Article
https://doi.org/10.1038/s41467-022-33449-9
Nano-electromechanical spatial light
modulator enabled by asymmetric
resonant dielectric metasurfaces
Hyounghan Kwon
1,2
, Tianzhe Zheng
1
&AndreiFaraon
1,2
Spatial light modulators (SLMs) play essential roles in various free-space
optical technologies, offering spatio-t
emporal control of amplitude, phase, or
polarization of light. Beyond conventional SLMs based on liquid crystals or
microelectromechan
ical systems, active metasurfaces are considered as pro-
mising SLM platforms because they coul
d simultaneously provide high-speed
and small pixel size. However, the active metasurfaces reported so far have
achieved either limited phase modulation or low ef
fi
ciency. Here, we propose
nano-electromechanical
ly tunable asymmetric dielectric metasurfaces as a
platform for re
fl
ective SLMs. Exploiting the strong asymmetric radiation of
perturbed high-order Mie resonances, the metasurfaces experimentally
achieve a phase-shift close to 290
∘
,over50%re
fl
ectivity, and a wavelength-
scale pixel size. Electrical control of d
iffraction patterns is also achieved by
displacing the Mie resonators using nano-
electro-mechanical forces. This work
paves the ways for future exploration of the asymmetric metasurfaces and for
their application to the next-generation SLMs.
Spatial light modulators (SLMs) enable spatiotemporal control of
phase, amplitude, or polarization of input free-space light. In parti-
cular, phase-dominant SLMs realize ef
fi
cient wavefront engineering
and play essential roles in various applications such as LIDAR
1
,holo-
graphic display
2
, optical computing
3
, and bio-imaging
4
,
5
. Most con-
ventional SLMs rely on liquid crystals or micromechanical systems,
which result in low speed and limited
fi
eld of view
6
. Recently, meta-
surfaces have emerged as diffractive optical elements where the pixel
size is on the scale of a wavelength
7
–
9
. Achieving similar spatial reso-
lution but with an active metasurface would enable high-speed and
high-resolution SLMs in a compact footprint
10
. Many seminal works
have been proposed in the context of the active metasurfaces, using
various active materials or mechanisms such as transparent conduct-
ing oxides
1
,
11
,
12
, liquid crystals
13
, electro-optic materials
14
–
17
,phase-
change materials
18
, 2D materials
19
–
22
, electromechanical systems
23
–
28
,
and semiconductors
29
. The active plasmonic metasurfaces based on
transparent conducting oxides
1
,
11
,
12
have successfully achieved com-
plex modulation. However, as they operate near the epsilon-near-zero
regime where the light is critically coupled to lossy plasmonic resonant
modes, most of the light is absorbed when a large phase shift occurs so
the ef
fi
ciency is signi
fi
cantly limited
1
. Regarding the photonic struc-
tures, most of the re
fl
ective active metasurfaces exploit mirrors to
achieve strong phase response at optical resonances
1
,
11
,
12
,
18
,
20
,
29
.The
presence of the mirror ensures that the radiation of the resonance is
matched with the input light, enhancing the phase response in
re
fl
ection
30
. However, including a mirror in the structure complicates
fabrication, and a way to achieve strong phase shift and high re
fl
ection
without the mirror has remained illusive.
Here, we propose nano-electromechanically tunable asymmetric
metasurfaces to realize phase-dominant SLMs. In particular, by
exploiting asymmetric high-Q Mie modes and nano-electromechanical
system (NEMS), the active metasurfaces operate as ef
fi
cient re
fl
ective
SLMs without mirrors. First, we provide an analytical model that not
only describes the physical picture of the proposed system, but also
offers design intuitions. Then we numerically and experimentally
verify that the proposed metasurfaces achieve strong phase
Received: 28 March 2022
Accepted: 20 September 2022
Check for updates
1
T. J. Watson Laboratory of Applied Physics and Kavli Nanoscience Institute, California Institute of Technology, 1200 E. California Blvd., Pasadena
,CA91125,
USA.
2
Department of Electrical Engineering, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125, USA.
e-mail:
faraon@caltech.edu
Nature Communications
| (2022) 13:5811
1
1234567890():,;
1234567890():,;
modulation, high re
fl
ection, and a wavelength-scale pixel size. Finally,
we experimentally demonstrate electrically controllable diffraction.
Results
Theoretical and numerical study of asymmetric resonant
metasurfaces
Figure
1
a shows a conceptual illustration of the proposed metasurface.
