1
Supplementary
Information
Overcoming Evanescent Field Decay Using 3D
-
Tapered Nanocavities for On
-
Chip Targeted Molecular Analysis
Kumar
et al.
2
Supplementary Note 1
: Device Optimization
-
B
ody
For the design purpose, the device was divided into three parts;
the body, the taper, and the tip
(
Supplementary
Figure 1a). The body width (
w
body
)
, height
(
h
body
)
, and length (
l
body
)
were
optimized for efficient coupling of excitation light to the taper. The taper angle (
α
) was
optimized for efficient coupling of guided AS SPP mode (
Supplementary
Figure 1b) to the ti
p as
well as uniform and high electric
-
field (
|
퐄
|
2
) enhancement for optimized emission response from
molecules. The tip length (
l
tip
) was optimized for longitudinal confinement of light for detection
of targeted number of molecules. The tip
width (
w
tip
)
and height (
h
tip
) were set to 20 nm and 50
nm, respectively.
w
tip
= 20 nm enabled controlled assembly of 1D
-
array antibodies (~15 nm
diameter).
h
tip
was determined by adjusting the thickness of the
evaporated Au layer during
fabrication, and it was twice the skin depth of Au (~25 nm) or 50 nm.
A higher contrast between the effective refractive index inside the channel (
n
eff
)
and the
refractive index of the substrate (
n
SiO2
=
1.45) results in a higher tail
-
end coupling efficiency; the
smaller the
w
body
a
nd
h
body
are
, the larger the
n
eff
and better the tail
-
end coupling of excitation
light into the body (
Supplementary
Figure 1c)
. However, the smaller
cross
-
sectional
dimensions
also
reduced
the propagation length
L
m
(calculated based on
Supplementary
Eq
uation
1) of the
guided AS mode (
Supplementary
Figure 1d)
, which
led to inefficient coupling of the tail
-
end
excitation
to the ta
per as the guided mode
experienced
significant loss throughout propagation
inside the body. The body with
w
body
~ 150 nm and
h
body
≥ 150 nm showed the best coupling
efficiency to the taper for a
l
body
= 3
휇
m device (
Supplementary
Figure
1e). Therefore, both the
w
body
and
h
body
were set to 150 nm,
which resulted
in
n
eff
= 1.67 (>
n
SiO2
= 1.45)
,
L
m
=
3
휇
m, and
the 1.12% tail
-
end coupling efficiency to the taper.
l
body
was set to 3 μm, which is similar to the
propagation length of the guided mode, to efficiently couple the ta
il
-
end excitation light into the
taper. In addition to tail
-
end excitation, the open
-
top channel of this device enables excitation of
the guided mode throughout the body, which will be discussed in
Supplementary Note
2.
Supplementary
Eq
uation
1
L
m
=
1
/
(
2
Im
(
퐤
m
)
)
3
Supplementary F
igure 1:
Optimization of the body width and height
a
Schematic showing
3D
-
tapered nanocavity
dimensions represented by symbols used in manuscript. Length of the
body
is
l
body
, heig
ht is
h
body
, and the taper angle is represented as
α
.
b
E
lectric
-
field profile of the
fundamental anti
-
symmetric (AS) mode at the cross
-
section of the body.
c
Effective refractive
index
n
eff
of the guided mode inside the body with varied
w
body
and
h
b
ody
. As the
w
body
and
h
body
increase,
n
eff
decreases and the guided mode becomes less confined.
d
Propagation length
퐿
m
(
Supplementary
Eq
uation
1)
of the guided mode inside the body with varied
w
body
and
h
body
. As
the
w
body
and
h
body
increase, the p
ropagation length increases and provides more efficient coupling
of guided modes into the taper.
e
Coupling efficiency to the taper with varied
w
body
, and
h
body
for a
l
body
= 3 μm device..
4
Supplementary Note 2
: Device Optimization
-
T
aper angle
The coupling efficiency (
P
tip
/P
body
)
was calculated based on the power at
the
cross
-
sections right
before (
P
body
)
and after (
P
tip
) the taper.
|
퐄
|
2
was calculated at the
narrower end of th
e
taper.
