of 9
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 East California Boulevard, Pasadena, California 91125, USA
2
Department of Electrical and Computer Engineering, University of Massachusetts Amherst,
151 Holdsworth Way, Amherst, Massachusetts 01003, USA
(Received 23 June 2017; published 6 December 2017)
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.
DOI:
10.1103/PhysRevX.7.041056
Subject Areas: Metamaterials, Optics
I. INTRODUCTION
The concept of angular correlation is schematically
depicted in Fig.
1(a)
for a diffraction grating. In gratings,
the diffraction angle
θ
m
of order
m
is related to the incident
angle
θ
in
by the relation
d
(
sin
ð
θ
m
Þ
sin
ð
θ
in
Þ
)
¼
m
λ
,
where
λ
is the wavelength, and
d
is the grating period,
determined solely by the geometry. Therefore, a grating
adds a fixed
linear 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 illuminated from a different
angle [Fig.
1(c)
]. The concept that we introduce here is
shown schematically in Fig.
1(b)
for an angle-multiplexed
grating that adds a different
linear momentum
depending
on the angle of incidence, and in Fig.
1(d)
for an angle-
multiplexed hologram that displays a different image
depending on the angle of incidence. Breaking this funda-
mental correlation and achieving independent control over
distinct incident angles is conceptually new and results in
the realization of a new category of compact multifunc-
tional devices that allow for embedding several functions
into a thin single metasurface.
Optical metasurfaces are two-dimensional arrangements
of a large number of discrete meta-atoms that enable
precise control 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 compo-
nents like gratings
[24,25]
, lenses
[14,26
28]
, waveplates
[29
31]
, polarizers
[18,32]
, holograms
[33,34]
, and orbital
angular-momentum generators
[35,36]
, or provide novel
functionalities
[18,29,37
42]
that are not feasible with
conventional components. For mid-IR to optical wave-
lengths, high contrast dielectric metasurfaces are very
versatile as they can be designed to control different
properties of light on a subwavelength resolution and with
large reflection or transmission efficiencies
[43
56]
.
Similar to other diffractive devices, metasurfaces that
locally control the optical wavefront (e.g., lenses, beam
deflectors, holograms) generally have a fixed responsewhen
illuminated 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 correlated behavior is the constant locations of the
Fresnelzoneboundaries(i.e.,thegeneralizedgratingperiod)
that determine the device function irrespective of the
incident angle
[59,60]
. Moreover, almost in all the demon-
strated diffractive and metasurface structures, the phase and
its local gradient (which is proportional to the local
momentumchange) havea smalldependenceon theincident
angle
[58,61]
, which results in a large optical memory effect
range
[62]
. Here, we introduce angle-multiplexed metasur-
faces for simultaneously encoding of different arbitrary
phase profiles in different illumination angles of a single
*
Corresponding author:
A.F:faraon@caltech.edu
Published by the American Physical Society under the terms of
the
Creative Commons Attribution 4.0 International
license.
Further distribution of this work must maintain attribution to
the author(s) and the published article
s title, journal citation,
and DOI.
PHYSICAL REVIEW X
7,
041056 (2017)
2160-3308
=
17
=
7(4)
=
041056(9)
041056-1
Published by the American Physical Society
subwavelength thick metasurface. We introduce a novel
angle-dependent platform based on reflective high-contrast
dielectric meta-atoms to break the fundamental optical
memory effect of metasurfaces and provide independent
control over the reflection phase of light at two different
incident angles. As a result, any two different functionalities
can be embedded in a metasurface that can be separately
accessed with different illumination angles. As proof of
concept, we experimentally demonstrate angle-multiplexed
reflective gratings with different effective grating
periods under TE-polarized 0° and 30° illumination angles
[Fig.
1(b)
]. In addition, we demonstrate an angle-multi-
plexed hologram, which encodes and projects different
holographic images under normal and 30° illumination
angles with TE polarization [Fig.
1(d)
].
II. OPERATION THEORY AND DESIGN
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.
2(a)
. The
amorphous silicon (
α
-Si) meta-atoms have a U-shaped
cross section (we 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 electric field is highly localized in
the nanoposts, the low-loss, low-index, dielectric spacer
between the nanoposts and the metallic reflector is neces-
sary to avoid the high losses from metal. In addition, the
spacer layer allows for efficient excitation of the resonance
modes under both angles of illumination through a con-
structive interference between the incident and reflected
fields inside the nanoposts. Therefore, the nanoposts act as
one-sided multimode resonators
[37
39]
. For a 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 lattice
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 simu-
lation 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.
2(b)
]. Therefore, any two
arbitrary and independent phase profiles for TE-polarized
0° and 30° illumination angles can be designed simulta-
neously (see Appendix
A
for design procedure details).