The metasurface consists of suspended silicon (Si) nano-bars with
rectangular cross-sections perturbed with notches at one of the cor-
ners. Furthermore, each pair of nano-bars is connected to an electrode
enabling its lateral movement
27
. As a result, the metasurface actively
manipulates the wavefronts of re
fl
ected light as a function of the
applied biases.
First, we model the suspended metasurface with temporal cou-
pled mode theory (TCMT) to get a rigorous physical picture of the
system as well as design intuition
30
,
31
.AsshowninFig.
1
b, the meta-
surface under normal incidence can be generally modeled by a reso-
nator coupled to two ports
32
,
33
. When driving the metasurface with a
continuous laser, whose frequency is
w
, the complex re
fl
ection coef-
fi
cient for each port,
r
1
and
r
2
, can be derived by (see Supplementary
Note 1 for detailed derivation):
r
1
=
ir
ð
w
w
0
Þ
±
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
τ
2
1
+
2
τ
2
2
r
2
τ
2
tot
1
r
2
σ
2
q
1
r
σ
i
ð
w
w
0
Þ
+
1
τ
tot
,
ð
1
Þ
r
2
=
ir
ð
w
w
0
Þ
±
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
τ
2
1
+
2
τ
2
2
r
2
τ
2
tot
1
r
2
σ
2
q
+
1
r
σ
i
ð
w
w
0
Þ
+
1
τ
tot
,
ð
2
Þ
where
r
is the real re
fl
ection coef
fi
cient of the direct scattering process;
w
0
is the resonant frequency;
1
τ
1
and
1
τ
2
are the resonator
’
sradiative
decay rates into port 1 and port 2, respectively;
1
τ
tot
=
1
τ
1
+
1
τ
2
and
1
σ
=
1
τ
1
1
τ
2
represent total radiative decay rate and the difference between the
two radiative decay rates, respectively. In general, the coupling con-
dition between the port and the resonator determines the phase
response of the re
fl
ected light
30
. When a decay rate into a certain port
is larger than the sum of other decay rates including radiative and non-
radiative decay rates, the resonance is over-coupled to the port that
results in almost 2
π
phase shift across the resonance frequency. In
contrast, when the resonance is under-coupled to the port, the phase
shift becomes negligible. To achieve high phase modulation, we aim to
design an over-coupled resonator and tune its strong phase response
near the resonance frequency
34
.InEqs.(
1
)and(
2
), the coupling
conditions are determined by
1
σ
.If
1
σ
> 0, the port 1 is over-coupled and
the port 2 is under-coupled, and vice versa. Besides, strong asymmetric
radiation makes the magnitude of
1
r
σ
comparable to the magnitude of
1
τ
tot
in Eqs. (
1
)and(
2
), leading to the decrease of the re
fl
ection loss at the
resonance and the phase-dominant response
34
.Finally,theratio
Wavelength (nm)
1526 1528 1530 1532 1534
-3
-2
-1
0
1
2
3
Reflected phase (rad)
1526 1528 1530 1532 1534
0.75
0.8
0.85
0.9
0.95
1
Reflection
e
f
cd
0
x
z
Wavelength (nm)
Modeling
Resonator
Port 1
Port 2
b
y
z
x
(V/m)
V
n+1
(
t
)
V
n
(
t
)
t = t
1
t = t
2
t = t
3
Wavefronts of
input light
Wavefronts of
reflected light
V
n-1
(
t
)
y
z
x
a
Fig. 1 | Conceptual schematic of nano-electromechanically tunable asymmetric
metasurfaces and numerical investigations of their resonant re
fl
ection beha-
vior. a
Conceptual illustration of the nano-electromechanically tunable meta-
surfaces composed of asymmetric suspended nano-beams. Each pair of nano-
beams is connected to individually addressable electrodes. The electrical biases
induce electrostatic forces between the neighboring bars, leading to lateral
movements along the
x
axis (see blue arrows). The asymmetric metasurface re
fl
ects
normally an incident plane wave and dynamically manipulates the wavefront of the
re
fl
ected light as a function of the applied biases.
t
1
,
t
2
,and
t
3
represent different
electrical biasing conditions.
b
Schematic of a periodic metasurface (top) and
illustration of the corresponding analytical model based on an optical resonator
coupled to two ports (bottom). The model describes the asymmetric metasurface
under normal incident light.