Supplementary
Figures 2a,
b
show th
e
|
퐄
|
2
and the coupling efficiency of devices with varying
tip lengths (
l
tip
= ∞, 500 nm, 20 nm) for taper angles (
α
) ranging from 10
to 70
at
the
750
-
nm
wavelength
. Both the
|
퐄
|
2
and the
coupling efficiency showed
the best performance
within
the
range of 20° ≤
α
≤ 30
for the various tip lengths.
Experimental results showed the same trend as
s
een
in Supplementary Figure 3.
For
small
α,
the taper length increase
s
,
and this
results in great
er
absorption
4
-
6
.
When
α
becomes large,
the abrupt angle in the taper geometry results in the severe
scattering of guided modes due to mismatch between the wave vectors inside the taper and the
tip
4
-
6
. In addition, small fluctuations in the
|
퐄
|
2
and coupling efficiency in the range of 10
≤
α
≤
70
are observed as impedance matching condition fluctuates with
α
(
Supplementary
Figures
2
c
-
e);
Z
body
=
Z
tip
at the peak
locations observed in
Supplementary
Figures
3a,
-
b, where
Z
body(tip)
is
the impedance of the body (tip).
Z
body
was calculated based on
Supplementary
Eq
uation
2
7
.
Z
tip
at each
α
was calculated by iteration of
Supplementary
Equation
3
8
for 100 segments (
Z
n
, 1 ≤ n ≤
100) along each taper length, where
Z
n
is the impedance of n
-
th segment calculated using
Supplementary
Eq
uation
2
,
Z
(n)in
is the input impedance of n segments,
k
n
is the complex
propagation constant of the n
-
th segment, and
l
n
is the segment
length.
퐙
=
R
−
iX
=
V
I
=
∫
E
푥
푑푥
∫
H
푦
푑푦
Supplementary
Eq
uation
2
퐙
(
n
)
in
=
퐙
n
퐙
(
n
−
1
)
in
−
i
퐙
n
tanh
(
퐤
n
푙
n
)
퐙
n
−
i
퐙
(
n
−
1
)
in
tanh
(
퐤
n
푙
n
)
Supplementary
Eq
uation
3
Supplementary
Figure
2e shows the
uniformity of the
|
퐄
|
2
enhancement in the range of
10
≤
α
≤
70
. The uniformity of the
|
퐄
|
2
enhancement was calculated based on a 2
-
D normalized
|
퐄
|
2
(setting 1 as the highest) profile at the cross
-
section of the tip.
A smaller
α
showed better
uniformity in the
|
퐄
|
2
enhancement, as a larger
α
increases scattering of guided modes
4
-
6
.
The total transversal EM energy
U
A
and average transversal EM energy density
u
̅
A
plotted in
Figure 2b were calcu
lated based on Supplementary Equations
4, 5
.
The
efficient transversal
confinement of EM energy
inside the nanocavity allows
uniform
|
퐄
|
2
enhancement; Figure 2b
shows
U
A_body
~
U
A_tip
, which results in an order of magnitude greater
u
̅
A
at the tip
.
5
U
A
=
U
퐄
,
A
+
푈
퐇
,
A
=
∫
1
2
휀
0
|
퐄
|
2
A
+
∫
1
2
휇
0
|
퐇
|
2
A
Supplementary
Eq
uation
4
u
̅
A
=
U
A
/
(
cross
−
section
of
tip
)
=
(
U
퐄
,
A
+
U
퐇
,
A
)
/
(
cross
−
section
of
tip
)
Supplementary
Eq
uation
5
6
Supplementary
Figure
2
:
Optimization of the taper angle
a
Average
|
퐄
|
2
enhancement
(
|
퐄
|
̅
̅
̅
̅
2
)
at the tip with varied taper angle
α
.
b
Coupling efficiency from the body to the tip with var
ied
taper angle
α
.