The corresponding reflection amplitudes (
j
r
1
j
and
j
r
2
j
) and
(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
g
1
k
in
k
out
k
g
2
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.
SEYEDEH MAHSA KAMALI
et al.
PHYS. REV. X
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achieved phase shifts are shown in Fig. 1 of Ref.
[63]
. The
independent control of the phase at different incident angles
is a result of exciting different modes of the U meta-atom
under two distinct illumination angles. Figure
2(c)
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.
2(b)
by a star
symbol. Modes that are excited under a 30° illumination
angle are different from the excited modes at normal
illumination as seen in Fig.
2(c)
. There are two categories
of symmetric and antisymmetric resonant modes. In normal
incidence, only symmetric modes are excited, while in
oblique illumination, both the symmetric and antisymmet-
ric modes are excited. This is a key factor in realizing this
independent control for different angles in a local metasur-
face platform. As the metasurface is still assumed to be
local (i.e., the coupling between adjacent 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.
2(b)
. In addition, because of the symmetry of
the nanoposts (and also as verified from simulation results),
the polarization conversion of the metasurface platform
from TE to TM is negligible.
III. EXPERIMENTAL RESULTS
The freedom provided by the proposed platform to
simultaneously control the phase of light at two distinct
incident angles allows for the implementation of a variety of
new compact 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 angles 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
þ
33
.
2
°, respectively. The corre-
sponding effective periods are
31
λ
(blazed for
1
diffraction
order) and
21
λ
(blazed for
þ
1
diffraction order) for 0° and
30° illuminations, respectively (
λ
¼
915
nm is the free-
space wavelength). The designed devices were fabricated
using standard semiconductor fabrication techniques as
described in Appendix
A
. Optical and scanning electron
microscope images of the fabricated angle-multiplexed
grating are shown in Fig.
3(b)
. Figure
3(a)
shows the
measured diffracted light intensities versus angle under 0°
(top)and 30° (bottom) TE-polarized illuminations, aswell as
thesimplifiedmeasurement setupschematics. Themeasured
reflectance as a function of observation angle shows a
dominant peak at the designed angles (i.e.,
1
.
85
° under
normal illumination and
þ
33
.
2
° under 30° incident angle).
Orange dashed lines show deflection angles corresponding
to both effective periods, which are
31
λ
(blazed for
1
diffraction order) and
21
λ
(blazed for
þ
1
diffraction order).
A regular grating with a
31
λ
period, blazed for
1
diffraction
order, would deflect normal incidence into
1
.
85
°, and 30°
incident angle into 27.88°. Similarly, another regular grating
with a
21
λ
period, blazed for
þ
1
diffraction order, would
deflect normal incidence into
þ
2
.
7
° and 30° incident angle
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 undergoes different phase
shifts as it reflects 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. From (b), one can find the dimensions of a meta-atom
that imposes
φ
1
and
φ
2
phase shifts under 0° and 30° illuminations, respectively. (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, 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 are 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 a wavelength of 915 nm. (
α
-Si: amorphous silicon, SiO
2
: silicon dioxide.)
ANGLE-MULTIPLEXED METASURFACES: ENCODING
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PHYS. REV. X
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into 33.2°. The angle-multiplexed grating, on the other hand,
deflects 0° and 30° incident angles into
1
.
85
° and
þ
33
.
2
°,
respectively, with no strong deflection peaks at the angle
corresponding to the other grating periods (which are
þ
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 Fig. 2 of Ref.
[63]
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-domain,
full-wave electromagnetic solver
[64]
(see Note 1 and Fig. 3
in Ref.
[63]
for simulation results). The simulated deflection
efficiencies are 63% and 54% for 0° and 30° operation,
respectively. To consider the possible fabrication errors,
we also simulated the grating with a random error added to
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. The simulated deflection
efficiencies with the added errors are 46% and 39% under
0° and 30° incident angles. We attribute the remaining
difference between simulated and measured efficiencies
to two factors: First, the deposited aluminum reflected layer
has a significant surface roughness. This may result in the
existence 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 measure-
ments, one of the devices with good performance under both
illumination angles is selected and characterized (i.e., there
are other fabricated gratings that demonstrate higher effi-
ciencies for one of the angles). As a result, the characterized
device might differ 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
that projects two different images under 0° and 30°
illumination angles was designed, fabricated, and charac-
terized. 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 fabricated hologram are shown in Fig.
4(b)
.
Simulated and measured intensity profiles for two different
illumination angles (top and bottom) are shown in Fig.
4(a)
,
along with simplified schematics of the measurement
setups. The Caltech logo is created under normal illumi-
nation. 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
TE-Polarized
915-nm laser
Camera
BS
TE-Polarized
915-nm laser
Camera
0
1
-4
-2
0
2
4
degree
Intensity (a.u.)