S
+
1
(
S
+
2
)and
S
1
(
S
2
) are incoming and outgoing waves
through the port 1 (port 2), respectively. The resonance decays into the port 1 and
2 with decay rates,
1
τ
1
and
1
τ
2
, respectively.
c
Schematic illustration of the asym-
metric metasurfaces showing the perturbed gratings and the notches placed at
the right top corners. The TE-polarized light is normally incident from either the
top or the bottom side of the metasurface.
∣
r
TE
,1
∣
(
∣
r
TE
,2
∣
) and
φ
TE
,1
(
φ
TE
,2
) are
re
fl
ected amplitude and phase for the top (bottom) illumination, respectively.
d
Simulated electric
fi
eld pro
fi
le (
y
-component, 1531 nm wavelength) of the
asymmetric metasurface's eigenmode at
Γ
point. Scale bar denotes 500 nm.
e
,
f
Calculated re
fl
ection and re
fl
ected phase spectra of the asymmetric meta-
surfaces for top and bottom illuminations.
e
The re
fl
ection spectra are identical
for both illumination conditions, thus plotted by one solid black curve.
f
Solid and
dashed curves represent the re
fl
ected phase spectra for top and bottom illumi-
nations, respectively.
Article
https://doi.org/10.1038/s41467-022-33449-9
Nature Communications
| (2022) 13:5811
2
between the two decay rates is bounded by the direct scattering
process
32
:
1
r
1+
r
≤
τ
2
τ
1
≤
1+
r
1
r
:
ð
3
Þ
Equation (
3
)indicatesthathigh
r
is necessary for the desired strong
asymmetric radiation. In contrast to the asymmetric cases, the sym-
metric resonators always cause critical coupling, resulting in negligible
re
fl
ection and ~
π
phase shift near the resonance (See Supplementary
Note 1 for details). The TCMT describing the asymmetric resonators
has been explored previously
32
,
33
, and the asymmetric resonator has
been recently demonstrated in experiment
35
. However, the phase
responses of the asymmetric resonances have been investigated very
recently by passive slanted gratings and guided mode resonances
36
.Up
to our best knowledge, the asymmetric metasurfaces
’
potentials in
active devices have not been explored yet.
To physically implement such an asymmetric resonator, we
break the symmetry of conventional gratings in Fig.
1
c, making a
notch at one of the top corners of each nanobar. The nano-bars are
841 nm wide, 838 nm thick and are periodically arranged with lattice
constant of 1093 nm. Based on Eq. (
3
), the thickness, width, and lat-
tice constant of the unperturbed structures are selected to make
r
higher than 0.9 in the telecom wavelength range. Each notch has a
square cross-section with 184 nm side length. The electric
fi
eld pro-
fi
le of the eigenmode at
Γ
point is shown in Fig.
1
d, originating from
the high-order Mie mode of an isolated Si nanobar (see Supple-
mentary Figure 1 for details). It is worth explicitly noting why we
select the high-order Mie mode instead of the guided mode. Sup-
ported by the individual nanostructure instead of the periodic lat-
tice, the Mie mode ef
fi
ciently supports wavefront shaping with the
small pixel size. Speci
fi
cally, in the scheme of the nano-
electromechanical modulation shown in Fig.
1
a, each pair of the
nanostructures individually hosts the resonance and works as an
independent re
fl
ective resonant antenna
7
. In addition, the notches
simultaneously break the mirror symmetry in the
z
-direction as well
as the even symmetry of the resonant mode under
C
2
rotation (180
∘
rotation around the
z
axis). The former aims to improve phase
responses through asymmetric radiations, while the latter enables
coupling between the Mie mode and normally incident light. The
spectra of the re
fl
ection and re
fl
ected phase are calculated for top
and bottom illuminations and plotted in Fig.
1
e, f. The calculated
re
fl
ection spectra are identical for both illumination conditions in
Fig.
1
e, whereas the phase responses in Fig.
1
f show strong and
negligible phase responses for the top and bottom illuminations,
respectively. The illumination-dependent phase responses in Fig.
1
f
result from the distinct coupling conditions determined by the two
radiative decay rates. In particular, for the top illumination, the
metasurfaces simultaneously achieve ~2
π
phase shift and high
re
fl
ection over 78% over the spectrum. We also
fi
t the simulated
spectra in Fig.
