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Angle-multiplexed metasurfaces: encoding independent wavefronts in a single metasurface under
different illumination angles
Seyedeh Mahsa Kamali,
1
Ehsan Arbabi,
1
Amir Arbabi,
2
Yu Horie,
1
MohammadSadegh Faraji-Dana,
1
and Andrei Faraon
1,
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 and Computer Engineering,
University of Massachusetts Amherst, 151 Holdsworth Way, Amherst, MA 01003, USA
The angular response of thin diffractive optical elements is highly correlated. For example, the angles of
incidence and diffraction of a grating are locked through the grating momentum determined by the grating
period. Other diffractive devices, including conventional metasurfaces, have a similar angular behavior due to
the fixed locations of the Fresnel zone boundaries and the weak angular sensitivity of the meta-atoms. To alter
this fundamental property, we introduce
angle-multiplexed metasurfaces
, composed of reflective high-contrast
dielectric U-shaped meta-atoms, whose response under illumination from different angles can be controlled
independently. This enables flat optical devices that impose different and independent optical transformations
when illuminated from different directions, a capability not previously available in diffractive optics.
The concept of angular correlation is schematically de-
picted in Fig. 1a for a diffraction grating. In gratings, the
diffraction angle
θ
m
of order
m
is related to the incident an-
gle
θ
in
by the relation
d
(sin(
θ
m
)
sin(
θ
in
)) =
, where
λ
is the wavelength, and
d
is the grating period, determined
solely by the geometry. Therefore, a grating adds a fixed “lin-
ear momentum”, dictated by its period, to the momentum of
the incident light regardless of the incident angle. Similarly,
a regular hologram designed to project a certain image when
illuminated from a given angle will project the same image
(with possible distortions and efficiency reduction) when illu-
minated from a different angle (Fig. 1c). The concept that we
introduce here is shown schematically in Fig. 1b for an angle-
multiplexed grating that adds a different “linear momentum”
depending on the angle of incidence, and Fig. 1d for an angle-
multiplexed hologram that displays a different image depend-
ing on the angle of incidence. Breaking this fundamental cor-
relation and achieving independent control over distinct inci-
dent angles is conceptually new and results in the realization
of a new category of compact multifunctional devices which
allow for embedding several functions into a thin single meta-
surface.
Optical metasurfaces are two-dimensional arrangements of
a large number of discrete meta-atoms that enable precise con-
trol of optical wavefronts with subwavelength resolution[1–
13]. Several devices with the ability to control the phase [14–
17], polarization [18–20], and amplitude [21–23] of light have
been demonstrated. They can directly replace traditional bulk
optical components like gratings [24, 25], lenses [14, 26–28],
waveplates [29–31], polarizers [18, 32], holograms [33, 34],
orbital angular momentum generators [35, 36], or provide
novel functionalities [18, 29, 37–42] not feasible with conven-
tional components. For mid-IR to optical wavelengths, high
contrast dielectric metasurfaces are very versatile as they can
be designed to control different properties of light on a sub-
wavelength resolution and with large reflection or transmis-
sion efficiencies [43–56].
Similar to other diffractive devices, metasurfaces that lo-
cally control the optical wavefront (e.g. lenses, beam deflec-
tors, holograms) generally have a fixed response when illumi-
nated from different incident angles, with possible distortions
and reduction in efficiency at illumination angles other than
the design value [37, 57, 58]. The main reason for this cor-
related behavior is the constant locations of the Fresnel zone
boundaries (i.e., the generalized grating period) that determine
the device function irrespective of the incident angle [59, 60].
Moreover, almost in all the demonstrated diffractive and meta-
surface structures the phase and its local gradient (which is
proportional to the local momentum change) have a small de-
pendence on the incident angle [58, 61], which results in a
large optical memory effect range [62]. Here, we introduce
angle-multiplexed metasurfaces for simultaneously encoding
of different arbitrary phase profiles in different illumination
angles of a single sub-wavelength thick metasurface. We in-
troduce a novel angle-dependent platform based on reflective
high-contrast dielectric meta-atoms to break the fundamental
optical memory effect of metasurfaces and provide indepen-
dent control over the reflection phase of light at two differ-
ent incident angles. As a result, any two different function-
alities can be embedded in a metasurface that can be sepa-
rately accessed with different illumination angles. As proof
of concept, we experimentally demonstrate angle-multiplexed
reflective gratings with different effective grating periods un-
der TE-polarized 0
and 30
illumination angles (Fig. 1b).
