Supplementary Information for “Angle-multiplexed metasur-
faces: encoding independent wavefronts in a single metasurface
under different illumination angles”
Seyedeh Mahsa Kamali, Ehsan Arbabi, Amir Arbabi, Yu
Horie, MohammadSadegh Faraji-Dana, and Andrei Faraon
1
SUPPLEMENTARY NOTE 1: ANGLE-MULTIPLEXED GRATING SIMULATION RESULTS
The central
∼
200-
μ
m-long portion of the grating presented in the main text, was simulated for
comparison. The simulated grating is 445 lattice constants long in the
x
direction and 1 lattice
constant long in the
y
direction. Periodic boundary condition was considered in the
y
direction.
The grating was simulated at the wavelength of 915 nm in MEEP [1] and normal and
30
◦
incident
y-polarized (TE) plane-waves were used as the excitation. Angular distribution of the reflected
power at
0
◦
and
30
◦
incident angles are shown in supplementary Figs. 3a and 3b, respectively.
The far field reflected power was analyzed by taking the Fourier transform of the reflected field
above the meta-atoms. The deflection efficiency was calculated by dividing the deflected power
to the desired order by the total input power. The simulated deflection efficiency for
0
◦
and
30
◦
incident angles were 63
%
and 54
%
respectively. Existence of no other strong diffraction order
in supplementary Figs. 3a and 3b, and the high deflection efficiencies achieved demonstrate the
independent control of the platform at each incident angle. To consider the possible fabrication
errors, the grating with a random error added to all the in-plane sizes of the meta-atoms is also
simulated. The error is normally distributed with a zero mean, a 4-nm standard deviation, and a
forced maximum of 8 nm. Angular distribution of the reflected power at
0
◦
and
30
◦
incident angles
for the grating with a random error are shown in supplementary Figs. 3c and 3d, respectively. The
simulated deflection efficiencies with the added errors are 46
%
and 39
%
under
0
◦
and
30
◦
incident
angles. Although the deflection efficiency of the grating drops by adding a random random, its
general functionality remains the same according to the supplementary Figs. 3c and 3d.
2
SUPPLEMENTARY FIGURES
3
0
φ
1
/(2
π
)
1
0
1
φ
2
/(2
π
)
|r
1
|
0
1
0
φ
1
/(2
π
)
1
0
1
φ
2
/(2
π
)
|r
2
|
Reection amplitude
Side view
k
|r
1
|e
i
φ
1
k
1
Side view
x
y
z
1
k
|r
2
|e
i
φ
2
k
θ
i
0
φ
1
/(2
π
)
1
0
1
φ
2
/(2
π
)
Achieved
φ
1
/(2
π
)
0
1
0
φ
1
/(2
π
)
1
0
1
φ
2
/(2
π
)
Reection phase
Achieved
φ
2
/(2
π
)
x
y
z
a
b
Supplementary Fig.
1.
Simulated achieved reflection amplitudes and phases for the selected meta-
atoms. a
, Simulated reflection amplitudes at
0
◦
and
30
◦
incident angles as a function of required phase
shifts for the periodic array of selected meta-atoms that can span the full 2
π
by 2
π
phases for both incident
angles.
b
, Simulated achieved phase shifts of the chosen nano-posts versus the required phase shift values.
4
OL
FC
915 nm laser
PC
P
RS
1
RS
2
Camera
BS
L
1
a
FC
P
L
1
RS
1
RS
2
Camera
L
2
OL
915 nm laser
PC
b
FC
P
L
1
RS
1
RS
2
PD
Iris
915 nm laser
PC
FC
915 nm laser
PC
P
RS
1
RS
2
BS
L
1
PD
Iris
L
2
Supplementary Fig.
2.
Measurement setup used to characterize the grating. a
, Schematic drawing of
the measurement setup used for characterization of the grating under oblique (left) and normal (right) illu-
mination angles.
b
, Schematic illustration of the measurement setup used for characterization of deflection
efficiency for oblique (left) and normal (right) illuminations. BS: beam splitter, L: lens, PC: polarization
controller, FC: fiber collimator, P: polarizer, PD: photodetector. RS: rotation stage. OL: objective lens. The
focal lengths of lenses
L
1
and
L
2
are
f
1
= 10 cm
and
f
2
= 20 cm
, respectively.
5
0
10
20
30
40
50
60
0
1
Power (a. u.)
θ
ο
(
degree
)
d
-30
-20
-10
0
10
20
30
0
1
Power (a. u.)
θ
ο
(
degree
)
c
a
θ
ο
(
degree
)
-30
-20
-10
0
10
20
30
0
1
Power (a. u.)
BS
TE Polarized
915 nm laser
θ
ο
BS
TE Polarized
915 nm laser
θ
ο
Fabricated grating
Fabricated grating with possible fab error
Fabricated grating with possible fab error
b
Fabricated grating
0
10
20
30
40
50
60
0
1
Power (a. u.)
θ
ο
(
degree
)
TE Polarized
915 nm laser
θ
ο
TE Polarized
915 nm laser
θ
ο
Supplementary Fig.
3.
Simulation results of the angle-multiplexed grating. a
and
b
, Distribution of
reflected power versus observation angle under
0
◦
(a) and
30
◦
(b) incident angles for a
∼
200-
μ
m-long
portion of the fabricated grating.
c
and
d
, The same graphs as (a) and (b), but with a random error added to
the all in-plane sizes of the meta-atoms. The error is normally distributed with a zero mean, a 4-nm standard
deviation, and a forced maximum of 8 nm.
6
915 nm laser
Camera
FC
PC
P
L
RS
1
RS
2
OL
a
OL
915 nm laser
FC
PC
P
RS
1
RS
2
L
Camera
BS
b
Supplementary Fig.
4.
Measurement setup used for the hologram. a
and
b
, Schematic drawing of the
measurement setup used for characterization of the hologram under oblique (a) and normal (b) illumina-
tion angles. BS: beam splitter, L: lens, PC: polarization controller, FC: fiber collimator, P: polarizer, PD:
photodetector. RS: rotation stage. OL: objective lens. The focal length of lens L is
f
1
= 6 cm
.
SUPPLEMENTARY REFERENCES
[1] Oskooi, A. F.
et al.
MEEP: A flexible free-software package for electromagnetic simulations by the
FDTD method.
Comput. Phys. Commun.
181
, 687–702 (2010).
7