1
e, f by using Eqs. (
1
)and(
2
) (see Supplementary
Figure 2 for details). The
fi
tted results in Supplementary Figure 2
show good agreement with the numerical eigenmode analysis in
Supplementary Figure 3. In addition to the asymmetric cases, the
metasurfaces possessing mirror symmetry in the
z
-directions are
investigated, showing limited phase response and negligible re
fl
ec-
tion at the resonance (see Supplementary Notes 1 and 2 and Sup-
plementary Figure 4 for details).
Numerical investigations on nanomechanical phase modulation
We numerically investigate the phase modulation, utilizing the nano-
electromechanical displacement in lateral directions
27
,
28
.Everytwo
pairs of nano-bars, is either grounded or connected to an external bias
in Fig.
2
a, with
g
1
and
g
2
the gaps between nano-bars with different and
same biases, respectively. The applied bias enables continuous control
of the nanomechanical movement, expressed by
g
1
g
2
2
.Toinvestigate
the nano-electromechanical tuning, a pair of nano-bars is simulated by
changing
g
1
g
2
2
. As the period of a pair of the nano-bars, 2
Λ
,is657nm
larger than the design wavelength of 1529 nm in Fig.
2
a, the induced
nanomechanical movement causes unwanted diffraction orders at
±44
∘
. Nevertheless, the unwanted diffractions at ±44
∘
become more
suppressed when the structures are re-arranged for the desired
c
b
2
2186 nm
GND
GND
GND
GND
d
a
-3
-2
-1
0
1
2
3
(rad)
020406080
0.2
0.4
0.6
0.8
1
y
z
x
0 20406080100120
1524
1526
1528
1530
1532
1534
Wavelength (nm)
0
0.2
0.4
0.6
0.8
1
(arb. u.)
0 20 40 60 80 100120
1524
1526
1528
1530
1532
1534
)
m
n
(
h
t
g
n
e
l
e
v
a
W
(nm)
(nm)
(nm)
Fig. 2 | Simulations on nano-electromechanical phase modulation. a
Schematic
illustrations of an array of pairs of the asymmetric nanostructures. For every two
pairs, one pair is connected to ground (GND, pink) and the other pair is connected
to an external bias (
V
e
, red). Left: when the external bias is applied, induced elec-
trostatic forces result in lateral movements (see black arrows). Right: side view of
the asymmetric metasurfaces is shown with design parameter de
fi
nitions.
b
Calculated spectra of re
fl
ected power coef
fi
cient and phase of the 0th order
diffraction,
∣
r
0th
∣
2
and
φ
0th
. The spectra are plotted as a function of the nano-
mechanical tuning
g
2
g
1
2
.
d
Calculated nanomechanical tuning of
∣
r
0th
∣
2
and
φ
0th
/2
π
at the wavelength of 1529 nm.
∣
r
0th
∣
2
and
φ
0th
/2
π
are plotted by black and red curves
as a function of
g
2
g
1
2
, respectively. The corresponding data is noted by black
dashed lines in
b
,
c
.
Article
https://doi.org/10.1038/s41467-022-33449-9
Nature Communications
| (2022) 13:5811
3
wavefront engineering. The re
fl
ection power coef
fi
cient and phase of
the 0th order,
∣
r
0
th
∣
2
and
φ
0
th
, are calculated and plotted in Fig.
2
b, c,
respectively. In Fig.
2
b, the blue-shift of the resonances and the
decrease of the minimum re
fl
ection are observed when
g
1
g
2
2
increases.
The decrease of the minimum re
fl
ection dominantly results from the
±1st order diffractions (see Supplementary Figure 5 for details). In
Fig.
2
c, the mechanical tuning results in a continuous blue-shift of the
resonance while the strong phase response remains, indicating that
the phase can be modulated near the resonant wavelength. Speci
fi
-
cally, at the wavelength of 1529 nm,
∣
r
0
th
∣
2
and
φ
0
th
are plotted in Fig.
2
d
as a function of the nanomechanical tuning, revealing that the
nanoscale movement within 80 nm can lead to phase modulation up to
246
∘
with minimal
∣
r
0
th
∣
2
>0.47. In Fig.
2
d, we set the maximum
mechanical movement at 80 nm to avoid irreversible stiction of the
nanostructures, which is known as the pull-in effect. Utilizing a pair of
the asymmetric nanostructure as a building block, we also numerically
show the metasurfaces
’
capability of beam steering (see Supplemen-
tary Note 3 and Supplementary Figures 6 and 7 for details). It is worth
noting the substantial advancement that this work brings compared to
our previous work on nano-electromechanical metasurfaces
27
.The
introduction of the asymmetry uniquely enables single mode opera-
tion, wide phase tunability without mirror, and wavefront shaping in
wavelength scale.
