Reviewers' Comments:
Reviewer #1:
Remarks to the Author:
The manuscript is devoted to realization of electrically tunable metasurface based on III
-V
compound semiconducting MQW structures as resonant metasurface elements. The metasurface
consists of an array of two
-dimensional hybrid Mie
-guiding mode resonators which exhibit an
actively tunable optical response under applied bias in the near
-infrared wavelength range. The
amplitude and phase of the light reflected from the metasurface is shown to be continuously tuned
by applying DC electric field across the MQW metasurface elements, with a tunable optical
response from the quantum
-confined Stark effect. The topic of research presented is novel,
combination of the well-
established MQW technology with active subwavelength nanoantennas
seems modern and prospective. Two main experimental finding can be pointed out. The first one is
detection of large relative reflectance modulation of the metasurfcae (~270%) and a continuous
phase shift from 0° to 70° at the resonant wavelength of 917 nm. The second one is
demonstrati
on of the dynamic diffraction grating by electrically connected metasurface elements in
groups of three. In this case, the application of external bias leads to the appearance of diffraction
orders which can be treated as a beam steering.
The manuscript can be published in Nature Communications after minor revisions reflecting
following points.
1. The operation frequency of the device shown. The authors stated that “Since the amplitude
modulation is achieved via the electro-
optic effect rather than charge
carrier injection, the intrinsic
modulation frequency of our device can be GHz or higher”. However, amplitude of the external
bias is relatively small (several volts) and I do not see any experimental difficulty in application of
AC electric field in orde
r to obtain the temporal performance of the metasurface by lock
-in
technique. It would be great if authors perform these experiments.
2. Beam steering is achieved by switching the diffraction orders of dynamic grating. The efficiency
of such effect is rel
atively low. Is it possible to increase the ratio between diffracted and mirror
reflected beams?
3. Please check the Ref 3.
Reviewer #2:
Remarks to the Author:
The authors experimentally demonstrate electro
-optical tuning of an all-
dielectric metasu
rface
based on the quantum
-confined Stark effect in III
-V multiple quantum wells.
Tunable metasurfaces are a hot topic, and the employed tuning mechanism is novel in this context
and has good technical potential. Also, generally the work is well written and presented. However,
there are some technical issues and unclear aspects which need to be resolved. Therefore, the
following points should be addressed before the paper can be published in Nature
Communications:
-The design of the metasurface is not v
ery well motivated. Why is such a complicated resonator
geometry chosen, which supports a Mie resonance coupled to a guided mode resonance? Would
this approach also work with more common resonant dielectric metasurface geometries, having
e.g. electric and magnetic dipole Mie resonances? Also, the partially etched slits are
asymmetrically positioned with respect to the larger resonators. Does this asymmetry serve a
particular purpose? Finally, it would be helpful to add in the Supplementary Material a multip
ole
analysis of the higher
-order Mie modes, since from the mode profiles they cannot be identified
with typical Mie resonances.
-In the abstract and the main body of the manuscript, relative reflectance modulations are quoted.
However, if using the low r
eflectance value as the reference which appears in the denominator, the
relative reflectance modulation can get very high at wavelengths of low reflectivity. The 270%
achieved in this work sound a lot, but compared to the ideal modulator, which would have a value
of infinity for this measure, it is a moderate tuning performance. Also, in the wavelength range
where the relative reflectance modulation is highest, the maximum reflectance of the metasurface
is below 50%, which is not sufficient for high
-efficie
ncy devices. It would be more useful to quote
absolute reflectance values or the absolute reflectance modulation, also to allow fair comparison
with other tunable metasurfaces.
-On page seven it is stated „Higher
-order diffracted beams are absent since t
he period of the
sample is subwavelength p=910 nm at 0 V bias.“ On the same page, it also says: „The dynamic
diffraction pattern measurements have been performed at a wavelength of 917 nm...“. Thus, the
wavelength is very close to the lattice constant. For p
erfectly normal incidence and reflectance,
indeed no diffraction should occur (at least in reflection, which is considered here). However, for
slightly tilted incidence, as it effectively occurs when illuminating the sample with an objective or a
lens, dif
fractive orders will occur starting from some critical angle. The authors should provide
details of the measurement setup (in particular the NA of the focussing lens, if applicable) used to
measure the data presented in Fig. 3b and discuss the occurence of
diffraction under the relevant
conditions.
-The part on beam steering requires a more critical description and discussion. Usually, for a beam
steering device or also the other applications mentioned in the outlook (metalenses with
reconfigurable focal length, flat spatial light modulators etc), one would expect the strongest
(typically the fundamental) reflected or transmitted order to be manipulated. In this work, it is
only the first diffraction order, which carries only a small fraction of the reflec
ted intensity, that
can be manipulated. Also, there are first
-order beams. Therefore, I would rather consider this
structure a reconfigurable diffraction grating, not so much a beam steering device. For beam
steering, I would also expect to see a (quasi) continuus variation of the angle, whereas only
discrete angles can be achieved with the demonstrated device. In the light of these arguments, the
authors may want to consider renaming the device, which also affects the title of this work.