In addition, we demonstrate an angle-multiplexed hologram
which encodes and projects different holographic images un-
der normal and 30
illumination angles with TE polarization
(Fig. 1d).
A meta-atom structure capable of providing independent
phase control under TE-polarized light illumination with 0
and 30
incident angles is shown in Fig. 2a. The amorphous
silicon (
α
-Si) meta-atoms have a U-shaped cross section (we
will call them U meta-atoms from here on) and are located at
the vertices of a periodic square lattice on a low refractive
index silicon dioxide (
SiO
2
) and aluminum oxide (
Al
2
O
3
)
spacer layers backed by an aluminum reflector. Since the elec-
tric field is highly localized in the nano-posts, the low-loss
low-index dielectric spacer between the nano-posts and the
arXiv:1711.02265v1 [physics.optics] 7 Nov 2017
2
d
c
a
k
out
k
g
k
in
k
out
k
g
k
in
k
x
k
z
k
0
x
z
b
k
out
k
g1
k
in
k
out
k
g2
k
in
x
z
k
0
k
x
k
z
k
0
k
z
k
x
k
0
k
z
k
x
Conventional
Angle-multiplexed
FIG. 1.
Angle-multiplexed metasurface concept
.
a
, Schematic illustration of diffraction of light by a grating. A grating adds a fixed linear
momentum (
~
k
g
) to the incident light, independent of the illumination angle. If the illumination angle deviates from the designated incident
angle, light is deflected to a different angle which is dictated by the grating period.
b
, Illustration of the angle-multiplexed metasurface
platform. This platform provides different responses according to the illumination angle. For instance, two gratings with different deflection
angles (different grating momenta) can be multiplexed such that different illumination angles acquire different momenta.
c
, Illustration of a
typical hologram that creates one specific image (Caltech logo) under one illumination angle (left). The same hologram will be translated
laterally (and distorted) by tilting the illumination angle (right).
d
, Schematic illustration of an angle-multiplexed hologram. Different images
are created under different illumination angles. For ease of illustration, the devices are shown in transmission while the actual fabricated
devices are designed to operate in reflection mode.
Top view
x
y
Side view
k
|r
1
|e
i
1
k
1
D
x
D
y
D
xin
D
yin
SiO
2
-Si
Metal
Unit cell
x
y
z
1
k
|r
2
|e
i
2
k
i
a
60
390
0
1
/(2
)
1
0
1
2
/(2
)
D
x
(nm)
0
1
/(2
)
0
240
1
0
1
2
/(2
)
D
xin
(nm)
0
1
/(2
)
0
180
1
0
1
2
/(2
)
D
yin
(nm)
150
390
0
1
/(2
)
1
1
2
/(2
)
D
y
(nm)
0
b
y
x
z
0
90
y
z
0
250
0
250
0
30
x
z
0
150
0
200
x
y
i
=0°
i
=30°
c
D
x
D
y
FIG. 2.
The meta-atom structure and the design graphs. a
, Schematic drawing of various views of a uniform array of U-shaped cross-
section
α
-Si meta-atoms arranged in a square lattice resting on a thin
SiO
2
spacer layer on a reflective surface (i.e., a metallic mirror). The
array provides angle-dependent response such that TE-polarized light at 0
and 30
illumination angles undergo different phase shifts as they
reflect from the array.
b
, Simulated values of the U meta-atom dimensions (
D
x
,
D
y
,
D
x
in
, and
D
y
in
) for achieving full 2
π
phase shifts for
TE-polarized light at 0
and 30
illumination angles, respectively. One can find the values of the four dimensions of a meta-atom which
imposes
φ
1
and
φ
2
reflection phase shifts onto TE-polarized normal and 30
incident angle optical waves from (b).
c
, Electric energy density
inside a single unit cell in a periodic uniform lattice for a typical meta-atom (shown in (b) with a star symbol) at 0
and 30
illumination angles
is plotted in three cross sections. Blue arrows indicate in-plane electric field distributions excited at each illumination angle. Different field
distributions at normal and 30
incidence is an indication of excitation of different resonant modes under different incident angles. In all parts
of the figure, the meta-atoms are 500 nm tall. The silicon dioxide and aluminum layers are 125 nm and 100 nm thick respectively, the lattice
constant is 450 nm and all simulations are performed at the wavelength of 915 nm.
α
-Si: amorphous silicon,
SiO
2
: silicon dioxide.