Fabrication and optical char
acterization of the active
metasurfaces
We fabricate the active metasurface using a standard silicon-on-
insulator wafer and sequential nanofabrication process (see Methods
for details). Figure
3
a shows a photographic image of the device. In
Fig.
3
a, the device is wire-bonded to a custom-made printed circuit
board for connections to external electrical sources. Scanning electron
microscope images of the devices are shown in Fig.
3
b
–
d. In Fig.
3
d, the
fabricated asymmetric nanostructures show good agreement with the
design shown in Fig.
1
a. Figure
3
e illustrates the electrical con
fi
guration
of the device, showing that every four pairs of nanostructures are
connected to four different electrodes. In Fig.
3
e,
V
1
,
V
2
,
V
3
,and
V
4
denote the four different applied biases. The voltage differences
between the neighboring nanostructures locally determine the gap
sizes. The electrical con
fi
guration enables the nano-electromechanical
modulation with a periodicity of 4. In other words, four pairs of
nanostructures are nano-electomechanically modulated in a periodic
manner.
We
fi
rst characterize the tunable optical properties by imple-
menting the scheme shown in Fig.
2
a. While
V
1
and
V
3
are grounded,
V
2
and
V
4
areconnectedtothesameexternalbiases.WhentheTE-
polarized light is normally incident, the re
fl
ection spectra are mea-
sured under different external biases and plotted in Fig.
3
f(see
a
c
bd
gh
02468
0.5
0.6
0.7
0.8
0.9
R
device
/
R
gold
Applied Bias (V)
0246
100
200
300
400
8
Applied Bias (V)
Phase (degree)
0
ef
0V
4V
5V
6V
7V
8V
Wavelength (nm)
R
device
/R
gold
y
z
x
1500
1510
1520
1530
1540
0.4
0.6
0.8
1
Fig. 3 | Optical characterization of nano-electromechanical metasurface tun-
ing. a
Optical image of the fabricated metasurface. Electrodes in the device are
wire-bonded to a custom-printed circuit board.
b
–
d
Scanning electron microscopy
images of the metasurface. Every pair of nanostructure is connected to the elec-
trodes. Scale bars in
b
–
d
denote 500, 10, and 1
μ
m, respectively.
e
Schematic of
electrical con
fi
guration. Four different electrical biases,
V
1
,
V
2
,
V
3
,and
V
4
,areper-
iodically applied to every four pairs of the nanostructures.
f
–
h
V
2
=
V
4
and
V
1
=
V
3
=0.
f
Measured re
fl
ection spectra for TE-polarized normally incident light. The
spectra are measured under six different biases (see legend) and plotted in dif-
ferent colors.
g
Measured intensity modulation under different biases at the
wavelength of 1524 nm. The applied bias varies from 0 V to 8 V.
h
Measured phase
shift of the metasurface at the wavelength of 1524 nm as a function of the applied
biases from 0 V to 8 V. Error bars represent standard deviations of the estimated
phase shifts.
Article
https://doi.org/10.1038/s41467-022-33449-9
Nature Communications
| (2022) 13:5811
4
Methods and Supplementary Figure 8 for details). Without any bias,
theresonancedipwasobservedaround1526nminFig.
3
f, in agree-
ment with the simulated resonance dip at 1529 nm shown in Fig.
2
b.
The small deviation may result from slight errors in fabrication. When
the bias changes from 4V to 8V, blue-shift of the resonances and
decrease of the minimum re
fl
ection are observed in Fig.
3
f, showing
great agreement with the simulated results in Fig.
2
b. As an objective
lens in the setup cannot capture the diffraction at ~44
∘
, the decrease of
minimum re
fl
ection in Fig.
3
f can be explained by the increase of the
±1st-order diffractions at ~44
∘
(see Supplementary Figure 5 for details).
We experimentally investigate electrical modulations of re
fl
ection
and re
fl
ected phase, also implementing the scheme shown in Fig.
2
a.
To verify the intensity modulation, the re
fl
ection is measured at
1524 nm by increasing the applied bias from 0 to 8V, and as shown in
Fig.
3
g the minimum re
fl
ection is higher than 50% (see Supplementary
Figure 9 for measured intensity modulations at different wavelengths).