Reviewer #3:
Remarks to the Author:
In this manuscript, the authors take advantage of the strong quantum
-confined Stark effect in
multiple quantum well (MQW) structures to control the effective refractive index of the micro-
resonators and constructed metasurfaces base
d on those micro-
resonators. The authors
demonstrated the effective tuning of the refractive index, which resulted in substantial changes in
reflectance and large shifts of the phase of the reflected beam. The authors also showed dynamic
beam steering by c
ontrolling the refractive index distribution in the micro-
resonators to achieve
the modulation of the effective periodicity of the grating structure. But there are several issues
that need to be resolved. I would recommend publication of this manuscript if
the following
questions are successfully addressed.
1. The authors claimed that the resonance studied in this work is from the coupling of a Mie
resonance and a guided mode resonance. But in most cases when two resonances couple to each
other, there will be interferences and mode-
splitting or Fano-
type of resonances will be observed.
The mode studied here does not show those behaviors, why?
2. The authors concluded that the modulation is from pure electro-
optic effect. How did they
exclude the contribu
tion of the carrier injection? Some detailed analysis will be very helpful to
clarify this issue.
3. The authors showed a -
1° average phase shift at a wavelength of 924nm. How much is the
error level in the phase shift measurement? Although the -
45% chan
ge in the reflection is not as
high as the 270% change at 917nm, it’s still substantial. On the other hand, the -
1° phase shift is
quite small, which does not match the level of reflection change if we consider the K
-K relation.
Clarification is needed her
e. I noticed that there are some oscillations in the phase shift for 924nm
wavelength. Is that just noise or real oscillation? Did the author go beyond the 0V to -
10V range to
find out the trend?
4. In the beam steering results, multiple diffraction beam
s were observed, especially in the second
graph (red curve), there are two more beams with similar intensities as the claimed 1st order
beams. What are they and why are they not considered as the 1st order beams?
5. In the sentence "where the first diffr
action order angle becomes smaller as the metasurface
periodicity of is reduced via electrical control" (page 8), there are either some words missing or
the word "of" should be removed.
In this response letter, we offer a detailed poi
nt-by-point reply to each of the reviewers’
comments. Our responses are shown
in blue
.
REVIEWERS' COMMENTS:
Reviewer: 1
The manuscript is devoted to realization of
electrically tunable metasurface based on III-V
compound semiconducting MQW structures as res
onant metasurface elements. The metasurface
consists of an array of two-dimensional hybrid
Mie-guiding mode resonators which exhibit an
actively tunable optical response under applied bi
as in the near-infrared wavelength range. The
amplitude and phase of the light reflected from
the metasurface is shown to be continuously
tuned by applying DC electric field across th
e MQW metasurface elements, with a tunable
optical response from the quantum-confined Stark
effect. The topic of research presented is
novel, combination of the well-establishe
d MQW technology with active subwavelength
nanoantennas seems modern and prospective. Tw
o main experimental
finding can be pointed
out. The first one is detection
of large relative reflectance modulation of the metasurfcae
(~270%) and a continuous phase shif
t from 0° to 70° at the resonant wavelength of 917 nm. The
second one is demonstration of the dynamic di
ffraction grating by electrically connected
metasurface elements in groups of three. In this ca
se, the application of external bias leads to the
appearance of diffraction orders which can be treated as a beam steering.
The manuscript can be published in
Nature Communications
after minor revisions reflecting
following points.
We thank the reviewer for the positive evalu
ation of our work and the recommendation for
publication after minor revisions.
1.
The operation frequency of the device shown. Th
e authors stated that “Since the amplitude
modulation is achieved via the electro-optic eff
ect rather than charge
carrier injection, the
intrinsic modulation frequency of our device ca
n be GHz or higher”. However, amplitude of
the external bias is relatively small (sever
al volts) and I do not
see any experimental
difficulty in application of AC electric field in
order to obtain the temporal performance of
the metasurface by lock-in technique. It w
ould be great if authors perform these
experiments.
We thank the reviewer for this comment. We
agree with the reviewer that high speed
measurements can allow us to feasibly examine the modulation speed of MQW metasurfaces,
which is an important parameter for tunable met
adevices. To obtain the temporal performance
and experimentally evaluate the
modulation speed of our MQW
metasurface, we performed
amplitude modulation measurements with applicat
ion of an AC electric field. The measured
temporal response reveals that (see Supplemen
tary Fig. 12b) the modulation speed of our
fabricated MQW metasurface is on the order of
MHz. We also theoretically estimate the RC
delay in our MQW system (see Supplementary Note
7). The calculations s
how that the highest
modulation speed can be on the or
der of MHz, which agrees well w
ith the measured results. We
emphasize that our device, which exploits the
quantum confined Stark effect, can access its
inherent limiting bandwidth operating with GHz m
odulation speed if the in
trinsic RC delay is
further minimized (Lewen, R., Irmscher, S., Wester
gren, U., Thylen, L. & Eriksson, U. Segmented
transmission-line electroabsor
ption modulators. J. Light
wave Technol. 22, 172-179 (2004)).
