1
Supplementary Materials for
Dynamic Beam Steering with All
-
Dielectric Electro
-
Optic
III
-
V Multiple
-
Quantum
-
Well Metasurfaces
Pin Chieh Wu
1,2
,
*
, Ragip A. Pala
1
, Ghazaleh Kafaie
Shirmanesh
1
, Wen
-
Hui Cheng
1
,
Ruzan Sokhoyan
1
, Meir Grajower
1
, Muhammad Z. Alam
1
, Duhyun Lee
1,3
, and
Harry A. Atwater
1,4
,
*
1
Thomas J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, California
91125, USA
2
Department of
Photonics, National Cheng Kung University, Tainan 70101, Taiwan
3
Samsung Advanced Institute of Technology, Suwon, Gyeonggi
-
do 443
-
803, South Korea
4
Kavli Nanoscience Institute, California Institute of Technology, Pasadena, California 91125, USA
Corresponding author
s
:
Pin Chieh Wu (pcwu@gs.ncku.edu.tw);
Harry A. Atwater
(
haa@caltech.edu
)
2
Supplementary Note 1
Analysis
of reflectance and phase modula
tion
s
by resonant MQW heterostructures
To experimentally identify the optimal operation wavelength for observation of
tunable amplitude and phase modulations, we fabricate a number of planar
DBR/MQW/PMMA/Au heterostructures, which support high
-
Q Fabry
-
Pérot
resonances
(see
Supplementary
Fig
.
1b
). The thickness of the Au layer is 35 nm. The spectral position
of th
e high
-
Q resonances supported b
y these planar heterostructures can be controlled by
changing the thickness of the PMMA layer. The change of the real part of the MQW
refractive index (∆
n
)
can be evaluated by examining the shift of the resonant wavelength
under applied bias. On the other hand, the change of the imaginary part of the MQW
refractive index (∆
k
) can be evaluated by studying the change of the full width at half
maximum (FWHM) of
the resonance while applying bias. To fairly evaluate the index
change at different wavelengths, we utilize the same resonant mode (i.e. the first Fabry
-
Pérot
cavity resonant mode), which can be gradually shifted by changing the thickness of
the PMMA laye
r in the DBR/MQW/PMMA/Au heterostructure.
Supplementary
Fig
.
1c
shows the measured reflectance spectra for different thicknesses of the PMMA layer. It is
obvious that the first
Fabry
-
Pérot
resonant mode exhibits a red shift when the thickness of
the PMMA layer is increased. The second and third
Fabry
-
Pérot
resonant modes start
showing up
when the thickness of the PMMA
layer exceeds 210 nm. Since in the case of
438 nm
-
t
hick PMMA layer, the f
irst
Fabry
-
Pérot
resonant mode shifts out of spectral
window of our interest, we analyze the optical modulation with applying bias only in the
first six cases shown in
Supplementary
Fig
.
1
c (that is, for the thicknesses of the PMMA
layers of 0 nm, 22 nm, 3
7 nm, 167 nm, 210 nm
, and 250 nm).
3
Supplementary Figure
1
.
(a) Schematic of material combination for the reconstruction of MQW. (b)
Schematic of the planar MQW heterostructure. A dielectric PMMA layer is sandwiched between an Au film
and a layer of MQWs. The thickness of the PMMA film
t
can be varied during fabric
ation. (c) Measured
reflectance spectra of planar DBR/MQW/PMMA/Au heterostructures for different thicknesses of the PMMA
layer. In (c), the legend indicates the thickness of the PMMA layer.
Supplementary
Fig
.
2
shows the measured reflectance spectra of pl
anar
DBR/MQW/PMMA/Au heterostructures for different applied biases. Each subfigure of
Supplementary
Fig
.
2
corresponds to a different thickness of the PMMA layer
t
, which is
identified in the legend of the subfigure. Each curve shown in each subfigure of
S
upplementary
Fig
.
2
corresponds to the reflectance of the first
Fabry
-
Pérot
resonant mode
for the applied bias identified in the legend of
Supplementary
Fig
.
2
f. Our measurements
show stronger amplitude modulation and larger wavelength shifts at shorter wa
velengths.
To gain a deeper insight, we use the data displayed in
Supplementary
Fig
.
2
to extract
the measured bias
-
induced wavelength shift of the first
Fabry
-
Pérot
resonance supported
by the planar DBR/MQW/PMMA/Au heterostructure (see
Supplementary
Fig
.