3
metallic reflector is necessary to avoid the high losses from
metal. In addition, the spacer layer allows for efficient excita-
tion of the resonance modes under both angles of illumination
through a constructive interference between the incident and
reflected fields inside the nano-posts. Therefore, the nano-
posts act as one sided multi-mode resonators [37–39]. For the
wavelength of 915 nm, the meta-atoms are 500 nm tall, the
SiO
2
layer, the
Al
2
O
3
layer, and the aluminum reflector are
125 nm, 30 nm, and 100 nm thick, respectively, and the lat-
tice constant is 450 nm. A uniform array of U meta-atoms
provides an angle-dependent response such that TE-polarized
light waves incident at 0
and 30
undergo different phase
shifts (
φ
1
and
φ
2
, respectively) as they are reflected from the
array. A periodic array of U meta-atoms was simulated to
find the reflection amplitude and phase at each incident angle
(see Appendix A for simulation details). Any combination
of
φ
1
and
φ
2
from 0 to 2
π
can be simultaneously obtained
by properly choosing the in-plane dimensions of the meta-
atoms (i.e.
D
x
,
D
y
,
D
x
in
, and
D
y
in
as shown in Fig. 2b).
Therefore, any two arbitrary and independent phase profiles
for TE-polarized 0
and 30
illumination angles can be de-
signed simultaneously (see Appendix A for design procedure
details). The corresponding reflection amplitudes (
|
r
1
|
and
|
r
2
|
) and achieved phase shifts are shown in Supplementary
Fig. 1. The independent control of phase at different inci-
dent angles is a result of exciting different modes of the U
meta-atom under two distinct illumination angles. Figure 2c
shows the excited electric energy density for a typical meta-
atom in a periodic array at three different cross-sections under
0
and 30
incident angles (top and bottom receptively). The
example meta-atom dimensions and corresponding phases at
each illumination angle are shown in Fig. 2b by a star symbol.
Modes that are excited under 30
illumination angle are dif-
ferent from the excited modes at normal illumination as seen
in Fig. 2c. There are two categories of symmetric and an-
tisymmetric resonant modes. In normal incidence only sym-
metric modes are excited, while in oblique illumination both
the symmetric and antisymmetric modes are excited. This is
a key factor in realizing this independent control for different
angles in a local metasurface platform. As the metasurface
is still assumed to be local (i.e., the coupling between adja-
cent meta-atoms is neglected in the design), any two arbitrary
different wavefronts can be simultaneously designed for the
two different illumination angles by using the design graphs
shown in Fig. 2b. In addition, due to the symmetry of the
nano-posts (and also as verified from simulation results) the
polarization conversion of the metasurface platform from TE
to TM is negligible.
The freedom provided by the proposed platform to simul-
taneously control the phase of light at two distinct incident
angles allows for the implementation of a variety of new com-
pact optical components. To demonstrate the versatility of this
platform, we fabricated and characterized two examples of
angle-multiplexed metasurfaces. First, an angle-multiplexed
grating was designed to operate at 0
and 30
incident an-
gles with two different effective grating periods. The angle-
multiplexed grating has a diameter of 1 mm and deflects 915-
nm TE-polarized light incident at 0
and 30
into -1.85
and
+33.2
respectively. The corresponding effective periods are
31
λ
(blazed for -1 diffraction order) and 21
λ
(blazed for +1
diffraction order) for 0
and 30
illuminations, respectively
(
λ
=
915 nm is the free space wavelength). The designed
devices were fabricated using standard semiconductor fabri-
cation techniques as described in Appendix A. Optical and
scanning electron microscope images of the fabricated angle-
multiplexed grating are shown in Fig. 3b. Figure 3a shows
the measured diffracted light intensities versus angle under 0
(top) and 30
(bottom) TE-polarized illuminations, as well as
the simplified measurement setup schematics. The measured
reflectance as a function of observation angle shows a dom-
inant peak at the designed angles (i.e. -1.85
under normal
illumination and +33.2
under 30
incident angle). Orange
dashed lines show deflection angles corresponding to both ef-
fective periods, which are 31
λ
(blazed for -1 diffraction order)
and 21
λ
(blazed for +1 diffraction order). A regular grating
with a 31
λ
period, blazed for -1 diffraction order, would de-
flect normal incidence into -1.85
, and 30
incident angle into
27.88
. Similarly, another regular grating with 21
λ
period,
blazed for +1 diffraction order, would deflect normal inci-
dence into +2.7
and 30
incident angle into 33.2
. The angle-
multiplexed grating, on the other hand, deflects 0
and 30
incident angles into -1.85
and +33.2
respectively, with no
strong deflection peaks at the angle corresponding to the other
grating periods (which are, +2.7
and 27.88
). The deflection
efficiency of the grating at each incident angle is defined as the
power deflected by the grating to the desired order, divided
by the power reflected from a plain aluminum reflector (see
Appendix B for measurement details and Supplementary Fig.