Nonetheless, MHz modulation is
adequate for many applications such as, e.g., LiDAR. Based on
these analyses, we added the following discussion
and figures to the main text as well as the
Supplementary Information.
We revised the sentence in
the main manuscript:
On Page 6
“... the intrinsic modulation frequency of our device can be MHz
(see Supplementary Fig. 12) or
higher
31, 45, 46
”
We also added the following paragraph and figure
to the Note 7 of Supplementary Material:
“We first theoretically estimate the modula
tion speed of the MQW metasurface. The
conductivity of the p-GaAs
(with doping level of 10
19
cm
-3
):
ߤݍ=ߪ
=1.610ݔ
ିଵଽ
∙110ݔ
ଵଽ
∙67≅107 [
ଵ
ஐ∙ୡ୫
]
,
where
q
is the electron charge,
p
is the carrier concentration,
μ
p
≅ 67
[
ୡ୫
మ
∙ୱ
]
is the hole mobility
5
.
The RC delay of the MQW system is
= ܥܴ
ఙௗ
భ
௪
్
ఌ
బ
ఌ
ೝ
௪
్
ௗ
ܮ =
ଶ
ఌ
బ
ఌ
ೝ
ఙௗ
భ
ௗ
=1.81610ݔ
ିଽ
[
s
]
,
where
L
= 100
μ
m 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
=݂
ଵ
ଶగோ
=87.66 [MHz]
.
To experimentally evaluate the modulation sp
eed 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 InGaAs
detector is used to detect the temporal am
plitude 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 deviat
ion 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 th
eoretical estimation. In
principle, the quantum
confined Stark effect can yield
the devices operating with GHz m
odulation speed if the intrinsic
RC delay is further minimized, which can be accom
plished by reducing the
length of resonators,
increasing the thickness of p-GaAs,
etc
. Note that the signal is di
storted in the case of 1 MHz
modulation speed due to the bandwidth limitati
on of the power amplifier.”
Supplementary Figure 12.
Experimental performance of modulation speed measurement in all-dielectric MQW
metasurface. (a) Schematic of the optical setup combined
with a high-speed detector
(Thorlabs DE
T10C) and an
oscilloscope (Tektronix TDS 2001C). The AC electric fi
eld 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 MH
z. The wavelength of incident light
is fixed at 917 nm.
with three additional references
5. Casey H. C., Stern F. Concentrationdepe
ndent absorption and s
pontaneous emission of
heavily doped GaAs.
J. Appl. Phys.
47
, 631-643 (1976).
6. Brennan K., Hess K. High field
transport in GaAs, InP and InAs.
Solid State Electron.
27
,
347-357 (1984).
7. Won-Pyo H., Bhattacharya P. K. High-fiel
d transport in InGaAs/InAlAs modulation-doped
heterostructures.
IEEE T. Electron. Dev.
34
, 1491-1495 (1987).
2.
Beam steering is achieved by switching the di
ffraction orders of dynamic grating. The
efficiency of such effect is relatively low.
Is it possible to increase the ratio between
diffracted and mirror reflected beams?
We thank the reviewer for bringing up this point.
In principle, it is possible to increase the
ratio between diffracted and mi
rror reflected beams by us
ing the all-dielectric MQW
metasurface design discussed in our work. To impr
ove the directivity (which is defined as the
peak intensity ratio between diffracted and mirror
reflected beams), we need to have an almost
constant reflectance accompanied with large phase shift when applying electrical bias. These
conditions can be satisfied as
long as the MQW system can prov
ide a substantia
l change in the
real part of the refractive index,
Δ
n, to sufficiently shift the
resonances, and maintain a small
change in imaginary part of the refractive index (absorption),
Δ
k, to enable a sharp resonance
within operation wavelength range. As a re
sult, the larger th
e figure of merit,
Δ
n/
Δ
k of MQW,
the larger tunable phase shift c
an be observed. The large tunable
phase shift would yield the
reflected beam with higher directivity. The
Δ
n/
Δ
k of the MQW utilized in this work is 1-5 (see
Google Patents, assignee US20150286078A1 2015). As
a proof of concept, we designed a
tunable metasurface with an asymmetric coupl
ed quantum well (ACQW) which can possess a
larger
Δ
n/
Δ
k equal to 10-18 (see IEEE J. Quant
um Elect. 34, 1197-1208 (1998)). The
metasurface unit element is still based on the double-
slit structure, as shown in Fig. R1a. After
structural optimization, we found that about 200
°
phase shift with a
Δ
n of 0.02 can be obtained
(see Fig. R1b). The simulated far-field radiation pa
tterns show that in this case, the intensity of
steered beam is much higher than the in
tensity of the specula
rly reflected beam.
