Compact Folded Metasurface Spectrometer: Supplementary
Material
MohammadSadegh Faraji-Dana, Ehsan Arbabi, Amir Arbabi,
Seyedeh Mahsa Kamali, Hyounghan Kwon, and Andrei Faraon
1
SUPPLEMENTARY NOTE 1: SIMULATION AND DESIGN
Ray tracing simulations of the spectrometer were performed using Zemax OpticStudio. In
the simulations, metasurfaces were assumed to be phase-only diffractive surfaces. The grating
was modeled as a blazed grating with a linear phase along the direction of dispersion (
y
), and
independent of the other direction (
x
). The phase was chosen to correspond to a period of 1 μ
m
,
resulting in deflection angles of 31.6
◦
and 36.35
◦
at 760 nm and 860 nm, respectively. The angles
were chosen such that the focused light could be captured by an objective with a numerical aperture
of 0.95, while maximizing the dispersive power. The second and third surfaces were modeled
as a summation of Cartesian coordinate polynomials (Binary 1),
Σ
n,m
a
m,n
x
m
y
n
, and cylindrical
coordinate radially symmetric polynomials (Binary 2)
Σ
i
b
2
i
ρ
2
i
. The coefficients were optimized to
reduce geometric aberrations by minimizing the root mean square geometric spot radii for several
input wavelengths covering the bandwidth. The optimized coefficients are given in Supplementary
Table
1
. As shown in to Fig.
2
b, all focal spots are optimized and are within the airy disks.
This indicates that the designed spectrometer has small geometrical aberrations. The diffraction-
limited resolution curve obtained is shown in Fig.
2
c. The simulations and optimizations were first
performed in an unfolded configuration for simplicity. There were several constraints in finding
the sizes for input and output apertures. Two opposing factors existed in determination of the 790-
μ
m
input aperture diameter. On one hand, a larger input aperture results in a higher throughput
and more captured light as well as a higher numerical aperture and potentially better resolution.
On the other hand, the aperture size for the folded platform cannot be arbitrarily large because
different metasurfaces should not overlap. Thus, the 790-μ
m
aperture diameter was chosen in
the ray-tracing simulations as the largest size for which metasurface overlap can be avoided and
diffraction-limited focusing can be achieved. The output aperture spatially filters the out of band
wavelengths while passing through the bandwidth of interest. Therefore, its size was chosen as
the smallest possible aperture that allows for all wavelengths of interest to pass through. Using the
ray-tracing simulations, this optimum size was found to be 978 μ
m
.
The rigorous coupled wave analysis (RCWA) technique [1] was used to obtain reflection phases
of the nano-posts. For each specific set of dimensions, a uniform array of the
α
-Si nano-posts
was illuminated with a plane wave at the wavelength of 810 nm under an illumination angle of
33.9
◦
and the reflected amplitudes and phases were extracted for each polarization. To choose
the height of the nano-posts, we performed these simulations for nano-posts with square cross-
2
sections and different heights and side lengths [Supplementary Figure
1
]. The height was then
chosen to minimize the variation of the derivative of the phase with respect to wavelength for
different side lengths, while providing a full 2
π
phase coverage and high reflectivity. Considering
the results of Supplementary Figure
1
b and Supplementary Figure
1
d, we chose the thickness to
be 395 nm. Although this height is slightly less than
λ
/2, it is large enough to provide a full 2
π
phase coverage as the device operates in reflection mode. The lattice constant was chosen to be
246 nm in order to satisfy the sub-wavelength condition and avoid higher order diffractions, which
require
l
c
< λ/n
(1 + sin(
θ
max
))
, where
l
c
is the lattice constant,
n
is the refractive index of the
substrate, and
θ
max
is the maximum deflection angle [2]. We chose
sin(
θ
max
) = 1
/n
, since light
traveling at larger angles will undergo total internal reflection at the output aperture. To make the
two focusing metasurfaces polarization-insensitive, reflection phase and amplitudes were obtained
for nano-posts with rectangular cross section under oblique illumination with both TE and TM
polarizations [Fig.
3
]. The design curves were then generated by determining a path in the
D
x
-
D
y
plane along which TE and TM reflection phases are almost equal.