2 for measurement setups). Deflection efficiencies of 30
%
and 41
%
were measured under 0
and 30
incident angles,
respectively. For comparison, we simulated the central
200
μ
m-long portion of the grating with a finite difference time do-
main full-wave electromagnetic solver [63] (see Supplemen-
tary Note 1 and Supplementary Fig. 3 for simulation results).
The simulated deflection efficiencies are 63
%
and 54
%
for 0
and 30
operation, respectively. To consider the possible fab-
rication errors, we also simulated the grating 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 stan-
dard deviation, and a forced maximum of 8 nm. The simulated
deflection efficiencies with the added errors are 46
%
and 39
%
under 0
and 30
incident angles. We attribute the remain-
ing difference between simulated and measured efficiencies
to two factors: first, the deposited aluminum reflected layer
has a significant surface roughness. This may result in exis-
tence and excitation of local surface plasmon resonances that
contribute to both increased loss and reflection phase error.
Second, to counter the effects of systematic fabrication errors,
an array of gratings with different biases added to each size
of the meta-atoms is fabricated. In the measurements, one of
the devices with good performance under both illumination
angles is selected and characterized (i.e., there are other fabri-
4
TE Polarized
915 nm laser
Camera
T
R
BS
TE Polarized
915 nm laser
Camera
T
R
0
1
-4
-2
0
2
4
T
R
degree
Intensity (a.u.)
0
1
26
28
30
32
34
T
R
degree
Intensity (a.u.)
a
1
P
m
200
P
m
b
FIG. 3.
Angle-multiplexed grating
.
a
, Simplified schematic of the measurement setup (left), and measured reflectance of the angle-
multiplexed grating under normal illumination of TE-polarized light as a function of the observation angle
θ
0
(right). The grating deflects
0
and 30
TE-polarized incident light to -1.85
and +33.2
respectively. Orange dashed lines indicate the designed deflection angles (-1.85
and +33.2
under 0
and 30
incidence respectively), and the deflection angles corresponding to regular gratings with fixed grating periods
(2.7
under normal and 27.88
under 30
illumination angle assuming grating periods of 21
λ
and 31
λ
, respectively). See Appendix B and
Supplementary Fig. 2 for measurement details.
b
, Optical image of the angle-multiplexed grating. The inset shows a scanning electron
micrograph of the top view of meta-atoms composing the metasurface. See Appendix B for fabrication details. BS: beam splitter.
Simulation
Measurement
Intensity (a.u.)
0
1
TE Polarized
915 nm laser
TE Polarized
915 nm laser
BS
500
m
1
m
a
b
FIG. 4.
Angle-multiplexed hologram a
, Simplified drawing of the measurement setups under normal and 30
illumination angles (left). The
angle-multiplexed hologram is designed to create two different images under different incident angles (Caltech and LMI logos under 0
and
30
, respectively). Simulated and measured reflected images captured under 915-nm TE-polarized light at 0
and 30
illumination angles
are shown on the right. See Appendix B and Supplementary Figs. 3 for measurement details.
b
, Optical image of a portion of the angle-
multiplexed hologram. The inset shows a scanning electron micrograph under oblique view of meta-atoms composing the metasurface. See
Appendix B for fabrication details. BS: beam splitter.
5
cated gratings that demonstrate higher efficiencies for one of
the angles). As a result, the characterized device might dif-
fer from the one with sizes closest to design values. This may
justify the different balances between measured and simulated
values for efficiencies under the two illumination angles.
As a second example, an angle-multiplexed hologram
which projects two different images under 0
and 30
illu-
mination angles was designed, fabricated, and characterized.
The hologram covers a 2 mm by 2 mm square, and projects
the Caltech and LMI logos when illuminated by TE-polarized
light at 915 nm at 0
and 30
incident angles. Optical and
scanning electron microscope images of a portion of the fab-
ricated hologram are shown in Fig. 4b. Simulated and mea-
sured intensity profiles for two different illumination angles
(top and bottom) are shown in Fig. 4a, along with simplified
schematics of the measurement setups. The Caltech logo is
created under normal illumination. By scanning the incident
angle from 0
to 30
, the projected image changes from the
Caltech logo to the LMI logo. The change in the recorded
image with incident angle is shown in Supplementary Movie
1. The good agreement between the simulation and measure-
ment results confirms the independent control of this platform
over distinct incident angles. In order to avoid an overlap be-
tween the holographic image and the zeroth-order diffraction,
the holograms are designed to operate off axis (see Appendix
A for details of hologram design).
