Nanoelectromechanical tuning of dual-mode resonant dielectric
metasurfaces for dynamic amplitude and phase modulation
Hyounghan Kwon
1,2,3
,
Tianzhe Zheng
1,3
,
Andrei Faraon
1,2,*
1
T. J. Watson Laboratory of Applied Physics and Kavli Nanoscience Institute, California Institute of
Technology, 1200 E. California Blvd., Pasadena, CA 91125, USA
2
Department of Electrical Engineering, California Institute of Technology, 1200 E. California Blvd.,
Pasadena, CA 91125, USA
3
These authors contributed equally
Abstract
Planar all-dielectric photonic crystals or metasurfaces host various resonant eigenmodes including
leaky guided mode resonance (GMR) and bound states in the continuum (BIC). Engineering these
resonant modes can provide new opportunities for diverse applications. Particularly, electrical
control of the resonances will boost development of the applications by making them tunable.
Here, we experimentally demonstrate nanoelectromechanical tuning of both the GMR and the
quasi-BIC modes in the telecom wavelength range. With electrostatic forces induced by a few
voltages, the devices achieve spectral shifts over 5 nm, absolute intensity modulation over 40%,
and modulation speed exceeding 10 kHz. We also show that the interference between two
resonances enables the enhancement of the phase response when two modes are overlapped in
spectrum. A phase shift of 144° is experimentally observed with a bias of 4V. Our work suggests
a direct route towards optical modulators through the engineering of GMRs and quasi-BIC
resonances.
For Table of Contents Only
*
Corresponding author: A.F.: faraon@caltech.edu.
AUTHOR CONTRIBUTIONS
H.K. and A.F. conceived the project. H.K. designed the device. H.K. and T.Z. fabricated the samples, performed the measurements,
and analyzed the data. All authors co-wrote the manuscript.
CONFLICT OF INTERESTS
The authors declare no competing financial interests.
ASSOCIATED CONTENT
Supporting Information
This material is available free of charge via the internet at
https://pubs.acs.org/
.
Measurement procedure, design parameters for all nanomechanical gratings, schematic illustration of the experimental setup,
measurement of angle-sensitive reflection spectra, numerical investigation related to spectral shifts of the resonances induced by
actuation, calculated reflection and reflected phase spectra for single BIC mode, and fringe analysis for phase response measurement
HHS Public Access
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Published in final edited form as:
Nano Lett
. 2021 April 14; 21(7): 2817–2823. doi:10.1021/acs.nanolett.0c04888.
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Keywords
Photonic crystal; Metasurface; NEMS; Bound states in the continuum; Guided mode resonance;
Optical modulator
Photonic crystals or metasurfaces composed of low-loss dielectric materials are known to
host highly resonant modes including leaky guided mode resonances (GMR) [
1
–
3
] and
bound state in the continuum (BIC) modes [
4
,
5
]. GMR is a leaky resonance offering
a large optical signal via efficient coupling between leaky radiation and free-space light.
Since the GMR can provide resonances that can be easily accessed from free-space, there
has been a large volume of work focusing on how GMR can be used for diverse optical
elements such as optical filters, polarizers, and bio-sensors [
1
–
3
]. Recently, the BIC mode
has received significant interests because these exotic resonant states could still be perfectly
trapped in the extended structures despite its existence within the energy spectrum of the
continuum [
4
,
5
]. While the GMR has large coupling to free-space modes, the quasi-BIC
modes enable sophisticated control of the radiative lifetime through a symmetry-lowering
perturbation, which provides a versatile platform for various applications such as lasers [
6
,
7
], nonlinear light generation [
8
,
9
], modulators [
10
–
13
], and sensors [
14
]. Complementary
to GMR and BIC concepts, passive metasurfaces have shown an extraordinary capability
for controlling diverse aspects of light such as phase, amplitude, polarization, and spectrum
[
15
,
16
]. Furthermore, reconfigurable metasurfaces can exploit new degrees of the freedom
to manipulate light in time domain [
17
]. To achieve substantial tunability of the optical
properties, the required optical response should generally be sensitive to small perturbations.