3
). In
Supplementary
Fig
.
3
, the wavelength shift ∆
λ
is defined as an amount of the spectral shift
in the resonance position when the bias is changed from 0 V to
–
10 V, that is, ∆
λ
=
λ
–
10V
–
λ
0V
.
Supplementary
Fig
.
3
also displays a bias
-
induced variation
of the FWHM of the
considered
Fabry
-
Pérot
resonance as a function of wavelength.
4
Supplementary
Figure
2
.
Measured reflectance spectra of DBR/MQW/PMMA/Au heterostructure for
different PMMA thicknesses under different applied bias voltages.
In
Supplementary
Fig
.
3,
the FWHM difference is defined as a change in FWHM
when the applied bias changes from 0 V and
–
10 V. We observe that both the wavelength
shift ∆
λ
and the change in FWHM adopt larger values at shorter wavelengths. Our results
are consi
stent with the analysi
s described in the prior work
1
, which reports the III
-
V
compound MQW design used in our work. Based on the trend shown in
Suppleme
ntary
Fig
.
3
, we believe that the strongest refractive index modulation occurs at wavelengths very
close to the absorption band edge of our quantum wells, which we expect to corre
spond to
the wavelength of ~
915 nm.
5
930
940
950
960
970
980
0.0
0.2
0.4
0.6
0.8
1.0
Wavelength (nm)
(nm)
0.0
0.1
0.2
0.3
0.4
0.5
FWHM difference (nm)
Supplementary
Figure
3
.
Measured wavelength shifts (black dots) and (b) FWHM difference (blue dots) at
the first
Fabry
-
Pérot
resonant mode. The presented data is extracted from the curves shown in
Supplementary
Fig.
2
.
Supplementary Note 2
Calculation of m
ultipole d
ecomposition
To
further analyze the modes supported by the MQW metasurface
, we performed
a
multipole decomposition analysis using the charge
-
current expansion framework
2
-
4
.
In
our calculations, we account for contributions of electric
and magnetic dipoles,
quadrupoles, and octupoles
.
Supplementary Fig
.
4 shows results of the radiated electric
field intensity contributed from various electromagnetic multipoles
.
For
simplicity
, only
the first three leading terms are shown.
As expect
ed from the field distribution presented
in Figs. 2c and 2d,
the magnetic octupole
(which can be
interrupted
as a high
-
order Mie
resonance)
plays a significant role in the
optical response
under
x
-
polarized illumination.
6
Supplementary Figure 4.
Simulated
z
-
component of
far
-
field electric intensity
for electromagnetic
multipoles. For simplicity, only the first three leading terms are presented.
Asymmetry issue in hybrid Mie
-
GM resonant mode
To study how asymmetric slit positioning affects the op
tical performance of the
device (which is originally caused by the misalignment of the electron beam lithography
process), we calculated the reflectance for different values of the offset parameter
s
(see
Supplementary Fig. 5a). The offset parameter
s
is d
efined as the spatial displacement of
center of the topmost partially etched slits with respect to the underlying MQW slab. Since
the partially etched slits act as a light coupler and assist in excitation of guide
-
mode
(GM)
resonance, the generation of hyb
rid Mie
-
GM resonance is not significantly influenced by
the structural asymmetry. Our simulations show that the hybrid Mie
-
GM resonance exists
in all three cases,
s
= 0 nm, 40 nm, and 80 nm. However, this resonance blue
-
shifts when
the spatial offset (
s
) i
s increased. To observe significant optical modulation, we need to
ensure such high
-
quality resonance is spectrally located in the wavelength region where
the utilized MQW exhibits the largest index modulation (that is, from 915 nm to 920 nm).
Supplementar
y Fig
.
5(b) indicates that the largest acceptable spatial offset
s
is about 80 nm
(it is about 50 nm in our first fabricated MQW metasurface).
7
Supplementary Figure
5
.
(a) Schematic for the hybrid Mie
-
GM resonant metasurface. The unit element
dimensions are defined as follows:
w
c
= 180 nm,
g
= 100 nm,
t
= 1230 nm,
h
= 40 nm, and
p
= 910 nm. The
parameter
s
is defined as the spatial offset of the partially etched slits fr
om the center of the underlying MQW
slab. (b) Simulated reflectance spectrum
for different
spatial offset
s
s
.
