of 8
S
upporting
Information
Synthesis an
d Characterization of Plasmonic
Resonant
Guided Wave Networks
Stanley P. Burgos
1,
2,
, Ho W. Lee
1,
2,
, Eyal Feigenbaum
1
, Ryan M. Briggs
1
,
and
Harry A. Atwater
1
,2,
1
T
homas J. Watson Laboratories of Applied Physics, C
alifornia Institute of Technology, United
States
2
Kavli Nanoscience Institute,
California Institute of Technology, United
States
Corresponding
author e
-
mail:
haa@caltech.edu
Equal author contribution
Keywords
Pla
smonics, nanocircuits, resonant structures, power splitters,
silicon photonics,
logic device
1.
Coupling Efficiency
Here, we
investigate the coupling efficiencies associated in
going from the photonic Si
-
ridge
waveguide mode to the subwavelength
CPP
mod
e
.
1
,
2
Previous work has focused on coupling to the SPP
mode of various structures, including DLSPP
3
,
4
, v
-
groove mode structures
5
-
8
, and hybrid plasmonic
-
photonic modes
9
-
14
.
As seen from the simulated mode patterns of v
-
groove CPP mode and Si
-
ridge
wavegu
ide mode in
Fig. 1
c and Fig.
1e in the main text,
the CPP mode is
1/5 the transverse size of the
Si
-
ridge TE mode, so that we heuristically expect to have coupling efficiencies on this order.
However
,
due to fabrication imperfections,
we find that the sep
aration between the v
-
groove and Si
-
ridge waveguide is nonzero, and this reduces the coupling efficiency to a value smaller than their modal
volume ratios. The
coupling
efficiency
into the v
-
groove
plasmonic waveguide
mode
will depend on the
number of acce
ssible modes that couple light from the Si
-
ridge to the CPP waveguide or to free space.
S
ince we are coupling through a volume of free space, there is a large number of freespace modes that
contribute to the coupling, making this
calculation difficult to d
o analytically. Thus we have performed
coupling efficiency calculations using full
-
wave finite
-
difference time domain simulations in which we
launch light from a Si
-
ridge waveguide aligned to a v
-
groove waveguide separated by
different
distance
s
and
vertic
al offsets relative to their t
op surfaces (Fig. 1c
-
e
in main text
).
The coupling efficiency is
calculated by monitoring the power transmitted into the v
-
groove waveguide when excited by the TE Si
-
ridge mode at 1520 nm
As shown in the results in Fig. S
1
,
we
get a maximum coupling efficiency of
14% at an offset of
100 nm
for a zero separation
, which is only slightly lower than expected based on their modal volumes
alone.
However, this efficiency quickly drops as the separation is increased, going down to
< 10% for 500
nm separation, and < 5% for 1000 nm separation.
From NSOM measurements at 1520 nm, we
measured
a
coupling efficiency of
8%, consistent with FDTD calculated value
s for the geometries (Fig. S
1
, green
dotted
). We
also
measure
d
the wavelength d
ependent coupling efficiencies by varying the excitation
wavelength between 1490
-
1520 nm and repeating the power coupling calculation for the resulting NSOM
images. The
re
sulting data are shown in Fig S1
, demonstrating coupling efficiencies in the 7
-
8% ran
ge
.
To increase
the coupling efficiency
, we introduced
a taper to the plasmonic v
-
groove waveguide
(Fig.
S2
a)
.
1
,
1
5
This figure (together with Fig.
S1
) clearly shows that the nanotaper indeed significantly
increase
s
the coupling coefficient and
that
high
efficiency can be achieved with careful design o
f
the taper
geometries.
The resulting transmission data is shown in Fig.
S2
a, from which we can see that
with the
introduction of taper with short taper length (
with zero separation
)
, we can obtain a maximum
coupling
efficiency of
40%, almost independ
ent of taper width. However the
efficiency
also
drops as the
separation is increased, shown in Fig.
S2
b going down to ~ 10% for 500 nm separation. From FIB cross
-
sections of
the
fabricated devices, we observed that the waveguides are s
eparated by
200 nm and offset
by
-
50 nm, with taper dimension of dx = 250 nm, dy = 850 nm, thus placing our devices in the 20 %
theoretical range for 1520 nm light, which is consistent with the value measured from the NSOM
measurement (22.5 %,
Fig. S2b
, green dotted data).
Figure. S
1
:
Coupling efficiency as a function of waveguide position at
λ
0
= 1520 nm. Horizontal axis
corresponds to vertical offset between S
i
-
ridge and v
-
groove waveguides
relative to their surface tops. The three
colored
curves
correspond to three different waveguide separations, with the blue corresponding to zero
separation, black to 500 nm separation, and red to 1000 nm separation. The green dotted data corresponds to
coupling efficiencies extracted from NSOM measurements for
wavelengths
λ
0
= 1500, 1510, and 1520 nm.