Figure R1. Simulated QW resonant metasurface with higher
Δ
n/
Δ
k. (a) A schematic for all-dielectric asymmetric
coupling quantum well (ACQW) metasurface. The unit element dimensions are defined as follows: w
c
= 90 nm, w =
60 nm, g = 100 nm, t = 1230 nm, and h = 80 nm. The periodicity p is 560 nm. (b) Simulated phase shift as a function
of
Δ
n of an ACQW resonant metasurface under an x-polarized normal illumination. (c) Simulated intensity of the
scattered light in the far-field as a function of diffraction ang
le. The plotted diffracted light intensity is normalized to
the light intensity at 0°. Right panel shows the corresponding phase profile for each case. The first-order diffracted
beam shows much higher intensity as compared to intensity of the specularly reflected beam. The phase shift and
light intensity are plotted for a wavelength of 808.8 nm. Black arrows indicate the position of the first-order
diffracted beams. Due to the spatial symmetry, only half of
the radiation pattern is presented. The total number of
unit elements is set at 120.
To address this issue, we revised the di
scussion of the last part of main text:
On Page 9 of the main text
“The performance of the proposed
all-dielectric meta
surface with hybrid Mi
e-GM resonance can
be further improved by utilizing alternative QW
systems which exhibit larger modulation of the
real part of the refractive index and lower optical
loss as compared to the QW used in the present
work
51, 52
(see Supplementary Note 13)”
with an additional reference
52. Hao F., Pang J. P., Sugiyama M., Tada K., Naka
no Y. Field-induced optical effect in a five-
step asymmetric coupled quantum
well with modified potential.
IEEE J. Quantum Elect.
34
,
1197-1208 (1998).
We also added a paragraph and a figure to
the Supplementary Material.
Supplementary Note 13
Improvement of optical performance
“To improve the optical performance, the quant
um well system has to provide a substantial
change in the real part of the refractive index,
Δ
n
, to sufficiently shift the resonances, and
maintain a small change in the imaginar
y part of refractive index (absorption),
Δ
k
, to enable a
sharp resonance within the operating wavelength range.
As a result, the larger the figure of merit,
Δ
n
/
Δ
k
of a quantum well, the better optical perf
ormance can be achieved in the tunable
metasurface. As a proof of concept, we desi
gned a tunable metasurface with an asymmetric
coupled quantum well (ACQW)
which can possess a larger
Δ
n
/
Δ
k
(about 10-18)
11
. As a
comparison, the
Δ
n
/
Δ
k
of the utilized MQW in this work
is 1-5 (see Ref. 1). The unit element
is also based on the double-slit
structure, as shown
in Supplementary Fig. 18a. After structural
optimization, we found that about 200
°
phase shift with a
Δ
n
of 0.02 can be obtained at a
wavelength of 808.8 nm (see Supplementary Fig.
19b). We also numerically study the beam
steering functionality using such an ACQW me
tasurface, which is realized by varying the
periodicity of the metasurface (see Supplementary
Fig. 19c). The simulated far-field radiation
patterns even show that the intensity of the steere
d beam is much higher than the intensity of the
specularly reflected beam when th
e utilized QW possesses larger
Δ
n
/
Δ
k
. These results indeed
verify that the optical performance (in particul
ar, directivity, which is defined as the peak
intensity ratio between diffracted and mirror re
flected beams) of tunable quantum well-based
metasurfaces can be significantly improved when the quantum well system exhibits larger
Δ
n
/
Δ
k
. Since this is a proof-of-concept demons
tration, the working wavelength here (
λ
= 808.8 nm)
is slightly different from the one used in th
e main manuscript. By
appropriately choosing a
quantum well, we can shift the operation
wavelength to the range of interest
12, 13
.”
Supplementary Figure 19
. Simulated QW resonant
metasurface with higher
Δ
n
/
Δ
k
. (a) A schematic for all-
dielectric asymmetric coupling quantum well (ACQW) me
tasurface. The unit element dimensions are defined as
follows:
w
c
= 90 nm,
w
= 60 nm,
g
= 100 nm,
t
= 1230 nm, and
h
= 80 nm. The periodicity
p
is 560 nm. (b)
Simulated phase shift as a function of
Δ
n
of an ACQW resonant metasurface under an
x
-polarized normal
illumination. (c) Simulated intensity of the scattered light
in the far-field as a function of diffraction angle. The
plotted diffracted light intensity is normalized to the light
intensity at 0°. Right panel shows the corresponding phase
profile for each case. The first-order diffracted beam shows much higher intensity as compared to intensity of the
specularly reflected beam. The phase shif
t and light intensity are plotted for a wavelength of 808.8 nm. Black arrows
indicate the position of the first-order
diffracted beams. Due to the spatial symmetry, only half of the radiation
pattern is presented. The total number of unit elements is set at 120.
with three additional references
11. Hao F., Pang J. P., Sugiyama M., Tada K., Na
kano Y. Field-induced optical effect in a five-
step asymmetric coupled quantum
well with modified potential.
IEEE J. Quantum Elect.
34
,
1197-1208 (1998).
12. Xu Z., Wang C., Qi W., Yuan Z. Electro
-optical effects in strain-compensated
InGaAs/InAlAs coupled quantum wells with modified potential.
Opt. Lett.
35
, 736-738 (2010).
13. Mohseni H., An H., Shellenbarger Z. A., Kwak
ernaak M. H., Abeles J. H. Enhanced electro-
optic effect in GaInAsP–InP three-step quantum wells.
Appl. Phys. Lett.
84
, 1823-1825 (2004)
3.