Supplementary Note
3
Origin
of
the resonant modes in
MQW
resonators
To investigate the origin of each resonant mode in the MQW resonators, here we
perform the simulations
for the MQW structures
,
which
are comprised
of the partially
etched double
-
slits (see
Supplementary
Fig
.
6
a).
Note that in
Supplementary
Fig
.
6
a, the
air
gap between the resonant elements, which is otherwise present in the fabricated
structures, is absent.
Supplementary
Fig
.
6
b shows the simulated reflectance spectrum, in
which two resonant features are observed.
The spatial distribution of the
x
-
component
of
the
electric
field
intenstity
E
x
shows that the MQW layer supports
a
Fabry
-
Pérot
resonance
within the MQW layer
at the shorter
-
wavelength
r
e
sonant dip
(see
Supplementary
Fig
.
6
c)
.
Since
E
x
is primarily enhanced
in the spatial region between the groups of double
-
slits, this
Fabry
-
Pérot
cavity resonance
will be strongly suppressed when
the fully etched air gap is
present
(see
Supplementary
Fig
.
7
a)
.
H
owever, we still
observe
strong filed enhancement
within the ful
ly etched air gap, which is mainly from the near
-
field interaction
between
MQW slabs (see
Supplementary
Fig.
7
a).
More interestin
g
ly, the double
-
slit structure can
assist in exciting a guided
-
mode resonance (GMR)
, resulting in the
large
E
z
intensity at the
topmost
interface
of
the MQW
structure
(see
Supplementary
Fig.
6
d).
Concurrently
, we
observe a quite signifcant
E
z
intensity
inside the MQW layer (see
Supplementary
Fig.
6
d).
On the other hand,
for the longer
-
wavelength resonant dip,
we
observe that the double
-
slit
8
stru
cture act
s
as a
coupler
,
which
effectively guide
s
the incident light into the MQW layer
,
yielding
a strong field confinement in the slits, as shown in
Supplementary
Fig.
6
c
.
As a
result, a
Fabry
-
Pérot
-
like resonance can still
survive
when the MQW la
y
er is truncated (see
Supplementary
Fig.
7
b).
This light coupler can
also
weakly
convert the incident electric
field from
x
-
to
z
-
component, as shown in
Supplementary
Fig.
6
d
.
Supplementary Figure
6
.
(a)
Schematic for
the simulated structure
. The unit element dime
nsions are defined
as follows:
w
= 180 nm,
g
= 100 nm,
t
= 1230 nm,
h
= 40 nm
, and
p
=
910 nm.
(b) Simulated reflectance
spectrum of the
double
-
slit structure illustrat
ed in (a). (c) and (d) show the spatial distributions of the
E
x
and
E
z
intensities at the wavelengths corresponding to the
spectral
dips.
The incident polarization is along
x
-
axis.
Supplementary
Figure
7
.
Simulated
x
-
component of electric field
intensity in MQW resonator
at
a
wavelength of (a) 915.9 nm and (b)
936.3
nm, respectively.
9
Supplementary Note
4
Mode
splitting in
the
hybrid Mie
-
GM resonant
metasurface
905
915
925
935
945
0
20
40
60
80
Reflectance (%)
Wavelength (nm)
Supplementary Figure
8
.
Simulated reflectance spectrum of a Mie
-
GM resonant metasurface under an
x
-
polarized normal illumination. Here, we extend the wavelength range to shorter wavelengths as compared to
the wavelength range over which we performed our simulations. The structura
l parameters are identical to
the ones described in Fig. 2.
Supplementary Note
5
Optical setup for
measurement of reflectance spectrum
To
optically characterize the reflectance of
the
MQW metasurface, w
e utilized a
coherent NIR laser beam
(
Toptica
Photonics CTL 950
)
as a light source
and a power meter
as a detector (
Thorlabs PM100D
)
, as shown in Supplementary Fig.
9
. A
n uncollimated
white light source from a halogen lamp
is used
to visualize the sample surface. When
measuring the
reflectance spectra
,
t
he laser beam was focused using a long working
distance objective with 10× magnification and 0.28 numerical aperture.
Supplementary Figure
9
.
Schematic of optical setup used for spectral measurement.
M: mirror; ND: neutral
density filter
(Thorlabs
ND
C
-
50C
-
4M
)
; I: iris; L: lens; P: linear polarizer
(Thorlabs
LPNIR100
-
MP
)
; BS:
10
beam splitter
(Thorlabs
CCM1
-
BS014
)
; O: objective
(
Mitutoyo
10× magnification
with
0.28 numerical
aperture
)
; PM: power
meter
.
