Supporting information: Nanoelectromechanical tuning of dual-mode
resonant dielectric metasurfaces for dynamic amplitude and phase
modulation
Hyounghan Kwon,
1, 2, 3
Tianzhe Zheng,
1, 3
and 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
∗
Corresponding author: A.F.: faraon@caltech.edu
1
MEASUREMENT PROCEDURE
All of the reflection spectra presented in this paper are characterized using the set-ups shown
schematically in Figure S1 [1]. A tunable laser (Photonetics, TUNICS-Plus) is used as the light
source and the wavelength of the light is tuned from 1450 nm to 1580 nm. We use a beam splitter
in front of the fiber 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 captured by a InGaAs
detector (Thorlabs, PDA10CS). Due to variation in polarization states from the laser, a quarter
waveplate in front of a polarization beamsplitter (PBS) is used to prevent low transmission through
PBS at specific wavelengths, increasing signal-to-noise ratio over the entire spectrum. The PBS, a
half waveplate (HWP), 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
×
infinity-corrected objective
lens (Mitutoyo, M Plan Apo NIR) and a tube lens with a focal length of 200 mm. As the tube lens
and the objective lens are forming a 4-f system, the movement of the tube lens in
푥
-axis enables
to adjust the angle of illuminated light. At the image plane, a pinhole with a diameter of 400
휇
m is inserted to select a region of interest with a diameter of 20
휇
m in the object plane. The
spatially filtered 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 spectra in this paper were obtained by dividing the signal from the sample by the signal from
the sources. Due to different input polarization states, the incidence power onto the sample varies
in different wavelengths. Thus, the spectra are further normalized by the spectra from the gold
electrode. For the measurement of dynamic responses shown in Figs. 3-5, bias voltages, both DC
and AC, are applied with a function generator (FeelTech, FY6600-60M).
To measure the phase response shown in Fig. 5d, we use a Michelson-type interferometer setup.
A part of the setup marked by a black dashed box in Figure S1 is only utilized for the phase
measurement. Specifically, the reference beam interferes with the reflected beam of the sample
and forms fringe patterns at both image and camera planes enabling the measurement of reflected
phase as a function of applied biases from 0V to 4V. As shown in Figures S5b and S5C, the fringes
are not shifted on the electrode but on the gratings under different external biases. The phase
responses under the external biases are calculated by using the corresponding shifts of the fringes
on the grating shown in Figure S5c. We used the formula
2
휋
훿푤
푤
0
to calculate the phase shifts, where
훿푤
is the averaged shift of the fringes in the unit of camera pixel number, and
푤
0
is the pixel
2
number of a period of the fringe. The measured
푤
0
is 10 camera pixels. Finally, the phase shifts
are averaged from all five pictures in Figure S5c and plotted in Fig. 5d.
3
Figure
2l (nm) w (nm) g
1
(
푛푚
)
g
2
(
푛푚
)
Figures 3b,3d, and 4 1400 495 245 165
Figures 3c and 3e 1320 495 185 145
Figure 5
1332 494 144 200
Figure S2a
1400 460 240 240
Figure S2b
1400 480 220 220
Table S1
Design parameters for all nanomechanical gratings in this work.
2
푙
: Lattice constant for a pair of
the silicon bars.
푤
: Width of the silicon bar.
푔
1
: Gap between the silicon bars having voltage difference.
푔
2
: Gap between the silicon bars having same voltage.
4
Figure S1 Schematic illustration of the experimental setup.
Red lines represent the paths of the light.
To achieve the reflection spectra of the TE-polarized input light, Pol. and HWP in front of the objective
lens are aligned to 45 and 67.5 degree, respectively. A black dashed box represents optical elements
exploited to generate reference beam for the phase measurement shown in Fig.
5d
of the main text and
Figure S5. Pol.: linear polarizer. BS: beamsplitter. PBS: polarizing beamsplitter. L: lens. PD:
photodetector. M: mirror. QWP: quarter waveplate. HWP: half waveplate. Obj.: microscope objective
lens. SWIR camera: short-wave infrared camera
5
Figure S2 Measurement of angle-sensitive reflection spectra. a
and
b
Red and blue curves show the
reflection spectra for normal and 6 degree tilted TE polarized incident light, respectively. With 500 nm
thickness and 700 nm period of the lattice, the design parameters of a and b are shown in Table S1.
6
Figure S3 Numerical investigation related to spectral shifts of the resonances induced by actuation.
The spectra are simulated under six different values of
푔
2
−
푔
1
and plotted in different colors. The value of
푔
2
−
푔
1
for each color is shown in legends. The width and lattice constant of the device are 480 nm and 700
nm, respectively.
7
Figure S4 Calculated reflection and reflected phase spectra for single BIC resonance.
The quasi-BIC
mode is apart from the peak of the GMR. At the resonance wavelength of 1543 nm, the calculated phase
response of the quasi-BIC mode is smaller than 55 deg. The width and the lattice of the structures are 475
nm and 666 nm, respectively.
8
Figure S5 Fringe analysis for phase response measurement. a
A camera image of the fringes on the
measured device. The red dashed square shows the position of the measured device. Five solid red lines
inside the red square and a black solid line show the places that we use to analyze the phase responses on
the grating and the electrode, respectively. Scale bar denotes 30
휇
m.
b
The fringe patterns on the electrode
under the external biases from 0V to 4V. The fringe patterns are captured along the black solid line in a.
The fringes are nearly identical and not shifted for the different voltages.
c
The five fringe patterns on the
grating under the external biases from 0V to 4V. The fringe patterns are captured at the center of the
grating along the five red solid line in a. The five plots show the clear shifts of the fringes. In b and c,
푥
-
and
푦
- axes are pixel number and pixel value of the camera, respectively. The applied biases for all colors
are denoted in outsets in b and c.
9
I. REFERENCES
[1] Horie, Y., Arbabi, A., Arbabi, E., Kamali, S. M. & Faraon, A. High-speed, phase-dominant spatial light
modulation with silicon-based active resonant antennas.
ACS Photonics
5
, 1711–1717 (2017).
10