Calculated
c
resistance and
d
reactance of the taper and body based on
Supplementary
Eq
uations 2,3
. Impedance matching between the taper and body happens at
α
~
20°.
e
Standard deviation of the normalized
|
퐄
|
2
enhancement di
stribution at the tip with varied
taper angle
α
.
7
Supplementary
Figure
3
:
Experimental
d
evice optimization
a
Experimental results showing
that the highest fluorescence intensity from the devices was obtained for taper angle (
α
) close to
20°, with the
body width maintained at 150 nm, tip length as 500 nm and width as 20 nm.
b
Experimental results showing that devices with body width around 150 nm had higher
fluorescence emission as compared to devices with wider body widths. Device taper angle was
m
aintained at 20° for these tests. The experimental results support the parameters indicated by
simulations
.
8
Supplementary Note 3: Device Optimization
-
Tip length
The length of the tip (
l
tip
) can be engineered to control the size, location, and enh
ancement
magnitude
of the hotspots formed inside the tip. A device with an infinite
l
tip
shows a gradual
decrease in
|
퐄
|
2
enhancement along the tip due to absorption
along
the sidewalls of the tip
(
Supplementary
Figure
s
4
a, b). On the other hand, a dev
ice with a finite
l
tip
experiences power
reflection at the end of the tip
9
. This
leads to
the formation of Fabry
-
Perot resonances of different
number of peaks (
m
) along the longitudinal direction of the
tip
10
. I
n
this
case
,
a
properly chosen
α
could
provide matching standing wave vectors inside the taper
that could
result in pronounced
|
퐄
|
2
enhancement of the resonances
in the
tip
. In addition, a shorter
l
tip
produces
intensity
pattern
s
with
fewer
periodic resonant peaks, which reduces the
overall
hotspot volume. When
l
tip
= 500 nm, the device exhibits greater
|
퐄
|
2
of the
m
= 4 Fabry
-
Perot resonance at
α
~ 20
and
α
~
45
(
Supplementary
Figure
4
a
, b
). When the tip is shorter (
l
tip
= 20 nm), the device shows further
increase in the
|
퐄
|
2
enhancement of the
m
= 1 Fabry
-
Perot resonance at
α
~ 20
and
α
~ 60
. The
overall
|
퐄
|
2
enhancement increases with a shorter
l
tip
due
to reflection from the tip end,
which
increases the average volumetric EM energy density
u
̅
V
inside the tip (
Supplementary
Figure
4
c)
.
u
̅
V
was calculated based on
Supplementary
Eq
uations
6, 7
. The hotspot volume shown in Figure
3f was calculated b
ased on the full
-
width
-
half
-
maximum
(FWHM)
of each resonant peak shown
in
Supplementary
Figure
4
b.
U
V
=
U
퐄
,
V
+
U
퐇
,
V
=
∫
1
2
ε
0
|
퐄
|
2
V
+
∫
1
2
μ
0
|
퐇
|
2
V
Supplementary
Eq
uation
6
u
̅
V
=
U
V
/
(
volume
of
tip
)
=
(
U
퐄
,
V
+
U
퐇
,
V
)
/
(
volume
of
tip
)
Supplementary Equation
7
9
Supplementary
Figure
4
:
Optimizat
ion of the tip length
a
Electric field distribution of the
guided mode with varied tip lengths (Infinite, 500 nm, 100 nm, 20 nm, from left to right).
b
Comparison between the |
E
|² enhancement profiles of different tip lengths. A shorter tip provides
higher enhancement in a more confined area.
c
Comparison between the stored energy
U
and
average energy density
u
̅
in tips of different lengths.
U
and
u
̅
were calculated based on
Supplementary
Eq
uation
6 and 7
, respectively. A shorter tip provides a h
igher density of the stored
energy inside the tip, whereas the total amount of stored energy decreases due to increased loss.
10
Supplementary
Figure
5
:
Molecular functionalization and imaging
a
Schematic showing
monolayer of PEG
-
biotin covering the base of the
3D
-
tapered nanocavity
.
b
Fluorescenc
e signal
when streptavidin molecules are in solution but not at the tip.
c
Signal when a molecule binds at
the tip region.