For designing the blazed diffraction grating, we chose to use the same
α
-Si thickness of 395
nm (for ease of fabrication). The lattice constant was set to be 250 nm, such that a grating period
contains four nano-posts, and the structure becomes fully periodic. This allows for using peri-
odic boundary conditions in the full-wave simulations of the structure, reducing the simulation
domain size significantly. The initial values of the post widths were chosen using a recently de-
veloped high-NA metasurface design approach [3]. The simulation results for nano-post-width vs
reflection-phase and the initial post widths are plotted in Supplementary Figure
3
a. These values
were then fed to a particle swarm optimization algorithm (using an RCWA forward solver) as a
starting point. The algorithm optimizes the deflection efficiency of the grating for both polariza-
tions at 11 wavelengths spanning the bandwidth of interest. The optimization parameters are the
side lengths of the rectangular nano-posts, while their thickness and spacing is fixed. Deflection
efficiencies of the initial and optimized gratings are plotted in Supplementary Figure
3
b. The
corresponding nano-post widths for both gratings are given in Supplementary Table
2
.
SUPPLEMENTARY NOTE 2: SAMPLE FABRICATION
A summary of the key steps of the fabrication process is shown in Supplementary Figure
4
.
A 395-nm-thick layer of
α
-Si was deposited on one side of a 1-mm-thick fused silica substrate
3
through a plasma enhanced chemical vapor deposition process at 200
◦
C. The metasurface pattern
was then generated in a
∼
300-nm-thick layer of ZEP-520A positive electron resist (spun for 1
minute at 5000 rpm) using an EBPG5200 electron beam lithography system. After development
of the resist in a developer (ZED-N50, Zeon Chemicals), a
∼
70-nm-thick alumina layer was evap-
orated on the sample in an electron beam evaporator. After lift-off, this layer was used as a hard
mask for dry etching the
α
-Si layer in a mixture of SF
6
and C
4
F
8
plasma. The alumina layer
was then removed in a 1:1 solution of H
2
O
2
and NH
4
OH. A
∼
2-μ
m
-thick layer of SU-8 2002
polymer was spin-coated, hard-baked and cured on the sample to protect the metasurfaces. The
output aperture (which is on the same side as the metasurfaces) was defined using photolithogra-
phy (AZ-5214E positive resist, MicroChemicals) and lift-off. A
∼
100-nm-thick gold layer was
deposited as the reflective surface. To protect the gold reflector, a second layer of SU-8 2002 was
used. To define the input aperture, a
∼
2-μ
m
-thick layer of SU-8 2002 polymer was spin-coated
and cured on the second side of the wafer to improve adhesion with gold. The input aperture was
then defined in a process similar to the output aperture.
SUPPLEMENTARY NOTE 3: DEVICE CHARACTERIZATION PROCEDURE
The measurement setups used to characterize the spectrometer are schematically shown in Sup-
plementary Figure
5
. Light from a tunable Ti-sapphire laser (SolsTiS, M-Squared) was coupled
to a single mode optical fiber and collimated using a fiber collimator (F240FC-B, Thorlabs). A
fiber polarization controller and a free space polarizer (LPVIS100-MP2, Thorlabs) were used to
control the input light polarization, and different neutral density filters were used to control the
light intensity. The beam illuminated the input aperture of the spectrometer at normal incidence.
The focal plane of the spectrometer, located
∼
200 μ
m
away from the output aperture, was then
imaged using a custom built microscope (objective: 100
×
UMPlanFl, NA=0.95, Olympus; tube
lens: AC254-200-C-ML, Thorlabs; camera: CoolSNAP K4, Photometrics). Since the field of view
is
∼
136 μ
m
(limited by the
∼
15-mm image sensor, and the
∼
111
×
magnification), while the total
length over which the wavelengths are dispersed in the focal plane exceeds 1 mm, the objective is
scanned along the dispersion direction to cover the whole focal plane at each wavelength (11 im-
ages captured for each wavelength). These images were then combined to form the full intensity
distribution at each wavelength. The measurements were performed at 11 wavelengths (760 nm
to 860 nm, 10-nm steps) to form the results shown in Figs.
4
b,
4
c , Supplementary Figure
6
, and
4
Supplementary Figure
7
. The measurements were also performed at a second set of wavelengths
(761.25 nm, 811.25 nm, and 861.25 nm). These results are summarized in Fig.
4
d and Fig.
4
e
for TE and TM polarizations. The resolution [Supplementary Figure
8
] was estimated by finding
the full-width-half-maximum (FWHM) at each wavelength, and the displacement rate of the focus
center along the y direction by changing the wavelength. The setup was slightly changed for mea-
suring the focusing efficiencies. The input beam was partially focused by a lens (
f
=
10 cm) such
that all the beam power passed through the input aperture (with a
∼
400
μ
m
FWHM). In addition,
the camera was replaced by a photodetector and a pinhole with a diameter of 3.5 mm in front of
it to measure the focused power. The pinhole, corresponding to a
∼
31-μ
m
area in the focal plane,
allows only for the in-focus light to contribute to the efficiency. The efficiency is then calculated
at each wavelength by dividing these measured powers by the total power tightly focused by a
10-cm focal length lens that was imaged onto the power meter using the same microscope (i.e.,
by removing the spectrometer and the pinhole). The experimental setup for capturing the sample
spectra is almost identical to Supplementary Figure
5
b, with the only difference of the polarizer
being replaced by the sample of interest, and an 840-nm short-pass filter inserted before the sam-
ple. The light source was also replaced by a supercontinuum laser (Fianium Whitelase Micro,
NKT Photonics).