Please check the Ref 3.
We thank the referee for
pointing this out. The authors’ names in Ref. 3
are checked and revised
.
3. Haffner C., Heni C., Fedoryshyn Y., Niegema
nn J., Melikyan A., Elder D. L., et al. All-
plasmonic Mach–Zehnder modulator enablin
g optical high-speed communication at the
microscale.
Nat. Photon.
9
, 525-528 (2015).
Reviewer: 2
The authors experimentally dem
onstrate electro-optical tuning of
an all-dielectric metasurface
based on the quantum-confined Stark eff
ect in III-V multiple quantum wells.
Tunable metasurfaces are a hot topic, and the
employed tuning mechanis
m is novel in this
context and has good technical poten
tial. Also, generally the work
is well written and presented.
However, there are some technical issues and
unclear aspects which need to be resolved.
Therefore, the following points should be addres
sed before the paper can be published in Nature
Communications:
We are thankful to th
e reviewer for th
e positive evaluation of our
work. We address the points
brought up by the reviewer below.
1.
The design of the metasurface is not very
well motivated. Why is such a complicated
resonator geometry chosen, which supports a Mie resonance coupled to a guided mode
resonance? Would this approach also work
with more common
resonant dielectric
metasurface geometries, having e.g. electric
and magnetic dipole Mie resonances? Also, the
partially etched slits are asymme
trically positioned with respect to the larger resonators. Does
this asymmetry serve a particular purpose?
Finally, it would be helpful to add in the
Supplementary Material a multipole analysis of
the higher-order Mie modes, since from the
mode profiles they cannot be iden
tified with typical Mie resonances.
We thank the reviewer for bri
nging up this point. First, we
would like to mention that
because of the relatively low index change of
the experimentally impl
emented MQW (modulation
of the real part of the refr
active index is on the order of
Δ
n = 0.01), fundamental electric and
magnetic dipolar Mie resonances
would not exhibit significant opt
ical modulation under applied
bias. This is because of the modest quality
factor of the fundamenta
l electric and magnetic
dipolar Mie resonant modes. Therefore, in our
work we utilize a resonator geometry supporting
higher order modes, which exhibit a
higher quality factor at resonance.
To motivate the choice of the utilized hybrid Mi
e-GM resonant metasurface element, we added
the following sentence to the revised manuscript:
On Page 5
“Since our MQWs exhibit relativ
ely modest refractive index ch
ange under applied bias, the
designed metasurface element has to support hi
gh quality factor resonant mode near the
semiconductor band edge in order to exhibit si
gnificant optical modulation under applied bias.
The fundamental electric or magnetic dipole modes of
typically utilized diel
ectric resonators do
not possess sufficiently
high quality factors.”
We also thank the reviewer for asking about th
e reasons behind the asymmetric placement of
the partially etched slits. This asymmetry is from
the misalignment of the two-step electron beam
lithography processes. To study how asymmetric
slit positioning affects the optical performance
of the device, we calculate the reflectance of
the metasurface for different positions of the
topmost slits with respect to
the center of the MQW slab, as s
hown in Fig. R2. 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 s
patial offset (s) is increased. To observe
significant optical modulation, we need to en
sure such high-quality re
sonance is spectrally
located in the wavelength region where the utili
zed MQW exhibits the la
rgest index modulation
(that is, from 915 nm to 920 nm). Figure R2(b) indi
cates that the largest a
cceptable spatial offset
s is about 80 nm (it is about 50 nm in
our first fabricated MQW metasurface).
Figure R2. (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 from the
center of the underlying MQW slab. (b) Simulated reflectance
spectrum for different spatial offsets s.
To address this issue, we added the followi
ng discussions and figure to the revised
Supplementary Information
.
Supplementary Note 2
Asymmetry issue in hybrid Mie-GM resonant mode
“To study how asymmetric slit pos
itioning affects the
optical 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 defined as the spatial disp
lacement of center of the topmost
partially etched slits with respect to the underlyi
ng MQW slab. Since the partially etched slits act
as a light coupler and as
sist in excitation of guide-mode res
onance, the generation of hybrid 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
) is increased. To observe
significant optical modulation, we need to ensu
re 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). Supplementary Fi
gure 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).”
Supplementary Figure 5.
(a) Schematic for the hybrid Mie-GM resona
nt metasurface. The un
it 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
from the center of the underlying MQW slab. (b) Simulated
reflectance spectrum for
different spatial offsets
s
.
Finally, we agree with the reviewer that
the multipole decomposition analysis will be
instrumental for understanding the high-order
Mie-GM resonance excited within the MQW
metasurface. Thus, we performed a calcul
ation based on the char
ge-current expansion
framework
(Phys. Rev. B 89, 205112 (2014); ACS Nano 12, 1920-1927 (2018); Light: Science &
Applications 7, 17158 (2018)). To clearly class
ify the contribution of each electromagnetic
multipole, fundamental (electric dipole) and high-
order modes (magnetic di
pole, electric and
magnetic quadrupoles and octupoles) are considered
in the calculation. According to the
calculated results, the magnetic oc
tupolar mode dominates the spectra
l range of interest. This is
consistent with the simulated field
profiles shown in Figs. 2c and 2d.