Measured
a
bso
l
u
te
reflectance modulation
Supplementary Figure
10
.
Measured absolute reflectance modulation ∆
R
of the hybrid Mie
-
GM resonant
metasurface.
Supplementary Note
6
Influence of
oblique illumination on the
optical diffraction
Because of the slight difference in structural period (910
nm) and laser wavelength
(917 nm), optical diffraction can influence the far
-
field radiation pattern when the incident
angle is non
-
zero. To clarify this point, we performed numerical simulations of the far
-
field
radiation patterns for the MQW metasurface
at 0
V with different angles of incidence. As
shown in Supplementary Fig. 11a, we found that strong optical diffraction appears even
when the incident angle is 5°. However, those diffracted beams' intensities are high
compared as to the intensity of the ze
ro
-
order beam, which is not observed in our
measurements. This can be attributed to two different reasons; first, their diffraction angles
are too large to be collected (based on the numerical aperture of the objective we used, the
largest angle collected
is about 16°) and second, the incident angle is almost zero in the
real case. To experimentally eliminate this effect, we intentionally slightly defocused the
laser beam onto the MQW metasurface when performing the far
-
field radiation
measurements to minim
ize the incident angle.
11
To further verify the influence of non
-
zero incident angle on the far
-
field radiation
pattern, we performed other simulations which numerically demonstrate the active
switching of the first
-
order diffracted beam at different angles
of incidence. As shown in
Supplementary Fig. 11b, the intensity of the first
-
order diffracted beams are much h
igh
er
as compared with the specularly reflected beam
when the incident angle is greater than 5
°
,
which is in conflict with our measurement result
s
shown in Figs. 4d and 4e
. As a result, we
conclude that the MQW metasurface is under almost normal illumination (
0
°
≦
θ
in
≦
5
°
),
and the non
-
zero incident angle caused optical effect is fairly small in the real case. It is
worth noting that the first
-
ord
er diffracted beams can only be observed when electrical bias
is applied, indicating that the demonstration of active switching of first
-
order diffracted
beam is still valid even when the MQW metasurface is under oblique illumination.
Supplementary Figure
1
1
.
(a)
Simulation of far
-
field radiation patterns under oblique illumination
without
electrical bias. Strong diffraction can be observed when the incident angle is greater than 5
°
. (b) Simulation
of active switching of first
-
order dif
fraction for the case of normal (left panel) and oblique (middle and right
panels) illumination. Overall, the diffracted beams show much stronger intensity when incident angle is
greater than 5
°
. The incident wavelength is fixed at 917 nm.
12
Supplementary
Note
7
Theoretical analysis and
experimental
m
easurement
of
high
-
speed reflectance
modulation
We first
theoretically
estimate the modulation speed of the MQW metasurface. The
conductivity of the p
-
GaAs (with doping level of 10
19
cm
-
3
):
휎
=
푞푝
휇
푝
=
1
.
6
푥
10
−
19
∙
1
푥
10
19
∙
67
≅
107
[
1
Ω
∙
cm
]
(1)
where
q
is the electron charge,
p
is the carrier concentration,
μ
p
≅
67
[
cm
2
V
∙
s
]
is the
hole
mobility
5
. The RC delay of
the MQW system is
푅퐶
=
퐿
휎
푑
1
푤
MQW
휀
0
휀
푟
퐿
푤
MQW
푑
=
퐿
2
휀
0
휀
푟
휎
푑
1
푑
=
1
.
816
푥
10
−
9
[
s
]
(
2)
where
L
= 100 μm and
w
MQW
is the length and width of
the
hybrid Mie
-
GM resonant
structure respectively,
d
1
is the thickness of p
-
GaAs,
d
is the thickness of MQW,
ε
0
is the
permittivity in vacuum, and
ε
r
= 13.5 is the dielectric constant
6, 7
of the MQW. Therefore,
the estimated highest modulation
frequency
f
is:
푓
=
1
2
휋푅퐶
=
87
.
66
[
MHz
]
(3)
To experimentally evaluate the modulation speed of our MQW metasurface, an AC
electrical bias with frequencies of 0.1 MHz and 1 MHz is applied to the sample and a high
-
speed InG
aAs detector is used to detect
the te
mporal amplitude response (see
Supplementary Fig. 12a). As shown in Supplementary Fig. 12b, high
-
speed amplitude
modulation with 0.1 MHz frequency bandwidth is performed.