Both the GMR and the quasi-BIC mode are not only highly resonant, but also efficiently
coupled to free-space modes. Thus, the two resonant modes can potentially play a pivotal
role in the realization of active metasurfaces. Over the past decades, reconfigurable
devices hosting the GMR have been demonstrated through various platforms, such as
microelectromechanical tuning [
18
], thermal tuning [
19
], carrier injection [
20
], and electro-
optic polymer [
21
]. However, to the best of our knowledge, none of the works has been
related to the concept of the BIC mode. Thanks to the highly resonant characteristic of BIC
mode, tuning with the quasi-BIC mode can be superior in the quality factor (Q-factor)
compared to GMR in similar device size. In contrast to the devices hosting a single
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GMR mode, devices hosting both the GMR and the quasi-BIC modes can be beneficial
in exhibiting a larger phase response. Until now, the experimental demonstration of the
reconfigurable BIC mode was mostly limited to all-optical tuning[
10
–
12
]or global thermal
tuning[
13
]. In contrast to the previous tuning methods, electromechanical tuning can be
advantageous in terms of power efficiency, high modulation speed, and integration with
electronic circuits [
22
–
24
]. Moreover, the previous experimental demonstrations of the
reconfigurable BIC modes mostly focused on modulation of intensity rather than phase [
10
–
13
]. In this work, we experimentally demonstrate nanoelectromechanical tuning of both the
GMR and the quasi-BIC modes hosted by suspended silicon gratings. With a few volts, the
devices achieve reconfigurable spectral shifts, large reflection modulation, and modulation
speed over 10 kHz in air. It is also shown that the electrical tuning of the interference
between the GMR and the quasi-BIC mode can offer continuous tuning with large phase
response.
MAIN
The schematic of nanoelectromechanically tunable gratings is illustrated in Fig. 1a. The
gratings consist of two sets of pairs of doped silicon nanobars. Throughout this paper,
all structures are based on arrays of 500 nm thick and 30
μ
m long silicon bars. We also
ensure that the lattice constant of the pair of the nanobars is smaller than the wavelength of
interests to avoid unwanted diffraction. Figure 1b shows top and side views of illustrative
schematics of the gratings. One end of the suspended nanobars is connected to the large
silicon layer on which gold electrodes are deposited. To prevent bending or buckling of the
suspended structures, the other end of the suspended nanobars is connected to the anchors
marked in Fig. 1b. The gold electrodes are used to induce the Coulomb forces between the
nanobars thus enabling the actuation. The silicon gratings and the electrodes are fabricated
by sequential conventional nanofabrication procedures (see Method for details). Figure 1c
shows the scanning electron microscope images of the fabricated device, which consists of
two electrodes and an array of the gratings. The device is wire-bonded to a custom-made
printed circuit board so that it allows for connection to an external voltage source. The
optical image of the fabricated device and the printed circuit board is shown in Fig. 1d.
First, the optical characterization of the gratings is performed. The finite-sized gratings are
known to host both GMR and quasi-BIC modes that allow for coupling with free-space light
[
4
,
25
]. Figure 2a shows calculated reflection spectra for 6° tilted TE-polarized input light
(See Method for details). With a lattice constant of 700 nm, the widths of the nanobars vary
from 420 nm to 480 nm. A non-zero incident angle is chosen for efficient coupling with the
quasi-BIC mode. In other words, the coupling is achieved by breaking of the even symmetry
of the incident beam. Moreover, it is worth noting here that breaking the odd symmetry
of the mode can also result in efficient coupling at normal incidence [
26
]. In Fig. 2a, two
distinct resonant modes can be found. One mode at the shorter wavelength is the leaky GMR
mode and the other mode at the longer wavelength is the quasi-BIC mode. We fabricated
and measured seven corresponding devices with nanobar widths varying from 420 nm to
480 nm by 10 nm. A custom-built microscope setup is utilized to measure the reflection
spectra of the grating samples (See Supporting Information and Figure S1 for details about
the measurement). The spectrum is normalized by the reflection from the gold layer to
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estimate absolute reflection and remove fluctuations resulting from polarization variations
of the input light. Thus, the actual reflection values should be a few percentages lower than
the plotted reflection spectra presented in this paper considering the reflection loss of the 95
nm thick gold layer. The measured reflection spectra for the six degree tilted TE polarized
light are plotted in Fig. 2b showing good agreement with the simulation results in Fig. 2a.
The black and red circles show the positions of the GMR and quasi-BIC modes, respectively.