In addition, we measure the phase modulation at 1524 nm using a
Michelson-type interferometer setup
27
(see Methods and Supplemen-
tary Figure 8 for details). Figure
3
h shows measured phase shifts as a
function of the applied bias, with over 289.6
∘
shift for 8V.
Experimental demonstration of electrically controllable
diffraction
After validating the wide phase tunability and high re
fl
ection, we
demonstrate electrical control of the diffraction patterns. As shown in
Fig.
3
e, the device has a
fi
xed periodicity of 4, and it realizes beam
de
fl
ections into the ±1st orders and beam de
fl
ection into the +1st or
−
1st order with the diffraction angle of ±10
∘
.While
V
1
is connected to
ground, the values of
V
2
,
V
3
,and
V
4
are controlled to verify the dynamic
diffraction patterns. We image a Fourier plane of the metasurface such
that the diffraction patterns are directly measured (see Methods and
Supplementary Figure 8 for details). First, we only increase
V
4
from 0
to 8V continuously and observe the diffraction intensity changes in the
Fourier plane. In Fig.
4
a, the diffraction occurs near ±10
∘
for the large
bias over 6V. As shown in Fig.
4
a, b, negligible signals are observed at
10
∘
when no bias is applied. The strongest diffraction intensity is
observed when
V
4
is at 7.63V (Fig.
4
a, c), with the
−
1st order signal that
is stronger than the +1st order. This asymmetric diffraction mainly
results from the inherent asymmetry of the structure, showing
agreement in the numerical results shown in Supplementary Fig-
ures 5
–
7. Interestingly, when the
V
4
further increases up to 8V, the
devices achieve comparable ±1st order diffractions in Fig.
4
dsonearly
symmetric beam de
fl
ection into the ±1st order is realized. Next, we
control
V
2
,
V
3
,and
V
4
to demonstrate beam de
fl
ection into either the
−
1st or +1st order diffraction. In Fig.
4
e, the device achieves strong
−
1st
order diffraction with normalized intensity reaching 55.7%. Compared
to the results shown in
4
c, the +1st order diffraction is well suppressed
in
4
e and its normalized intensity is as small as 3.13%. Likewise, the
device can provide strong +1st order diffraction by adjusting the
electrical bias as shown in Fig.
4
f. In addition to the electrical diffrac-
tion control, we should mention that the lobes near 0
∘
in Fig.
4
a
–
eare
split. The degradation may stem from imperfect fabrication and
fi
nite
size effect. Nonetheless, we can readily move the resonance away from
the operating wavelength via electrostatic forces and the artifacts in
the large lobe near 0
∘
vanish (see Supplementary Figure 10 for details).
We should also note that such degradation has not been observed in
±1st diffraction order. For most of applications, the quality of the +1st
and
−
1st order diffractions are important.
a
-10
-5
0
5
10
8
7
6
5
4
3
2
1
0
0
0.5
1
)
V
(
Angle (degree)
(
) = (0,0,0,
)V
b
(
) = (0,1.43,8,0)V
d
(
) = (0,0,0,8)V
e
f
c
(
) = (0,0,0,7.63)V
0
0.5
1
y
t
i
s
n
e
t
n
I
d
e
z
i
l
a
m
r
o
N
Angle (degree)
0
0.2
0.4
0.6
0.8
1
-15
-10 -5 0
5 10 15
0
0.5
1
0.05k
0
0.05k
0
Normalized Intensity
Angle (degree)
-10 -5
0
5 10
0
0.2
0.4
0.6
0.8
1
-15
15
-15
15
0
0.5
1
0.05k
0
Normalized Intensity
Angle (degree)
-10 -5
0
5 10
0
0.2
0.4
0.6
0.8
1
-15
15
0.05k
0
(arb. u.)
(arb. u.)
(
) = (0,0,0,0)V
(
) = (0,8,0.928,0)V
0.05k
0
0.05k
0
0
0.5
1
(arb. u.)
Normalized Intensity
Angle (degree)
-10 -5
0
5 10
0
0.2
0.4
0.6
0.8
1
-15
15
0
0.5
1
Normalized Intensity
Angle (degree)
-10 -5
0
5 10
0
0.2
0.4
0.6
0.8
1
-15
15
0.05k
0
(arb. u.)
(arb. u.)
(arb. u.)