To address this issue, we added the follo
wing discussion in revised manuscript.
On Page 5
“The calculated field profiles show that at
a wavelength of 915.9 nm, the metasurface element
supports a high-order Mie resonance (left im
ages in Figs. 2c and 2d). The multipole
decomposition analysis
48-50
shows that the support
ed high-order Mie resonant mode is dominated
by the magnetic octupolar mode (see Supplementary Note 2).”
with three additional references:
48.
Savinov V., Fedotov V. A., Zheludev N. I.
Toroidal dipolar excitation and macroscopic
electromagnetic properties of metamaterials.
Phys. Rev. B
89
, 205112 (2014).
49.
Wu P. C., Liao C. Y., Savinov V., Chung T.
L., Chen W. T., Huang Y.-W., et al. Optical
anapole metamaterial.
ACS Nano
12
, 1920-1927 (2018).
50.
Zhu A. Y., Chen W. T., Za
idi A., Huang Y.-W., Khorasaninejad M., Sanjeev V., et al.
Giant intrinsic chiro-optical activity
in planar dielectric nanostructures.
Light: Science &
Applications
7
, 17158 (2018).
We also added the following discussions and figu
re to the revised Supp
lementary information.
Supplementary Note 2
Calculation of multipole decomposition
“To further analyze the modes supported by th
e MQW metasurface, we performed a multipole
decomposition analysis using the ch
arge-current expansion framework
2-4
. In our calculations, we
account for contributions of electric and ma
gnetic dipoles, quadrupoles, and octupoles.
Supplementary Figure 4 shows results of the radiat
ed electric field intensity contributed from
various electromagnetic multipoles. For simplicity,
only the first three leading terms are shown.
As expected from the field distribution presen
ted in Figs. 2c and 2d, the magnetic octupole
(which can be interrupted as a high-order Mie re
sonance) plays a significan
t role in the optical
response under
x
-polarized illumination.”
Supplementary Figure 4.
Simulated
z
-component of far-field electric intens
ity for electromagnetic multipoles. For
simplicity, only the first three leading terms are presented.
with three additional references:
2.
Savinov V., Fedotov V. A., Zheludev N. I.
Toroidal dipolar excitation and macroscopic
electromagnetic properties of metamaterials.
Phys. Rev. B
89
, 205112 (2014).
3.
Wu P. C., Liao C. Y., Savinov V., Chung T.
L., Chen W. T., Huang Y.-W., et al. Optical
anapole metamaterial.
ACS Nano
12
, 1920-1927 (2018).
4.
Zhu A. Y., Chen W. T., Za
idi A., Huang Y.-W., Khorasaninejad M., Sanjeev V., et al.
Giant intrinsic chiro-optical activity
in planar dielectric nanostructures.
Light: Science &
Applications
7
, 17158 (2018).
2.
In the abstract and the main body of the manu
script, relative reflectance modulations are
quoted. However, if using the lo
w reflectance value as the re
ference which appears in the
denominator, the relative reflectance modulatio
n can get very high at wavelengths of low
reflectivity. The 270% achieved in this work sound a lot, but compared to the ideal
modulator, which would have a value of infinity
for this measure, it is a moderate tuning
performance. Also, in the wavelength range where the relative reflectance modulation is
highest, the maximum reflectance of the metasurface is below 50%, which is not sufficient
for high-efficiency devices. It would be more us
eful to quote absolute reflectance values or
the absolute reflectance modulation, also to
allow fair comparison with other tunable
metasurfaces.
We thank the reviewer for bringi
ng up this point. We agree with the reviewer’s comment that
the relative optical intensity (reflectance or tran
smittance) modulation can
be infinity (for the
cases where the reference intensity is close to
zero). We also agree that reporting absolute
reflectance modulation can allow
fair comparison with other tunable metasurfaces. Based on the
reviewer’s suggestion, we prov
ided the measured results of absolute reflectance modulation in
Supplementary Fig. 10. We observe about +2
0% and -30% absolute
reflectance modulation
[defined as R(V
a
≠
0 V)–R(V
a
= 0 V)] at wavelengths of
917 nm and 924 nm, respectively.
Although they are quantitatively comparable, we would like to point out that both significant
phase modulation and optical diffraction switch
ing are experimentally observed only at a
wavelength of 917 nm (see Figs. 3d, 4, and Supplemen
tary Note 8), which
also yields higher
relative reflectance modulation. In a broader c
ontext of work on tunable metasurfaces, the
relative change of optical intensity (reflectan
ce or transmittance) has been widely used to
quantitatively evaluate the optical modulation capabi
lity of tunable metasurfaces (for example,
see Nano Lett. 14, 6526-6532 (2014); Nat. N
anotechnol. 8, 252-255 (2013); ACS Nano 9, 4308-
4315 (2015), etc.), especially for those ca
ses in which the base line reflectance R(V
a
= 0 V) is
greater than 1% (which is our case here). As
a result, we believe that
simultaneous reporting of
both relative and absolute reflectance modulation
values enables compre
hensive evaluation of
the performance of tunable metasurfaces. We
added the following discussion and results to the
revised manuscript text and Supplementary
information:
On Page 6 in the main text:
“It is worth mentioning that we observe about
+20% and -30% absolute reflectance modulation
[defined as
R
(
V
a
≠
0 V) –
R
(
V
a
= 0 V)] at wavelengths of ~917 nm and ~924 nm, respectively
(see Supplementary Figure 10). Although these valu
es are quantitatively comparable, the large
phase modulation and diffracted beam switching can
only be observed at a wavelength of 917
nm, when high-quality resonance is present
(which shows higher relative reflectance
modulation), as can be seen
in the following sections.”