Furthermore, three examples of the measured reflection spectra are shown in Fig. 2c. As
shown in Figure 2b, two distinct modes, GMR and quasi-BIC mode, are observed at the
three spectra shown in Fig. 2c and also marked by black and red circles. While broad dips
below 1510 nm show dips of the low-Q fano-shape GMRs, other narrow dips over 1520 nm
represent high-Q quasi-BIC modes. If the incident angle decreases from six to zero degree,
the BIC will be protected by symmetry [
4
,
26
]. As a result, the radiation channels of the
quasi-BIC mode are gradually closed, which increases Q-factor and decreases the amplitude
of the resonant signal (see Figure S2 for two measured reflection spectra for normal and 6°
tilted TE-polarized input light).
To demonstrate nanoelectromechanical tuning of the devices, static voltage is applied to
the electrodes and the induced changes in the optical reflection are evaluated. The shape
and position of both the GMR and the quasi-BIC mode highly depend on the gap size
between the nanobars, which can be continuously controlled as a function of the external
bias. Specifically, in the configuration shown in Fig. 3a every two nanobars are connected
to one electrode and biased by an external source or ground, so bars connected to different
electrodes will attract each other. In Fig. 3a,
g
1
(
g
2
) is the gap between the nanobars
having different (same) voltages. As the external bias is applied,
g
1
and
g
2
will decrease
and increase, respectively. Consequently, this nanomechanical actuation enables continuous
shifts of the resonances. It is worth noting here that similar laterally movable actuators
have been investigated with single-mode low-Q grating resonators [
22
,
27
]. The measured
reflection spectra under several bias voltages are shown in Figs. 3b and 3c. For the devices
used in Figs. 3b and 3c, it should be mentioned that
g
1
and
g
2
are adjusted in the fabrication
process to make
g
1
smaller than
g
2
such that the nanoelectromechanical tuning of the gaps
efficiently results in a large shift of the resonances (See Table S1 for the detailed information
about the device). In Figs. 3b and 3c, the static bias causes the red shift of the GMR mode
and blue shift of the quasi-BIC mode. The observed directions of the spectral shifts show
good agreement with the simulated results (see Fig. S3 for the numerical investigation about
spectral shifts of the resonances induced by the actuation). With the external bias of 7 V,
the peak shifts of the GMR and the quasi-BIC mode shown in Fig. 3b are as large as 5 nm
and −6 nm, respectively. The absolute spectral shifts over 5 nm indicate that the required
Q-factor for the spectral shift corresponding to the bandwidth of the resonance is around
300, which is readily achievable with quasi-BIC mode resonance even in a small array [
8
].
In general, the large spectral shift is beneficial in terms of robustness, stability, and operating
bandwidth. To illustrate the capability of reflection intensity modulation of the presented
devices, the absolute changes in reflection over spectrum are plotted in Figs. 3d and 3e. In
Fig. 3e, the maximum absolute change in the reflection is as high as 0.45. As we treat the
reflection of the 95nm thick gold electrode as 1 and use it as the normalization constant,
the reflection change induced by the nanomechanical tuning will be larger than 0.4 if a
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few percentage loss from the gold surface is considered. It is also worth noting that the
modulation can be readily improved by increasing the coupling between the resonant mode
and the free space light by using the structural symmetry-breaking perturbation. Moreover,
the measured values are not the real limit but the lower bound of the performance as the
spectral shifts and the intensity modulation are measured with the external bias below pull-in
voltage.
The temporal and frequency responses of the gratings are investigated in air. To explore
temporal responses first, a periodic square-wave signal with a modulation frequency of 3
kHz, amplitude of 6V, and duty cycle of 0.5 is applied to the electrodes (see Supporting
Information for details). The device used for Fig. 3b is measured with input light at 1562
nm. The measured output signals are plotted in Fig. 4a having the corresponding frequency
of 3 kHz. Fig. 4b shows measured rise time (up to 90% power) and fall time (down to 10%
power) of 41 and 66
μ
s, respectively. The rise and fall times indicate the speed limit of
15.2 kHz which is dominantly limited by air damping. The frequency response is measured
and plotted in Fig. 4c showing the 3 dB frequency of 25 kHz. In addition, the mechanical
resonant frequency in vacuum can be calculated by COMSOL
®
(see Method for details).
The mechanical resonance frequency of the devices presented in this paper is estimated to be
around 4.5MHz that could be observed with proper vacuum packaging [
22
,
28
]. Thus, our
device has the potential to operate in a few MHz regime with decreased driving voltage.