11
S
u
pplementary Note 4
: Two approaches to light coupling into the device
In the tail
-
end coupling method, light was incident only on the tail
-
end of the
device (Figure 3a).
In the full
illumination method, light was incident on the full device (Figure 3a). In
Supplementary
Fi
gure
6
a, the coupling efficiency into the body (blue solid line) was calculated using FDTD by
focusing a Gaussian light source and measuring power transmission through a cross
-
section at
each longitudinal position of the body (
z
). Despite the reduced cou
pling efficiency into the body
in the middle (0 μm <
z
< 3 μm), the amount of power coupled to the taper (
Supplementary
Figure
6
b) is doubled as
z
~ 3 μm due to the dramatically reduced propagation loss (
Supplementary
Figure
6
a, red dashed line) as can
be seen in
Supplementary
Eq
uation
8
. The total coupling efficiency to
the taper under full
illumination is calculated to be ~15% (
Supplementary
Figure
6
b), which is
~10× higher than tail
-
end only excitation.
Coupling
efficiency
into
taper
=
Couplin
g
efficiency
into
body
×
(
1
−
Propagation
loss
inside
body
)
=
Coupling
efficiency
into
body
×
(
1
−
e
−
2
훼
(
3
μ
m
−
푧
)
)
Supplementary
Equation
8
12
Supplementary
Figure
6
:
Coupling efficiency of full illumination mode
a
Coupling efficiency
into the body
(solid blue line) and propagation loss of the coupled light (dashed red line) at each
longitudinal location (z) along the body length.
b
Coupling efficiency to the taper at each
longitudinal location calculated based on
Supplementary
Eq
uation
8
. Integr
ating the coupling
efficiency along the body length, the total coupling efficiency under full
-
illumination is calculated
to be 15.5%, which is ~10x greater than tail
-
end coupling efficiency shown in
Supplementary
Figure 1e.
13
S
upplementa
ry Note 5
: Effect of nanocavity structure on fluorescence
Nanocavities were fabricated with the full body, just 3D taper and tip, and stand
-
alone tips (
l
tip
=
500 nm for all three cases) and the mean fluorescence intensity observed at the ti
ps was measured
for all the cases (
Supplementary
Figure
7
). The trend for the nanocavitie
s indicates that maximum
intensity was obtained for
the 3D
-
tapered nanocavity
with full body. Observed fluorescence
intensity sharply decreases when the
whole devi
ce is reduced to just the 3D
-
taper and tip and
decreases further for the stand
-
alone tip structures (
Supplementary
Figure
7
). These observations
agree with the FDTD simulation results (
Supplementary
Figure
8
)
, where scattering at
the backend
or the sidewalls of the
body
incite SPP propagation towards the tip. Drastic decrease in light
intensity for a taper
-
tip structure as well as standalone tip can be further attributed to loss in light
collected from back
scattering as well as ed
ge scattering along the open edges of the
body
at the
working wavelength.
Supplementary
Figure
7
:
Experimental study on effect
of nanocavity structure on
fluorescence
a
3D
-
tapered gap plasmon nanocavity
, taper and tip, and tip only s
tructures were
fabricated with fragmented body length and
b
normalized fluorescence intensities at the tip was
obtained for various structures demonstrating the effect of improved coupling through the device
body.
Data points, mean and
s.d.
for 5 samples at each condi
tion
are shown
.
14
Supplementary
Figure
8
:
Computational
study on effect
of nanocavity structure on
fluorescence
a
Full waveguide, taper and tip, and tip only s
tructures were simulated
.
|
E
|²
distribution at the tail
-
end of a tip (top), a taper
and a ti
p
(middle), and a
3
D
-
tapered gap plasmon
nanocavity
(bottom). A Gaussian beam centered at 750 nm with a spot size of 270
-
nm diameter
(obtained using a 1.4
-
NA objective lens) was incident at the tail
-
end of each structure.