In the Supplementary Material:
Supplementary Note 5
Measured absolute reflectance modulation
Supplementary Figure 10.
Measured absolute reflectance modulation
∆
R
of the hybrid Mie-GM resonant
metasurface.
3.
On page seven it is stated “Higher-order diffract
ed beams are absent since the period of the
sample is subwavelength p=910 nm at 0 V bias
.“ On the same page, it also says: “The
dynamic diffraction pattern measurements have
been performed at a wavelength of 917
nm...“. Thus, the wavelength is very close to
the lattice constant. For perfectly normal
incidence and reflectance, indeed no diffraction
should occur (at least in
reflection, which is
considered here). However, for slightly tilte
d incidence, as it effectively occurs when
illuminating the sample with an objective or a lens, diffractive orders will occur starting from
some critical angle. The authors should prov
ide details of the measurement setup (in
particular the NA of the focussing
lens, if applicable) used to
measure the data presented in
Fig. 3b and discuss the occurence of di
ffraction under the relevant conditions.
We thank the reviewer for hi
s/her insightful comment. We agr
ee with the re
viewer that
diffraction can contribute to the spectral feat
ures when structures are excited under oblique
illumination at angles larger than a critical angle. The details of the optical setup used for the
measurement of far-field radiat
ion patterns are provided in Fi
g. 4c and the corresponding figure
caption. Based on the used numeric
al aperture of the objective,
the largest inci
dent angle is
about 16
°
when the laser beam is tightly focused ont
o the MQW samples. To minimize the effect
of diffraction caused by the non-
zero angle of incidence, we inte
ntionally slightly defocused the
laser beam impinging on the MQW metasurface dur
ing the optical measurements of far-field
radiation pattern.
To clarify this point, we performed numerical
simulations of the far-field radiation patterns
for the MQW metasurface at 0V w
ith different angles of
incidence. As show
n in Supplementary
Fig. 11a, we found that strong optical diffracti
on appears even when the incident angle is 5
°
.
However, those diffracted beam inte
nsities are high compared to th
e intensity of the zero-order
beam, which is not observed in our measuremen
ts. This can be attributed to two different
factors; first, their diffraction angles are too
large to be collected (based on the numerical
aperture of the objective we used, th
e largest angle collected is about 16
°
) and second, the
incident angle is almost zero in the real case
(because we did not tightly
focus the laser beam in
such measurements). As a result, we did not see such diffracted beams in our measurement at
0V.
To further verify the influence of non-zero in
cident angle caused diff
raction on the far-field
radiation pattern, we performed other simulati
ons which numerically demonstrate the active
switching of the first-order diffracted beam at
different angles of incidence. As shown in
Supplementary Fig. 11b, for both cases of normal and
oblique illuminations, we can see that the
first-order diffracted beams appear only when the electrical bias is non-zero. In addition, the
intensity of the diffracted beams are very high
when the incident angle is greater than 5°, which
is in conflict with our measurem
ent results. As a result, we c
onclude that the MQW metasurface
is under almost normal illumination (
θ
in
is between 0° and 5°), whic
h minimizes the influence of
diffraction caused by non-normal illumination in
the real case. Moreover, no higher-order
diffracted beams appear within the angular range of interest in all simulated results.
We revised this senten
ce in the manuscript:
On Page 7
“Higher-order diffracted beams are absent
since the period of our metasurface,
p
= 900 nm, is
subwavelength at 0 V bias (see deta
ils in Supplementary Note 6).”
We also added a detailed discussion of the in
fluence of oblique incidence to the revised
Supplementary information as follows:
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-f
ield radiation patterns
for the MQW metasurface at 0V with different angl
es of incidence. As shown in Supplementary
Fig. 11a, we found that strong optical diffracti
on appears even when the incident angle is 5°.
However, those diffracted beams' intensities are
high compared as to the intensity of the zero-
order beam, which is not observed in our measurem
ents. 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 us
ed, 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 minimize the incident angle.
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 higher as compared with the
specularly reflected beam when the
incident angle is greater than 5
°
, which is in conflict with our
measurement results 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-order
diffracted beams can only be observed when electr
ical 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 11
. (a) Simulation of far-field radiation patterns under oblique illumination without
electrical bias. Strong diffracti
on can be observed when the incident angle is greater than 5
°
. (b) Simulation of active
switching of first-order diffraction for the case of normal (left panel) and oblique (middle and right panels)
illumination. Overall, the diffracted beams show much str
onger intensity when incident angle is greater than 5
°
. The
incident wavelength is fixed at 917 nm.