Finally, we investigate enhanced phase modulation based on the interference of the two
resonant modes. Temporal coupled mode theory can generally describe the optical response
of eigenmodes through ports [
29
]. With coupled mode equations describing a single mode
and a single port, it is known that large phase shift close to 2
π
can only be achieved
when the resonant mode is over-coupled to the input port [
30
–
32
]. Specifically, coupling
coefficient between the mode and the input is larger than intrinsic loss of the mode in
the over-coupled regime [
31
,
32
]. Furthermore, the over-coupling is often achieved by the
presence of the bottom mirrors, that ensure the radiation of the mode is matched with the
direction of the input [
31
,
32
]. The silicon nanobars shown here are surrounded by air, so
the structure is nearly symmetric in
z
-axis. This nearly symmetric environment results in
almost identical radiation in +
z
and −
z
directions, which hinders the over-coupling of light
through one direction. As a result, using a single GMR or quasi-BIC mode hosted by the
presented devices, it is very challenging to achieve large phase modulation of reflected light
if there is no bottom mirror (see Fig. S4 for numerical study about the phase response of
the single BIC resonance). In contrast, if there are multiple resonances in the frequency
range of interest, the overall reflected phase response is affected by interference effects of
the multiple resonant modes. Thus, the interference of dual modes can enable large phase
shifts with non-zero reflection. It is worth mentioning here that a similar mechanism of the
enhanced phase responses through dual modes has been investigated in the context of the
Huygens metasurfaces or Huygens BIC metasurfaces [
33
,
34
]. Figure 5a shows calculated
reflection intensity and phase spectra of a device for which the design parameters are
adjusted to place the narrow quasi-BIC mode resonance near the peak of the broad GMR
(see Table S1 for detailed designs of the device). In Fig. 5a, the minimum reflection at the
resonance is 0.237 and the reflected phase shows strong phase response close to 2
π
. To
numerically show the phase modulation via nanomechanical tuning, expressed by
g
2
−
g
1
,
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the spectra of the reflected phase are plotted in Fig. 5b as a function of
g
2
−
g
1
. In Fig.
5b, the mechanical tuning results in continuous blue-shift of the resonance while the strong
phase response remains at the resonance. The blue-shifts of the quasi-BIC mode shown in
Fig. 5b agree with the experimental observations in Figs. 3b and 3c. For the experimental
demonstration, a new device is fabricated with the corresponding design parameters and its
reflection spectra are plotted in Fig. 5c. The reflection spectra in Fig. 5c show electrical
tuning of the resonances and a good agreement with the spectra shown in Fig. 5a. The
measured Q-factor of the device used in Fig. 5c is
∼
244, which is less than simulated
Q factor of
∼
1836. The difference could be explained by the small size of the array and
imperfect fabrications. To experimentally characterize the phase response of the device
used in 5c, we used a Michelson-type interferometer setup (see Supporting Information and
Figure S1). Due to the small size of the device, the incident laser beam illuminates the
entire grating and the gold electrode at the same time and the interference patterns on both
interfaces are simultaneously collected by a camera. At the resonant wavelength of 1556 nm,
the fringes on the grating are shifted by external biases from 0 V to 4 V while the fringes on
the electrode are unchanged (see Supporting Information and Figure S5 for the details). The
induced phase modulation is estimated by the observed shifts of the fringes on the grating
and plotted in Fig. 5d. The largest phase shift of 144° is achieved at the external bias of 4V,
which is smaller than the simulation result shown in Figs. 5a and 5b. The deviation from
the simulation is primarily due to limited free-space coupling to the quasi-BIC mode. For
example, the absolute reflection dip shown in Fig. 5a is much smaller than the measured
dip in Fig. 5c indicating imperfect coupling to the quasi-BIC mode. We believe that this
inefficient coupling dominantly results from the finite size effect.
Although it might be expected that the introduction of a spatially varying perturbation for
each pair of the nanobars could allow electrically controlled wavefront shaping, it is worth
explicitly noting that the presented resonance mode doesn’t support efficient wavefront
shaping at subwavelength scale. The introduction of the spatially varying perturbations
at subwavelength scale may severely break the periodic condition of the structures, that
the two modes necessitate to resonate. Thus, the interference effect of the two resonant
modes is more suitable for spatial light phase-modulators having a pixel pitch of tens
of micrometers than the pixel pitch of subwavelength scale. However, we expect that
electrically controlled wavefront shaping in subwavelength or wavelength scale is possible
with judicious engineering of various resonance modes hosted by an array of dielectric
nanostructures [
13
,
35
–
37
].