3D
-
tapered
gap plasmon nanocavity
(bottom) shows a clear hotspot at the tip, which the upper two structures
do not show.
b
Tail
-
end coupling efficiency of the three different combination structures in (a)
plotted against wavelength (650
-
800 nm). Coupling efficiency is enhanced to more t
han an order
of magnitude when a
3D
-
tapered gap plasmon nanocavity
is implemented
.
15
Supplementary
Figure
9
:
Detection of low concentration molecules on 3D
-
tapered
waveguides (tip length 500 nm)
a
Log
-
log plot showing increase in signal with
increase in
concentration of added Streptavidin (10 pM
–
1000 pM).
b
F
luorescence
signal
obtained from
devices after
testing with
10 pM streptavidin
-
AF 750. Negative control device had no biotin layer.
Plot shows data points, m
ean and
s.d.
f
or
3
de
vices
at each condition
.
16
Supplementary
Figure
10
:
Tapping
-
mode images of the phase signal
of the PEG
-
biotin
conjugated antibody selectively coated on silica substrate showing the uniform monolayer
arrangement in large scale
High resolution imaging as sh
own in an inset reveals the average size
of the antibody of around 20 nm. The arrow highlights t
he typical three molecules with the tri
-
nodular flat orientation of the antibody. Scale bars, 200 nm (inset: 50 nm).
17
S
upplementary Note 6
: Calculation of quantum yield gain
Quantum yield gain
η
/η
0
of fluorophores inside the tip was calculated usin
g FDTD. A dipole source
was placed at varied locations along the
푥
or
푦
axis to monitor the radiation from the dipole and
the tip structure.
Normalized r
adiative decay rate
γ
r
/
γ
0
was obtained by measuring the
transmission through a closed box
containing the
3D
-
tapered nanocavity
tip structure
P
s
tructure
and
dividing it by the source power
P
0
(
Supplementary
Eq
uation
9
).
γ
r
γ
0
=
P
structure
P
0
Supplementary
Eq
uation 9
Normalized non
-
radiative decay rate
γ
nr
/
γ
0
was obtained by subtracting
P
structure
/P
0
from
the
normalized
transmission through a closed box
around a dipole sour
ce
P
dipole
/P
0
(
Supplementary
Eq
uation
10
).
γ
nr
γ
0
=
P
dipole
−
P
structure
P
0
Supplementary
Eq
uation 10
Quantum yield
gain
η
/
η
0
was calculated using
Supplementary
Eq
uation
11
11
.
η
η
0
=
γ
r
γ
0
⁄
1
−
η
0
+
γ
r
γ
0
⁄
+
γ
nr
γ
0
⁄
×
1
η
0
Supplementary
Eq
uation 11
18
S
upplementary Note 7
: Molecular binding tests
In order to test the behavior of smaller probes, dye molecules (AF
-
750) were covalently
linked
directly to the silica
-
base of the nanocavities. For molecule
-
specific bioassays, w
e utilized short
chain (length: 30 basepairs) single
-
stranded DNA aptamers labeled with AF
-
750 at the 5 ́ end.
These molecules form G
-
quadruplex tertiary structures wi
th dimensions ranging between 2
-
4 nm
12
and were used to detect insulin (monomer diameter: 2 nm
13
)
that was
physically adsorbed within
the nanocavities
14
. As shown previously (Fig
.
3b,
Supplementary
Figure
5
), proteins (Streptavidin
-
AF 750, diameter: 5 nm
)
15
, which recognized and bound to biotinylated monolayers, (expected
height: 3.5 nm)
16
, were also utilized for on
-
chip assays. The polymeric biotin
-
streptavidin
assembly provides an increase in probe
-
dimension as well as chang
e in orientation as compared to
the aptamer
-
based samples. Predominantly, bioassays rely on application of even larger proteins,
i.e. antibodies for highly
-
specific detection of target molecules. IgG antibodies have a globular
diameter around 15 nm, which
can vary depending on the molecular mass of the antibodies and
associated conjugates
17,18
. The expected average fluorophore height shown in Figure 4e includes
the diameter of the surface
-
bound antigen (insulin or biotin) added to the diameter of the
biorecognition element (apta
mer, streptavidin or antibody).