The angle-multiplexed metasurface platform allows for de-
vices that perform completely independent functions (i.e.
grating, lens, hologram, orbital angular momentum genera-
tor, etc.) for different angles of illumination. It is worth
noting that the concept and implementation of the angle-
multiplexed metasurfaces are fundamentally different from
multi-order gratings. While the multi-order gratings can be
designed such that the efficiencies of different diffraction or-
ders vary with the incident angle [69, 70], the grating mo-
mentum corresponding to each order (which is locked to the
period of the grating) remains fixed. This difference becomes
much clearer when considering the case of holograms. Un-
like in the demonstrated platform, it is not possible to encode
two completely independent phase profiles corresponding to
two completely independent functions in a multi-order holo-
graphic optical element (i.e., the generalized case of the multi-
order gratings).
In conclusion, we developed optical metasurfaces that
break the angular correlation of thin diffractive components,
and enable devices where independent phase masks can be
embedded in a single thin layer and accessed separately under
different illumination angles. Here, the shape of the meta-
atom was chosen intuitively and we expect that by utilizing
more advanced optimization procedures, the independent con-
trol can be extended to more angles and the device perfor-
mance can be improved significantly. From a technological
point of view, this is a novel class of metasurfaces that opens
the path towards ultracompact multifunctional flat devices not
feasible otherwise. This is complementary to the previously
demonstrated independent control over different polarizations
[18, 64] or wavelengths of the incident light [20, 65–67], and
thus significantly expands the range of applications for nano-
engineered metasurfaces.
ACKNOWLEDGEMENT
This work was supported by the DOE ”Light-Material In-
teractions in Energy Conversion” Energy Frontier Research
Center funded by the US Department of Energy, Office of
Science, Office of Basic Energy Sciences under Award no.
de-sc0001293. A.A., E.A., and M.F. were supported by Sam-
sung Electronics.
A.A. and Y.H were also supported by
DARPA. The device nanofabrication was performed at the
Kavli Nanoscience Institute at Caltech.
APPENDIX A: SIMULATION AND DESIGN
To find the reflection amplitude and phase of a uniform
array of meta-atoms, the rigorous coupled wave analysis
(RCWA) technique was used [68]. A normal and a 30
in-
cident plane wave at 915 nm wavelength were used as the ex-
citation, and the amplitude and phase of the reflected wave
were extracted. The subwavelength lattice for both normal
and oblique illumination angles results in the excitation of
only the zeroth order diffracted light. This justifies the use
of only one reflection value at each illumination angle for de-
scribing the optical behavior of the meta-atom at each illu-
mination angle. The
α
-Si layer was assumed to be 500 nm
thick. The
SiO
2
and aluminum layers were assumed to be
125 nm and 100 nm thick, respectively. Refractive indices at
915 nm wavelength were assumed as follows:
α
-Si: 3.558,
SiO2: 1.44, Al2O3: 1.7574, and Al: 1.9183-
i
8.3447. The
meta-atom in-plane dimensions (
D
x
,
D
y
,
D
x
in
, and
D
y
in
) are
swept such that the minimum feature size remains larger than
50 nm for relieving fabrication constraints.
The optimum meta-atom dimensions for each lattice
site at the two incident angles were found by mini-
mizing the total reflection error, which is defined as

=
|
exp(i
φ
1
)
r
1
|
2
+
|
exp(i
φ
2
)
r
2
|
2
, where
r
1
and
r
2
are
the complex reflection coefficients of the unit-cell at the two
incident angles. Therefore, for any desired combination of
phases
φ
1
and
φ
2
in the 0 to 2
π
range at the two incident an-
gles, there is a corresponding meta-atom (i. e.,
D
x
,
D
y
,
D
x
in
,
and
D
y
in
values) that minimizes the reflection error. To limit
the rapid jumps in dimensions shown in Fig.2b, some mod-
ification terms were added to the reflection error in order to
ensure that adjacent dimensions are preferred for the adjacent
phases. The modification terms were defined as an exponen-
tial function of the Euclidean distance between the in-plane
dimensions of the meta-atoms for adjacent phase values.