0
1
26
28
30
32
34
degree
Intensity (a.u.)
(a)
1
m
200
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
þ
33
.
2
°, respectively. Orange dashed lines indicate the designed deflection
angles (
1
.
85
° and
þ
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 angles assuming grating periods of
21
λ
and
31
λ
,
respectively). See Appendix B and Ref.
[63]
(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 is for beam splitter.
SEYEDEH MAHSA KAMALI
et al.
PHYS. REV. X
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is shown in Movie 1 in Ref.
[63]
. The good agreement
between the simulation and measurement results confirms
the independent control of this platform over distinct
incident angles. In order to avoid an overlap between
the holographic image and the zeroth-order diffraction, the
holograms are designed to operate off axis (see Appendix
A
for details of hologram design).
IV. DISCUSSION
The angle-multiplexed metasurface platform allows for
devices that perform completely independent functions (i.e.,
grating, lens, hologram, orbital angular-momentum gener-
ator, 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
orders vary with the incident angle
[65,66]
, the grating
momentum 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 holo-
grams. Unlike 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 holographic optical element (i.e., the general-
ized case of the multi-order gratings).
V. CONCLUSION
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 control can be extended to more angles and
the device performance 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 that are not feasible otherwise.
This is complementary to the previously demonstrated
independent control over different polarizations
[18,67]
or wavelengths of the incident light
[20,68
70]
and thus
significantly expands the range of applications for nano-
engineered metasurfaces.
ACKNOWLEDGMENTS
This work was supported by the DOE
Light-Material
InteractionsinEnergy Conversion
Energy Frontier Research
Center funded by the U.S. Department of Energy, Office
of Science, Office of Basic Energy Sciences under Grant
No. DE-SC0001293. A. A., E. A., and M. F. were supported
by Samsung 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
[71]
. A normal and a 30°
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 Ref.
[63]
(Fig.
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.
ANGLE-MULTIPLEXED METASURFACES: ENCODING
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PHYS. REV. X
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incident plane wave at 915 nm wavelength were used as the
excitation, 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 describing the optical behavior of
the meta-atom at each illumination 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, SiO
2
: 1.44, Al
2
O
3
:
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 minimizing the
total reflection error, which is defined as
ε
¼j
exp
ð
i
φ
1
Þ
r
1
j
2
þj
exp
ð
i
φ
2
Þ
r
2
j
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 angles, 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.
2(b)
, some modification
terms were added to thereflection error in order to ensure that
adjacent dimensions are preferred for the adjacent phases.
The modification terms were defined as an exponential
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 deflection angles of about 3°. The simu-
lation results presented in Fig.
4
were computed by
assuming that the coupling among adjacent meta-atoms
is 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
An aluminum layer of about 100 nm was evaporated on a
silicon wafer, followed by an Al
2
O
3
layer of about 30 nm.
A 125-nm-thick SiO
2
and a 500-nm-thick
α
-Si layer were
subsequently deposited using the plasma-enhanced chemi-
cal vapor deposition (PECVD) technique at
200
°C. A
Vistec EBPG5200 e-beam lithography system was used to
define the pattern in a nearly 300-nm-thick layer of ZEP-
520A positive electron-beam resist (spin coated at
5000 rpm for 1 min). The pattern was developed in the
resist developer (ZED-N50 from Zeon Chemicals) for
3 minutes. A nearly 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 peroxide at
80
°C.
The angle-multiplexed grating was measured using
the setup shown schematically in Fig. S2 in Ref.
[63]
.
A 915-nm fiber-coupled semiconductor laser was used for
illumination, and a fiber collimation package (Thorlabs
F220APC-780) was used to collimate the incident beam.
A polarizer (Thorlabs LPVIS100-MP2) was inserted to
confirm the TE polarization state of the incident light. An
additional lens with a focal length of 10 cm (Thorlabs
AC254-100-B-ML) was placed before the grating at a
distance of about 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
objective lens (Mitutoyo M Plan Apo 10X, NA
¼
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
beam splitter (Thorlabs NIR Non-Polarizing Cube
Beamsplitter) was inserted before the grating for measure-
ments under normal illumination. For efficiency measure-
ments of the grating, an iris was used to select the desired
diffraction order and block all other diffraction orders.
A power meter (Thorlabs PM100D) with a photodetector
(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 grating).
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 Fig. S3 in
Ref.
[63]
. The setup is similar to the grating measurement
setup with some modifications. The 10-cm focal distance
lens used to partially focus light to the grating was removed
to obtain a relatively 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.
4(a)
, as it is outside the holographic image
of interest because of 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
SEYEDEH MAHSA KAMALI
et al.
PHYS. REV. X
7,
041056 (2017)
041056-6
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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