Fig. 4 | Tunable diffraction with the asymmetric nano-electromechanical
metasurface. a
Measured intensity at the Fourier plane of the metasurface as a
function of the applied bias from 0 V to 8 V (
λ
= 1524 nm). At each bias, the intensity
is normalized by the peak intensity near 0
∘
.The±1storderdiffractionsstartto
appear ~±10
∘
when the applied bias is over 6 V. On top of the image, the values of
V
1
–
V
4
are noted and only
V
4
is changed.
b
–
f
Measured diffraction patterns for
various con
fi
gurations of the applied biases (
λ
= 1524 nm). (top) Normalized inten-
sity images are measured at the Fourier plane of the metasurface. The values of
V
1
–
V
4
are noted on top of the images. Scale bars are 0.05
k
0
where
k
0
is a magnitude
of wave vector in free-space. (bottom) Measured cross-sectional intensity pro
fi
les
are plotted as a function of the diffraction angle. The intensities are normalized by
the peak intensity at 0
∘
. The diffracted signals ~±10
∘
are denoted by red shades.
Article
https://doi.org/10.1038/s41467-022-33449-9
Nature Communications
| (2022) 13:5811
5
The strong 0th order signals are observed in Fig.
4
a
–
f, indicating
that the diffraction ef
fi
ciencies are not as ef
fi
cient as the numerical
results shown in Supplementary Figures 6 and 7. We expect that the
low experimental ef
fi
ciency mainly results from imperfect fabrications
and the
fi
nite size effect. To demonstrate more ef
fi
cient devices, we
fabricate another array of the metasurfaces with changes in the elec-
trical con
fi
guration (see Supplementary Figure 11 for details). The best
device shows the +1st and
−
1st order diffractions with normalized
intensities 6.05 dB and 3.75 dB larger than the 0th order diffraction,
respectively (see Supplementary Figure 11 for details). It experimen-
tally points out that further optimization in the nanofabrication pro-
cess improves the ef
fi
ciency of the device.
Discussion
We utilized the asymmetric dielectric metasurfaces for the realization
of tunable phase SLMs, revealing that asymmetric radiation is the key
characteristic for designing re
fl
ective SLMs without mirrors. The
asymmetric metasurfaces not only have shown interesting physical
properties such as a strong single-sided phase response, but also
have offered practical advantages. For example, it uniquely has
allowed for the use of standard silicon-on-insulator wafers in which
mirrors are usually not included. Furthermore, the strong phase
response can be modulated by not only NEMS, but various active
mechanisms for all-solid-state active metasurfaces
34
,
37
–
39
. Such all-solid-
state active metasurfaces are expected to overcome several limits of
mechanical systems such as fragility and limited aperture size.
Here we employed two sequential nanofabrication processes to
create asymmetric nanostructures shown in Fig.
3
d (see Methods for
details). The complexity of the multi-layer nanofabrication may hinder
the scalable production of the proposed devices. However, we envi-
sion that slanted gratings, which can also achieve asymmetric radiation
patterns
35
,
36
can replace the proposed structures for scalable produc-
tion as they can be fabricated with a single lithography step and angled
etching techniques.
In summary, we experimentally demonstrated nano-
electromechanically tunable phase SLMs enabled by asymmetric
metasurfaces. The active metasurfaces numerically and experimen-
tally achieved wide phase tunability, high absolute re
fl
ection, and
wavelength-scale pixel size. Finally, we demonstrated the nano-
electromechanical control of the di
ffraction patterns. In general, this
work experimentally showcases the potential of the asymmetric
resonant dielectric metasurfaces for applications in the next-
generation SLMs.
Methods
Simulation and design
The re
fl
ected spectra are calculated using the rigorous coupled wave
analysis technique
40
. Assuming in
fi
nite lengths for the silicon nanos-
tructures, 2D simulations were performed. While we assume that the
silicon structures are surrounded by air in Fig.
1
a, a 700-nm air gap, a
2300-nm thick silicon oxide layer, and a silicon substrate are added
underneath the silicon structure in Fig.
2
to simulate the fabricated
devices. The eigenmode analysis shown in Figs.
1
d, S1, and S3 are
performed using commercial software based on the
fi
nite elements
method, COMSOL®. Refractive indices of Si and SiO
2
for the telecom
wavelength in the simulation are 3.4 and 1.45, respectively.
