λ
, and the absence of wavelength dependence in the extinction
ratio. The TE-mode group index near
λ
= 1550 nm is 3.76, significantly smaller than the TM-
mode group index. Accounting for coupling loss, the TE-mode propagation loss is 3.7 dB/cm.
Numerical simulations:
We used COMSOL Multiphysics,
a commercial finite-element method
solver, to calculate the field dist
ribution and complex effective index,
n
eff
, of the DLSPP
waveguide modes. The real part
of the effective index was accurately fit by a quadratic function
5
for wavelengths between
λ
= 1500 to 1600 nm. The fit was used
in the interference model for
the spectral response of the DLSPP ring resona
tors. Loss due to material absorption,
α
abs
, was
determined from the imaginary part of the modal effective index as
α
abs
= 4
π
Im[
n
eff
]/
λ
.
Mode calculations were performed using
the Au index data measured by Johnson and
Christy.
7
To obtain a continuous function for the real
and imaginary parts of the index, we fit
Hermite interpolation functions between the m
easured data points as well as between the
reported error bars, as plotted in Fig. S3. The real
and imaginary parts of the effective index that
we report for the DLSPP waveguide mode between
λ
= 1500 to 1600 nm include the upper and
lower limits within these interpolated errors.
Lumerical FDTD, a finite-difference time-domai
n solver, was used to model the coupling
loss between DLSPP waveguides and SOI input/output
waveguides. The built-in mode solver
was used to define the SOI TM-mode source at
λ
= 1550 nm in the input waveguide, and the
power flux was monitored in the SOI output
waveguide 10 μm from the DLSPP-SOI output
transition. The monitor position was varied to en
sure that it captured only power coupled into
the (loss-less) output waveguide and not power
scattered from the DLSPP-SOI transitions. The
simulation boundaries were defined as perfectly
matched layers and positioned far enough away
from the waveguide so as to minimally impact th
e effective index of the calculated input mode.
To ensure stability, the input source was define
d temporally as a single pulse, and the field
amplitudes were allowed to decay to 0.001% of thei
r initial values. Spectral filtering was used to
extract the power transmission associated with the input wavelength.
6
Figure S3.
Real,
n
, and imaginary,
k
, parts of the index of refraction of Au used in the
numerical calculations. The data points are
from Ref. 7, and the curves are Hermite
interpolations between the data points and their associated error bars.
Characterization of the waveguide geometry:
The geometries of the SOI and DLSPP
waveguides were verified using atomic-force mi
croscopy (AFM). The AFM image in Fig. S4(a)
shows the topography of an etched SOI ridge
waveguide. A cross section from the image
indicates that the waveguide width is close to
the lithographically defined dimension of 740 nm,
and the etch depth is 30 nm. Figure S4(b) s
hows the topography of a PMMA wire on Au from
one of the SOI-waveguide-coupled DLSPP devices.
The PMMA wire is nearly 500 nm wide at
its top surface and approximately 560 nm tall.
The AFM images of both the SOI and DLSPP
waveguides were collected in non-contact mode, a
nd the scanning parameters had to be carefully
optimized to avoid damaging the soft, high as
pect-ratio PMMA wires. The DLSPP waveguide
geometry represented in Fig. S4(b) is consistent
with measurements from electron micrographs
of the patterned structures as well as film th
ickness measurements of unpatterned PMMA layers.
7
Figure S4.
(a) AFM image of an etched SOI waveguide
prior to coating with PMMA. A cross-
section of the topography is shown in blue
. (b) AFM image of a PMMA-on-Au DLSPP
waveguide. (c) Scanning electron micrograph of
a 20-μm wide recessed Au feature prior to
coating with PMMA. The AFM image below th
e electron micrograph shows the topography of
a feature of identical width after being coated
with PMMA. The recessed region is 20 μm wide,
indicating that the polymer coats the recessed Au with a uniform thickness. (d) A schematic
cross-section of the PMMA-coated feature, showing that the polymer is tapered at the edges of
the Si layer surrounding the Au region.