Figure S2
:
(a) Coupling efficiency as a function of taper length (dx) and width (dy) at
λ
0
= 1520 nm
(with zero
separation)
. (b) Coupling efficiency as a function of separation for dx and dy of 850 nm and 250nm,
respectively.
The green data points correspond to coupling efficiencies extracted from NSOM measurements for wavelengths
of
λ
0
= 1520 nm.
2
.
Propagation of CPP and SPP at
the x
-
junction
Fig
ure
. S
3
: NSOM image taken at
λ
0
= 1520 nm of x
-
junction
for (a) C
PP and (b) SPP modes (the dashed lines
indicate the location of the x
-
junction. Inset: simulated mode profiles of CPP and SPP modes.
Corresponding
simulated responses shown in (c) and (d), respectively.
To investigate the power splitting properties of the
highly confined CPP mode and less confin
ed SPP
mode, these two modes were
selectively e
xcited (with
the appropriate
excitation
angles
) and the
resulting
near
-
fiel
d profiles at the x
-
junction were measured, as shown in Fig. S
3
a
,
b
. It is clear from the fig
ure
s
that the CPP mode is split at the
x
-
junction
while the SPP mode is
simply
reflected
. This can be explained
from mode profile where the SPP mode is confined mainly on the top surface of the channel, resulting
in
a
reflection
of propagation due to
the d
iscontinuity
of the surface at the x
-
junction.
The simulated optical
responses of the structures are
shown in
Fig
s
. S
3
c
,
d, respectively,
with both
results
in
good agreement
of
each other
.
Th
ese results
further suggest the
uniqueness
of the highly confined
CPP mode
for
developing
unltracompact plasmonic nanocircuit where sharp bend
s
and power splitting
junctions
are required.
3. Silicon dielectric waveguide
modes
and dielectric x
-
junction splitter
Figure. S4
:
(a)
Simulated
mode profiles of
rectangular Si
-
wavegu
ide with different dimension (with
SiO
2
substrate
)
.
(b)
Simulated
responses of the propagating silicon photonic mode at dielectric x
-
junction.
The
mode profiles of the rectangular silicon photonic waveguide with different dimensions are simulated
u
sing finite element method and the results are shown in Fig. S4a.
As seen from the figure, the silicon
dielectric mode
extends
out to the waveguide
with
the dimension
below ~
700nm, thus increasing the
actual
transverse mode profile.
In addition, the propa
gation of the silicon dielectric mode
with dimension
of 350nm x 900nm
are simulated with FDTD calculations. As shown in Fig. S4b, the propagating mode
does not split to the side efficiently, instead most of the energy are propagated
in
to the forward direct
ion.
Comparing
this figure and F
ig. S3c, it is clear that only the highly confined
v
-
groove
CPP mode
is the
only possible mode to
be used as
a
n
efficient 4
-
way equal power splitter for ultracompact optical network
design and development.
4. Calculation of
splitting coefficients of x
-
junction
To calculate the back
-
reflected power in the power splitter we note that the length from the Si
-
slot/v
-
groove waveguide junction to the v
-
groove waveguide x
-
junction is only 7.5 microns, which is on the
order of the pr
opagation length of the v
-
groove waveguide, which is ~9 microns, as described in the
propagation length section. Thus, the round
-
trip of the transmitted wave from the Si
-
slot/v
-
groove
waveguide junction to the v
-
groove waveguide x
-
junction and back to the
Si
-
slot/v
-
groove waveguide
junction is ~15 microns, which is larger than the propagation length of the v
-
groove waveguide mode.
For example, if the x
-
junction produced a perfect back
-
reflection, that means that only
,
=19%
would reach the Si
-
slot/v
-
groove waveguide junction after being reflected by it. Furthermore, since we
know that the x
-
junction
is not
perfect reflector, but that it only reflects ~25% of the incident power based
on simulations, we get that only 25%
×
19%=4.5% is actually reac
hing the Si
-
slot/v
-
groove waveguide
junction after the wave is reflected by the x
-
junction. Thus, ignoring the small amount of power that does
reach the Si
-
slot/v
-
groove waveguide junction after it is reflected from the x
-
junction, we can use the
following
expression,
(1
)
In this case,
C
2
is gives a DC offset in the intensity profile, corresponding to the amplitude squared of the
incident wave onto the x
-
junction,
which is
the amount of light that transmitted into the v
-
groove channel.
But this is no longer the variable of interest, we are
interested in the variable
b
, which is related to the
amplitude of the cosine function, which tells us how much of the
incident wave is back
-
reflected in the
power splitter. Aside from
L
, which is the arm length of the x
-
junction,
k
v
-
groove
and
φ
b
are free fit
parameters of the intensity function profile, which do not impact the
b
-
coefficient, which is what we are
after. T
hus, by fitting the NSOM intensity profile in
the back
-
reflected arm to Eqn. 1
, we
can
extract the
amplitude of the back
-
reflected coefficient of the x
-
junction.