We also added details of the experimental setup
used for spectral measurement and a couple of
sentences to the main text and Supplementary as follows.
On Page 6 in the main text:
“Figure 3b shows the measured reflectance spectra
of the fabricated metasurface under different
applied biases (see Supplementary Fig.
9 for details of optical setup).”
Supplementary Note 5
Optical setup for measurement of reflectance spectrum
“To optically characterize the reflectance of the
MQW metasurface, we utilized a coherent NIR
laser beam (Toptica Photonics CTL 950) as a light
source and a power meter as a detector. An
uncollimated white light source from a halogen lamp is used to visualize the sample surface.
When measuring the reflectance spectra, the la
ser beam was focused using a long working
distance objective with 10× magnifica
tion and 0.28 numerical aperture.”
Supplementary Figure 9
. Schematic of optical setup used for spectral measurement. M: mirror; ND: neutral density
filter (Thorlabs NDC-50C-4M); I: iris; L: lens; P: linear
polarizer (Thorlabs LPNIR100-MP); BS: beam splitter
(Thorlabs CCM1-BS014); O: objective (Mitutoyo 10× magni
fication with 0.28 numerical aperture); PM: power
meter.
4.
The part on beam steering requires a more criti
cal description and discussion. Usually, for a
beam steering device or also the other applic
ations mentioned in th
e outlook (metalenses
with reconfigurable focal length
, flat spatial light modulators
etc
), one would expect the
strongest (typically the fundamental) reflected or
transmitted order to be manipulated. In this
work, it is only the first diffraction order, which carries only a small fraction of the reflected
intensity, that can be manipulated. Also, there are first-order beams. Therefore, I would
rather consider this structure a reconfigurab
le diffraction grating, not so much a beam
steering device. For beam steering, I would also
expect to see a (quasi)
continuus variation of
the angle, whereas only discrete angles can be
achieved with the demons
trated device. In the
light of these arguments, the au
thors may want to consider re
naming the device, which also
affects the title of this work.
We thank the reviewer for bringing up this issue. However, we respectfully disagree with the
reviewer’s comment. We agree that in this work,
the intensity of the steered beam is small.
However, we would like to note that the defi
nition of an optical component/device should be
determined by its mode of func
tionality rather than operation effici
ency. As noted in response to
the second comment from the first reviewer, the
optical performance of the demonstrated tunable
metasurface is actually limited by a non-optimal
choice of the quantum well material, rather
than the metasurface approach. Based on the di
scussions and simulated results shown in
Supplementary Note 13, we indeed show that th
e directivity (which is
defined as the peak
intensity ratio between diffracte
d and mirror reflected beams) of
our double-slit metasurface can
be significantly improved when the q
uantum well system possesses larger
Δ
n/
Δ
k.
The following discussions and simulated results
are added to the Supplementary Material.
Supplementary Note 13
Improvement of optical performance
“To improve the optical performance, the quant
um well system has to provide a substantial
change in the real part of the refractive index,
Δ
n
, to sufficiently shift the resonances, and
maintain a small change in the imaginar
y part of refractive index (absorption),
Δ
k
, to enable a
sharp resonance within the operating wavelength range.
As a result, the larger the figure of merit,
Δ
n
/
Δ
k
of a quantum well, the better optical perf
ormance can be achieved in the tunable
metasurface. As a proof of concept, we desi
gned a tunable metasurface with an asymmetric
coupled quantum well (ACQW)
which can possess a larger
Δ
n
/
Δ
k
(about 10-18)
11
. As a
comparison, the
Δ
n
/
Δ
k
of the utilized MQW in this work
is 1-5 (see Ref. 1). The unit element
is also based on the double-slit
structure, as shown in
Supplementary Fig. 18a. After structural
optimization, we found that about 200
°
phase shift with a
Δ
n
of 0.02 can be obtained at a
wavelength of 808.8 nm (see Supplementary Fig.
19b). We also numerically study the beam
steering functionality using such an ACQW me
tasurface, which is real
ized by varying the
periodicity of the metasurface (see Supplementary
Fig. 19c). The simulated far-field radiation
patterns even show that the intensity of the steere
d beam is much higher than the intensity of the
specularly reflected beam when the utilized QW possesses larger
Δ
n
/
Δ
k
. These results indeed
verify that the optical performance (in particul
ar, directivity, which is defined as the peak
intensity ratio between diffracted and mirror re
flected beams) of tunable quantum well-based
metasurfaces can be significantly improved wh
en the quantum well system exhibits larger
Δ
n
/
Δ
k
. Since this is a proof-of-concept demons
tration, the working wavelength here (
λ
= 808.8 nm)
is slightly different from the one used in th
e main manuscript. By appropriately choosing a
quantum well, we can shift the operation wavelength to the range of interest
12, 13
.”
Supplementary Figure 19
. Simulated QW resonant
metasurface with higher
Δ
n
/
Δ
k
. (a) A schematic for all-
dielectric asymmetric coupling quantum well (ACQW) me
tasurface. The unit element dimensions are defined as