SUPPLEMENTARY NOTE 4: ANGULAR RESPONSE MEASUREMENT
To measure the angular response of the device we used the setup shown in Supplementary
Figure
9
c, equipped with a rotating stage with 0.1
◦
precision in the
x
-
z
plane and 0.002
◦
in the
y
-
z
plane. The collimator (connected to the fiber coming from the source) was mounted on this
rotating stage, where the folded spectrometer was exactly located at its center. The incident angles
were adjusted accordingly for 0
◦
,
±
0.3
◦
,
±
0.6
◦
,
±
1
◦
angles. As can be observed in Supplementary
Figure
9
a, the focal spots did not vary much in size as the angle is sweeped between -1
◦
to +1
◦
in
x-direction. For measuring the tilt angle in the
y
-
z
plane, the distance from the collimator to the
device was measured to be 280 mm. In order to impose
±
0.15
◦
tilt in y direction, the mounted
collimator level is raised or lowered by 0.73 mm, and its tilt was adjusted accordingly such that
the beam hits the center of the input aperture. As shown in Supplementary Figure
9
b, such a tilt in
input incident angle does not degrade the spectral resolution of 1.25 nm.
5
SUPPLEMENTARY NOTE 5: INCREASED THROUGHPUT DESIGN
To further demonstrate the capabilities of the platform, we have designed a second spectrom-
eter with significantly increased throughput. In order to achieve higher throughput, a larger input
aperture was required, so the slab thickness was increased to 2 mm to give more freedom on the
non-overlapping condition for the metasurfaces. The design, as shown in Supplementary Figure
10
, has a 2.5mm input aperture. To further improve the throughput, the acceptance angle of the
device was increased. To achieve this goal, we took an approach similar to the fabricated spec-
trometer with the difference of adding extra phase terms to the input diffraction grating. This helps
with orienting the focuses on the image plane for different incident angles, as well as relaxing the
condition for focusing in the x-direction. This in turn allows for increasing the input incident angle
to
±
15
◦
degrees. The phase profile coefficients for metasurfaces 1 to 3 in Supplementary Figure
10
are given in Supplementary Table
3
. In the final design, the power is distributed in an area
close to 200 μ
m
wide in the x-direction in the focal plane, instead of a diffraction limited focus.
According to the intensity profiles shown in Supplementary Figure
10
b, the device can distinguish
between wavelengths spaced by 0.5 nm both at the center wavelength of 810nm, and also at the
side wavelengths of 760 nm and 860 nm. Based on the angular response of the device in the x-
z and y-z planes, and also the input aperture size of the device, an etendue of around
∼
13000
Sr
(
μ
m)
2
is estimated.
6
Supplementary Table
1
.
Phase profile coefficients in terms of
[
rad/mm
m
+
n
]
for metasurfaces 1 and 2
Metasurface
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
ρ
6
a
ρ
8
a
ρ
10
I (R=525.0 μ
m
)
−
4
.
02
−
2
.
08 0
.
47 0
.
20
−
5
.
68
e
−
4 7
.
55
e
−
3 2
.
36
e
−
3 1
.
93
e
−
4
−
3
.
22
e
−
6
−
5
.
886
e
−
9
II (R=582.5 μ
m
)
−
3
.
91
−
3
.
70
−
0
.
68
−
0
.
24 6
.
26
e
−
3 0
.
021 6
.
34
e
−
3
−
2
.
48
e
−
4 4
.
82
e
−
6
−
2
.
974
e
−
9
Supplementary Table
2
.
Optimized grating post sizes [nm] (
D
x
,D
y
)
Optimization
D
x
1
D
y
1
D
x
2
D
y
2
D
x
3
D
y
3
D
x
4
W
y
4
Maximizing first order diffraction Efficinecy
93
.
4 93
.
4
117 117
132
.
8 132
.
8
155
.
4 155
.
4
Particle Swarm Optimization
68 134
115
.
2 119
.
6
147
.
4 151
.
2
137
.
8 178
.
8
7