Device fabrication
We use a silicon-on-insulator wafer with a device layer of 1500 nm and
a buffered oxide layer of 3
μ
m on a 1 mm thick silicon substrate. First,
the device layer is thinned down to the target thickness of ~838 nm
using reactive-ion-etching with a gas mixture of SF
6
and C
4
F
8
.The
nanofabrication includes three sequential electron beam lithography
steps, the
fi
rst one for the grating structures, the second one for the
notches, and the last one for the electrodes. For all electron beam
lithography steps, a ~300-nm-thick positive electron resist (ZEP-520A,
Zeon) is spin-coated on the device. The patterns are generated by 100
kV electron beam exposure (EBPG5200, Raith GmbH), and the resist is
developed in a developer solution (ZED-N50, Zeon). To pattern the
gratings and notches, the ZEP resist is utilized as a soft mask in the
reactive-ion etching steps and then removed by remover PG (Micro-
chem). After the fabrication of the aysmmetric silicon nanostructures,
the electrodes were patterned by electron beam lithography, the
deposition of chrome and gold (5 nm and 65 nm) layers, and liftoff. To
etch the buffered oxide layer under the gratings, we exploit buffered
hydro
fl
uoric acid. Like the under-cut process in
27
, the time of the
under-cut process is adjusted carefully such that the anchors are
supported by the SiO
2
while the nanostructures are fully suspended.
After the under-cut, the device is dried by a critical point dryer. After
the drying process, severe out-of-plane or in-plane deformation of the
nanostructures has not been observed under the SEM images. Finally,
the device is connected to a custom-printed circuit board using a wire
bonder (WestBond 7476D). The fabricated metasurface shown in
Fig.
3
b
–
d consists of 36 pairs of asymmetric suspended nanos-
tructures. In this paper, all of the nanostructures are 50
μ
m long in
y
axis and both ends of the nanostructures are connected to
either anchors or large silicon layers that are supported by the buf-
fered oxide layers
27
. Furthermore,
g
1
and
g
2
are adjusted in the fabri-
cation process to make
g
1
120 nm smaller than
g
2
such that the nano-
electromechanical tuning leads to ef
fi
cient tuning of the resonance. As
shown in Fig.
3
e, the device has four different sets of electrodes. The
customized PCB is capable of providing four independent voltages to
the sets of electrodes in the device. The independent biases are pro-
duced by Arduino (Arduino Uno R3). Speci
fi
cally, four different pulse
width modulation (PWM) channels in Arduino are connected to four
PWM to DC converter modules (LC-LM358-PWM2V) and a custom
external circuit. As a result, the applied biases are individually con-
trollable by updating the four PWM channels, which are programmed
via a common laptop by using the Arduino software (IDE).
Measurement procedure
All of the measurements presented in this paper are characterized
using the set-ups shown schematically in Supplementary Figure 8
27
,
34
.
We use a tunable laser (Photonetics, TUNICS-Plus) as the light source. A
beam splitter is placed in front of the
fi
ber collimator (Thorlabs,
F260FC-1550) to capture the power from the source and send the light
to the sample. For reference, the power from the source is measured
by an InGaAs detector (Thorlabs, PDA10CS). A polarized beam splitter
(PBS), a half waveplate, and a polarizer are inserted to set the polarized
state of the incident light to TE polarization. The sample at the object
plane is imaged by a ×20 in
fi
nity-corrected objective lens (Mitutoyo, M
Plan Apo NIR) and a tube lens with a focal length of 200 mm. The
position of the tube lens and the mounting stage of the sample is
adjusted to ensure normal incidence. At the image plane, an iris
(Thorlabs, ID25) is inserted to select a region of interest with a dia-
meter of 45
μ
m in the object plane. The spatially
fi
ltered light was
either focused onto another InGaAs detector for the measurement of
the spectra, or imaged on an InGaAs SWIR camera (Goodrich,
SU320HX-1.7RT) using relay optics. All re
fl
ection signals were obtained
by dividing the signal from the sample by the signal from the sources.
Due to different input polarization states, the incident power onto the
sample varies at different wavelengths. Thus, the signals are further
normalized by the signals from the gold. To measure the phase
response shown in Fig.
3
h, we use a Michelson-type interferometer
setup
27
. A part of the setup marked by a black dashed box in Supple-
mentary Fig. 8 is only utilized for the phase measurement. As the
fi
eld
of view of the objective lens is larger than the device size, the input
light illuminates the metasurface and unpatterned regions at the same
time and forms fringes with a reference beam at the image plane. The
phase shift is mainly evaluated by the shift of the fringes on the
Article
https://doi.org/10.1038/s41467-022-33449-9
Nature Communications
| (2022) 13:5811
6