Modulation speed as high as
1 MHz is also demonstrated, which is on the order of the
theoretical expectation
.
The
difference between the theoretical calculation and the measured response is likely due to
the deviation between parameters (conductivity, dielectric constant,
etc
) used in
calculations and those of the real sample as well as
the fact that the contact resistance is
not taken into account in the theoretical estimation
.
In principle, the quantum confined
Stark effect can
yield
the devices operating with GHz modulation speed if the intrinsic RC
delay is further minimized, which ca
n be accomplished by reducing the length of resonators,
increasing the thickness of p
-
GaAs,
etc
. Note that the signal is distorted in the case of 1
MHz modulation speed due to the bandwidth limitation of the power amplifier
.
13
Supplementary
Figure
1
2
.
Experimental performance of modulation speed
measurement
in
all
-
dielectric
MQW metasurface. (a) Schematic of the optical setup combined with a hi
gh
-
speed detector (Thorlabs
DET
10C) and an oscilloscope (Tektronix TDS 2001C). The AC electric field is applied
from a function
waveform generator (Keysight 33220A) combined with a power amplifier (Thorlabs HVA200). (b) The
measured results of temporal response of hybrid Mie
-
GM metasurfaces. Blue curve: 1 MHz, red curve: 0.1
MHz. The wavelength of incident light is
fixed at 917 nm.
Supplementary Note
8
Measurement of
the
far
-
field radiation pattern
Supplementary
Figure
1
3
.
Experimental results of far
-
field radiation intensity profile under different
applied biases. No first diffraction order
is
observed at a wavelength of 924
nm even when the applied bias
voltage is
-
10 V.
14
Supplementary
Note
9
Optical
response and
modulation of the
beam steering
metasurface
Supplementary
Figure
1
4
.
(a
)
Simulated
reflectance
spectra
of
the
second hybrid
Mie
-
GM
resonator
array
for different applied bias voltages
. The
incoming light is polarized perpendicularly to the
MQW
stripes.
Structural parameters:
w
1
= 1
0
0 nm,
w
2
= 120 nm,
w
= 110 nm,
g
t
= 110 nm,
g
u
= 90 nm,
t
=
123
0 nm, and
h
= 80 nm
.
The periodicity
p
is 780 nm. (b)
Simulated
electromagnetic field profiles
at
a
wavelength of 917
nm.
Supplementary
Figure
1
5
.
(a) Measured reflectance spectra of the second Mie resonator array for different
applied bias voltages. The incoming light is polarized perpend
icularly to the MQW stripes. (b) Measured
relative reflectance of the second hybrid Mie
-
GM
resonant metasurface as a function of wavelength and
applied voltage. We consider the wavelength range from 915 nm to 925 nm with a step of 1 nm. Here, the
reflectan
ce of resonator under a
-
10 V bias is utilized as the reference. (c)
Measured phase modulation at two
different wavelengths. Red: 917 nm, blue: 924 nm.
Each data point corresponds to an average phase shift
measured at four different positions on the sample
while each error bar indicates the standard deviation of
the obtained four data points.
15
Supplementary
Note
10
Simulation of far
-
field radiation pattern
of the beam steering metasurface
with
varying lattice constant
Λ
Supplementary
Figure 1
6
.
Simulated
results of far
-
field
beam steering by changing the periodicity of
metasurface
Λ
.
The total number of metasurface unit element is assumed
to be (a)
3
0 and (b)
12
0. Black
arrows indicate the position of the first diffraction order. Incident
wavelength: 917 nm.
In order to take the
finite aperture effect into account, the top hat is utilized as the illumination condition when processing the far
field projection in Lumerical FDTD simulation.
Supplementary
Note
1
1
Measured
J
-
V curves of MQW
resonators
Supplementary Fig. 17 shows the measured leakage current density of two MQW
resonators. To avoid the dielectric breakdown, we applied a moderate bias ranging from 0
V to
-
10 V. For both of our samples, the measured current density is on the ord
er of mA/cm
2
,
which is much lower than the current density values (on the order of of ~kA/cm
2
) necessary
for observation for carrier
-
induced refractive index change in GaAs
-
based III
-
V
semiconductor compounds
8
-
10
.