1
M
OHAMMAD
S
ADEGH
F
ARAJI
-D
ANA
1,2
, E
HSAN
A
RBABI
1,2
, H
YOUNGHAN
K
WON
1,2
,
S
EYEDEH
M
AHSA
K
AMALI
1,2
, A
MIR
A
RBABI
3
, J
OHN
G. B
ARTHOLOMEW
1
,
AND
A
NDREI
F
ARAON
1,2,
Ü
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
Department of Electrical and Computer Engineering, University of Massachusetts Amherst, 151 Holdsworth Way, Amherst, MA 01003, USA
Ü
Corresponding author: faraon@caltech.edu
This
document
contains
supplementary
information
for
"Hyperspectral
imager
with
folded
metasurface
optics".
Section
S1
and
S2
provide
further
details
of
the
theoretical
and
experimen-
tal
methods
employed
to
design,
fabricate
and
characterize
the
device.
Figures
S1
–S8
contain
further
simulation
and
measurement
data.
S1. MA
TERIALS
AND METHODS
Simulation and design
The system level design and simulation of the folded metasurface hyperspectral imager is performed using Zemax OpticStudio, where
metasurfaces were defined as phase-only diffractive elements. The diffraction grating was modeled as a phase-surface with a linear
phase along the dispersion direction (i.e.,
y
direction). The blazed grating, with a period of 1
μ
m, deflects the normal incident light
into deflection angles of 31.14
◦
and 35.88
◦
at 750 nm and 850 nm, respectively. The phase profiles of metasurfaces I, II and III were
defined as polynomial expansions in Cartesian coordinates,
Σ
n
,
m
a
m
,
n
x
m
y
n
(named Binary 1 surfaces in Zemax OpticStudio). The
a
m
,
n
expansion coefficients were optimized to reduce geometrical aberrations for input angles within the range of -15
◦
to +15
◦
and
wavelengths in the range of 750 to 850 nm. This was done by minimizing the geometric radii of image-plane focuses corresponding
to each angle and wavelength, which finally leads to maximizing the angular and spectral resolution of the designed hyperspectral
imager. The optimized coefficients for metasurfaces I, II, and III, as shown in Fig. 2 of the main manuscript, are given in Table
S1.
The phased profiles of metasurfaces I, II, and III are plotted in Fig.
S1
a
. The point spread functions (PSFs) for three wavelengths
(750 nm, 800 nm, and 850 nm) and angles of 0
◦
, 5
◦
, 10
◦
, and 15
◦
are calculated for two cases. In the first case, shown in Fig.
S1
b
, the
PSFs for two beams with the same incident angle, but separated spectrally by 1.5 nm centered around the specified wavelengths
are plotted, and seen to be well resolved. In the second case, plotted in Fig.
S1
c
, PSFs for two beams with the same wavelength but
separated by 0.1
◦
around their corresponding incident angle show two resolved peaks. These verify the upper limits for spectral and
angular resolutions of
∼
1.5 nm and
∼
0.1
◦
, respectively. Due to the symmetry of the metasurfaces along the
x
-axis (see Fig.
S1
a
), the
same conclusion holds true for negative incident angles. Furthermore, although only three different spectral points and four angular
points were shown in Figs.
S1
b
and
c
, it is worth mentioning that the design is close to diffraction-limited for all wavelengths and
angles within the design range.
Table S1.
Optimized
phase profile coefficients for metasurfaces
Metasurface
Size
[
mm
2
]
a
x
2
y
0
a
x
0
y
2
a
x
2
y
1
a
x
0
y
3
a
x
4
y
0
a
x
2
y
2
a
x
0
y
4
a
x
4
y
1
a
x
2
y
3
a
x
0
y
5
I
2.1
×
1.1
-5.087
-9.197
0.052
0.234
1.84
e
-3
-2.064
e
-3
-4.002.
e
-3
-1.153
e
-4
2.754
e
-4
6.19
e
-5
II
2.48
×
0.8
-2.898
7.229
0.029
-1.494
-4.207
e
-3
6.308
e
-3
0.140
4.355
e
-4
-3.081
e
-3
-0.020
III
2.6
×
0.96
-3.513
11.137
-0.872
1.422
0.011
-6.571
e
-3
-0.043
-1.397
e
-3
2.947
e
-3
6.42
e
-3
The rigorous coupled wave analysis technique was used to simulate the nano-posts [
1
]. The unit cells for reflective (I and II) and
transmissive (III) metasurfaces are shown in Fig.
S2
a
and Fig.
S2
g
, respectively. The design method utilized to achieve high-efficiency
Hyperspectral
Imager
with
Folded
Metasurface
Optics:
supplementary
materials