Supporting Information: “High-speed,
phase-dominant spatial light modulation with
silicon-based active resonant antennas”
Yu Horie,
†
Amir Arbabi,
†
,
‡
Ehsan Arbabi,
†
Seyedeh Mahsa Kamali,
†
and
Andrei Faraon
∗
,
†
,
¶
†
T. J. Watson Laboratory of Applied Physics, California Institute of Technology, 1200 E
California Blvd, Pasadena, CA 91125, USA
‡
Present address: Department of Electrical and Computer Engineering, University of
Massachusetts, 151 Holdsworth Way, Amherst, MA 01003, USA.
E-mail: faraon@caltech.edu
In this Supporting Information, we present additional information on
Figure S1
Schematic of experimental setup,
Figure S2
Measured reflectivity spectra for phase measurements,
Figure S3
Simulated response times in temperature modulation, and
Figure S4
Simulated phased array beam deflection.
1
1550 nm
tunable laser
M1
CL
L1
BS1
(90/10)
BS2 (90/10)
QWP
Phase
Reectivity
PH
HWP
PBS
Pol1
PD1
PC
Iso
L4
L2
FG
MO (20x)
DUT
PD2
SWIR camera
L5
L3
M2
Pol2
HWP
Figure S1
: Experimental setup. A continuous-wave laser light emitted from a tunable external cavity
laser diode was used as a light source for the measurements. After transmitting through the PBS, the
laser beam was demagnified by a lens (L2, focal length: 200 mm) and a 20
×
microscope objective (MO),
resulting in a Gaussian beam waist of 75 μm on the object plane. The reflected light was then imaged
by the same lenses onto a pinhole (PH) with a diameter of 400 μm to select the region of interest with
a corresponding diameter of 20 μm in the object plane. After the PH, the intensity was measured by
focusing the light onto PD2 using a lens pair of L3 and L4, while the device image was monitored by a
SWIR camera. The image was created with the L3 and L5 lens pair. For the reflectivity measurement,
a polarizer and a HWP were inserted in the path, where the angle of the polarizer was set to 45
◦
with
respect to the axes of the PBS. For the phase extraction measurement, a QWP was inserted in place of the
polarizer in order to make the incident polarization state elliptical. Iso: optical isolator. PC: polarization
controller. CL: collimation lens. Pol: polarizer. BS: beamsplitter. L: lens. PD: photodetector. M: mirror.
PBS: polarizing beamsplitter. QWP: quarter waveplate. HWP: half waveplate. MO: microscope objective.
DUT: device under test. FG: function generator. PH: pinhole.
2
1500
1510
1520
1530
1540
1550
W
ave
lengt
h (nm
)
0
1
2
3
4
5
6
7
Re
ected signa
l (a.u.)
QW
P angl
e
0 deg
15
deg
30
deg
45
deg
Figure S2
: Measured reflectivity spectra for different QWP angles in a cross-polarized setup. These data
were used to fit the model to extract the phase curve in Fig. 2(b).
0
200
400
600
800
1000
Tim
e (μs)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Δ
T (a.
u.
)
33
μs
36
μs
Modul
ated
Input
Figure S3
: Simulated response times in temperature modulation. The time-dependent heat transfer simu-
lations were performed by FEM. The rise and fall response times were found 33 μs and 36 μs, respectively,
in fair agreement with measured values. The difference between the simulation and the measurement
should be attributed to the difference between thermal conductivities used in simulation and the actual
values. The response time here is defined as the time duration by which the temperature rises (or falls)
from 10% to 90% (or vice versa) of the steady-state when an input signal modulates the microheater.
3
(a)
(b)
(c)
Gaussian beam waist 75 μm
Far-eld intensity
Near-eld pattern
unmodulated
phase-only
amplitude-only
0.0
0.2
0.4
0.6
0.8
1.0
1 deg
phase = 0 rad
phase = π rad
amplitude = 1
amplitude = 0
−4
−3
−2
−1
0
1
2
3
4
Angl
e (deg)
0.0
0.2
0.4
0.6
0.8
1.0
Power (a.u.)
Am
plit ude
-onl
y
o
on
−4
−3
−2
−1
0
1
2
3
4
Angl
e (deg)
0.0
0.2
0.4
0.6
0.8
1.0
Power (a.u.)
Phase-onl
y
o
on
Figure S4
: Simulated phased array beam deflection. (a) Simulated near-field phase and amplitude profiles
in cases of amplitude-only and phase-only modulations. An incident Gaussian beam profile with a beam
waist of 75 μm was used. (b) Simulated far-field patterns. The dashed box indicates the
±
1
st order
diffraction angles imposed by the pixel pitch. (c) Corresponding 1D profiles of the simulated far-field
patterns along the deflection direction, showing that phase modulation can perform beam deflection with
a higher efficiency. This also confirms that the silicon active antennas used in the experiments do phase-
dominant modulation. The deflected beam appeared at the angles
θ
=
±
θ
max
=
±
1
.
7
◦
as denoted by the
yellow shades including the Gaussian divergence half angle of
0
.
37
◦
. The dashed line corresponds to the
angles of the
±
1
st diffraction orders resulting from the pixel pitch.
4