The holograms of different incident angles were designed
individually using the Gerchberg-Saxton (GS) algorithm with
3
deflection angles. The simulation results presented in
Fig. 4 were computed by assuming that the coupling among
6
adjacent meta-toms are negligible, such that each meta-atom
imposes the exact complex reflection amplitude found from
simulations of the periodic structure. The hologram area was
assumed to be illuminated uniformly with 0
and 30
incident
angle plane waves, and the projected holographic images were
found by taking the Fourier transform of the field after being
reflected from the phase mask.
APPENDIX B: SAMPLE FABRICATION AND
MEASUREMENT PROCEDURE
A
100-nm aluminum layer was evaporated on a silicon
wafer, followed by a
30-nm
Al
2
O
3
layer. A 125-nm-thick
SiO
2
and a 500-nm-thick
α
-Si layer were subsequently de-
posited using the plasma enhanced chemical vapor deposi-
tion (PECVD) technique at
200
C. A Vistec EBPG5200 e-
beam lithography system was used to define the pattern in a
300 nm thick layer of ZEP-520A positive electron-beam re-
sist (spin coated at 5000 rpm for 1 min). The pattern was de-
veloped in the resist developer (ZED-N50 from Zeon Chemi-
cals) for 3 minutes. A
50-nm-thick
Al
2
O
3
layer was evapo-
rated on the sample, and the pattern was then transferred to the
Al
2
O
3
layer by a lift off process. The patterned
Al
2
O
3
hard
mask was then used to dry etch the
α
-Si layer in a mixture of
SF
6
and
C
4
F
8
plasma. Finally, the
Al
2
O
3
mask was removed
in a 1:1 solution of ammonium hydroxide and hydrogen per-
oxide at
80
C.
The angle-multiplexed grating was measured using the
setup shown schematically in Supplementary Fig. S2. A 915-
nm fiber-coupled semiconductor laser was used for illumina-
tion and a fiber collimation package (Thorlabs F220APC-780)
was used to collimate the incident beam. A polarizer (Thor-
labs LPVIS100-MP2) was inserted to confirm the TE polar-
ization state of the incident light. An additional lens with a fo-
cal length of 10 cm (Thorlabs AC254-100-B-ML) was placed
before the grating at a distance of
8 cm to partially focus the
beam and reduce the beam divergence after being deflected by
the grating in order to decrease the measurement error. The
light deflected from the device was imaged using a custom
built microscope. The microscope consists of a 10X objec-
tive lens (Mitutoyo M Plan Apo 10X, NA= 0.28) and a tube
lens (Thorlabs LB1945-B-ML) with a focal distance of 20 cm,
which images the object plane onto a camera (CoolSNAP K4
from Photometrics). A rotation stage was used to adjust the
illumination angle and a 50/50 beamsplitter (Thorlabs NIR
Non-Polarizing Cube Beamsplitter) was inserted before the
grating for measurements under normal illumination. For ef-
ficiency measurements of the grating, an iris was used to se-
lect the desired diffraction order and block all other diffraction
orders. A power meter (Thorlabs PM100D) with a photode-
tector (Thorlabs S122C) was used to measure the deflected
power off the grating, as well as the reflected power from a
plain aluminum reflector (from an area adjacent to the grat-
ing). The grating efficiency was calculated by dividing the
power deflected to the desired order to the power reflected by
the aluminum reflector. Neutral density (ND) filters (Thorlabs
ND filters, B coated) were used to adjust the light intensity
and decrease the background noise captured by the camera.
The angle-multiplexed hologram was characterized using
the setup shown schematically in Supplementary Fig. S3. The
setup is similar to the grating measurement setup with some
modifications. The 10 cm focal distance lens used to par-
tially focus light to the grating was removed to obtain a rel-
atively uniform illumination of the hologram area. The input
beam being larger than the device in addition to fabrication
imperfections results in a strong zeroth-order diffraction. The
zeroth-order diffraction is cropped in Fig.4a, as it is outside
the holographic image of interest due to the off-axis design of
the hologram. The custom-built microscope was also altered
as follows: the objective lens was used to generate a Fourier
transform of the hologram plane in its back focal plane. The
tube lens was replaced by a lens with a focal length of 6 cm,
which images the back focal plane of the objective into the
camera. Two rotation stages were used in order to be able
to independently rotate the device and the illumination beam.
The camera and the imaging setups were not on the rotation
stages.
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9
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.
10
SUPPLEMENTARY FIGURES