In order to accurately model the full three-
dimensional structure of the SOI-waveguide-
coupled DLSPP devices, we also used AFM to
determine the topography of the spin-coated
PMMA at the Si-Au interf
ace. An essential feature of our waveguide design is the vertical offset
of between the Si waveguiding layer and th
e Au surface that supports the DLSPP mode;
however, this leads to varying topography on the top surface of the PMMA. The scanning
8
electron micrograph in Fig. S4(c) shows a rece
ssed Au region on an SOI sample without a
PMMA cover layer. The actual width of the recessed area is very close to the lithographically
defined width of 20 μm. The contact-mode AFM image shows a feature fabricated in the same
manner that has been subsequently coated with PMMA and baked at 180 °C for 5 min. We
observe that the polymer conforms to the topogr
aphy of the recessed structure, leading to a
uniform height along the entire 20-μm wide recessed
Au region. Furthermore, the vertical offset
in the PMMA layer across the Si-Au interface
is close to the 300-nm offset between the
underlying Si and Au surfaces. From this anal
ysis, we conclude that the PMMA uniformly
covers the recessed Au, and there is an approximate
ly 2-μm wide vertical taper in the polymer at
the edges of the Si layer, as depicted schematically in Fig. S4(d).
NSOM measurements:
To corroborate the surface plasmon propagation length obtained from
variable-length waveguide transmission measurements, we analyzed the same DLSPP devices
using near-field scanning optical microsc
opy (NSOM). NSOM/AFM measurements were
performed with a tuning-fork based Nanonics
MultiView 2000 scanning probe microscope in
contact mode using a 200-nm diameter aperture
probe in collection mode. Light was coupled
into the SOI input waveguide of each device at
a wavelength of 1520 nm using an identical
lensed-fiber arrangement as used for the wa
veguide transmission measurements, and light
collected by the scanning probe was detected using an InGaAs avalanche photodiode.
The NSOM analysis for a 30-μm long DLSPP waveguide is shown in Fig. S5. The AFM
and NSOM images in Fig. S5(b) and (c) were collected simultaneously using a high gain setting
for the tip deflection signal, which minimized da
mage to the polymer waveguide but led to a
noticeable increase in the noise associated
with the measured topography. Comparing the
scanning electron micrograph in Fig. S5(a) with th
e AFM image in Fig. S5(b), we observe that
9
the size and shape of the NSOM
tip affects the apparent width of the DLSPP waveguide in the
x
-
direction; however, we are primarily intere
sted in decay of the DLSPP mode along the
propagation (
z
) direction. Consequently, we integrated
the intensity in the NSOM image along
the
x
-direction, which is plotted on a normalized loga
rithmic scale in Fig. S5(d) as a function of
propagation distance along the
z
-direction. Other than an initial jump in intensity at the input
SOI-DLSPP transition, the intensity decay resemble
s an exponential with a decay constant of
approximately 50 μm. This is in agreement
with the DLSPP-mode propagation length extracted
from variable-length waveguide transmissi
on measurements and therefore supports our
quantitative analysis of the SOI-DLSPP waveguide coupling loss.
We observe significant intensity only along th
e polymer waveguide in the NSOM image,
indicating that optical power is preferentially
coupled into the DLSPP mode as opposed to air-
Au surface plasmons, which would be expected to spread out from the sides of the waveguide.
The beating in intensity along the propagation dir
ection is attributed to interference between
light in the DLSPP mode and light scattered into
radiation modes at the SOI-DLSPP transitions.
We note that oscillations of a similar period app
ear in the three-dimensional FDTD simulations
of the coupled waveguide structure. Finally, we
observe reduced intensity
at the surface of the
PMMA covering the SOI input/output waveguides
because the SOI waveguide mode is largely
confined to the buried Si layer.
10
11
Figure S5.
(a) Scanning electron micrograph of a 30-μm long DLSPP waveguide. (b) AFM and
(c) NSOM images collected simultaneously for
a device with the same geometry, where light
was coupled into the plasmonic section from the
buried SOI waveguide lying to the left of the
DLSPP device. (d) Total collected intensity
from the NSOM image integrated along the
x
-
direction as a function of position in the propagati
on direction. The measured intensity exhibits
a characteristic decay length of approximately 50 μm.
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