In summary, we demonstrate nanoelectromechanical tuning of the leaky GMR and the
quasi-BIC modes hosted by suspended silicon grating structures. With an external bias
below 7 V, the devices experimentally achieve a spectral shift of the resonance over 5
nm, intensity modulation exceeding 40%, and modulation speed over 10 kHz in air. The
required electrostatic bias can be further decreased by choosing the resonant modes that host
large electric fields in the gaps [
38
]. In addition, co-optimization of both mechanical and
optical properties is expected to improve the operating speed in air. With proper vacuum
packaging, the devices may operate at high mechanical resonant frequency around several
MHz. Moreover, we experimentally show that the interference between the GMR and
quasi-BIC mode can enhance the phase response. The phase shift of 144° is measured
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at the external bias of 4V. Engineering of the resonant modes via structural tuning will
improve the phase responses and enable dynamic wavefront shaping at subwavelength scale.
Thus, this work paves the way of nanoelectromechanical dynamic dielectric metasurfaces
towards diverse applications such as spatial light modulators, lasers, nonlinear or structured
light generation, pulse controller, polarization converters, and compact spectrometers for
bio-sensing.
METHODS
Simulation and design
The reflected spectra of the gratings with 6° tilted incidence light were calculated using
the rigorous coupled wave analysis technique [
39
]. Assuming the infinite length of silicon
nanobars, 2D simulations were performed. The silicon, air, and silicon oxide layers on a
silicon substrate were 500nm, 300 nm, and 2700 nm thick, respectively. Refractive indices
of Si and SiO
2
for the telecom wavelength in the simulation were 3.4 and 1.45, respectively.
The width and lattice constant were varied in the simulation to achieve the desired reflection
spectra (see Table S1 for detailed information about the design parameters).
The mechanical resonance frequency is calculated by a commercial software based on the
finite element method, COMSOL
®
. The eigenfrequency of the Si bar is extracted assuming
that both ends of the suspended nanobars are fixed. In the mechanical simulation, Young’s
modulus and density values for silicon were 170 GPa and 2329 kgm
−3
, respectively.
Device fabrication
The devices are fabricated using a silicon-on-insulator SOI wafer with a device layer of
500 nm and a buffered oxide layer of 3
μ
m on a 1 mm thick silicon wafer. The fabrication
includes two sequential e-beam lithography steps, the first one for the grating structures and
another for the electrodes. For both 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). For the silicon grating structures, the ZEP resist is
utilized as a soft mask to etch the silicon device layer and then removed by remover
PG (Microchem). Next, the electrodes were patterned by electron beam lithography, the
deposition of chrome and gold (5nm and 95nm) layers, and liftoff. Buffered hydrofluoric
acid is exploited to etch the buffered oxide layer under the gratings. The time of the
under-cut process is carefully controlled such that the anchors are supported by the SiO
2
while the gratings are fully suspended. The device is dried by a critical point dryer. Finally,
the device is bonded to a custom printed circuit board using a wire bonder (WestBond
7476D).
Supplementary Material
Refer to Web version on PubMed Central for supplementary material.
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ACKNOWLEDGEMENTS
We thank Jeong Oen Lee for helpful discussion about nanoelectromechanical system. This work was supported
by the National Institutes of Health (NIH) brain initiative program, grant NIH 1R21EY029460-01. The device
nanofabrication was performed at the Kavli Nanoscience Institute at Caltech. H.K. acknowledges a fellowship from
Ilju organization.
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Fig. 1. Nanoelectromechanical tunable suspended gratings
a
Schematic illustration of the nanoelectromechanically tunable gratings. The grating is
composed of pairs of silicon nanobars. The nanobars are connected to electrodes for
actuation through electrostatic force. Black arrows show the directions of the actuation.
b
Schematic illustration of top (top) and side (bottom) views of the grating. Top: Two gold
electrodes are deposited on top of the doped-silicon layers. Anchors and the gold electrodes
are marked. Bottom: Buffered silicon oxide layer under the silicon nanobars is partially
etched by 300 nm for the suspension while the anchors are supported by the oxide layer.
c
Scanning electron microscope images of the fabricated devices. Left: An array of the
gratings and two gold electrodes are shown. One of the gratings is marked by a purple box.
Right: Zoom-in scanning electron microscope image of the grating marked with the purple
box in the left image. The grating consists of 23 pairs of silicon nanobars. Scale bars in left
and right denote 500
μ
m and 5
μ
m, respectively.
d
Optical images of the fabricated device.
The device is wire-bonded to a custom printed circuit board that is connected to an external
source by a SMA cable.
Kwon et al.
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