of 7
ARTICLE
Received 28 Oct 2015
|
Accepted 14 Apr 2016
|
Published 19 May 2016
Decoupling optical function and geometrical form
using conformal flexible dielectric metasurfaces
Seyedeh Mahsa Kamali
1
, Amir Arbabi
1
, Ehsan Arbabi
1
, Yu Horie
1
& Andrei Faraon
1
Physical geometry and optical properties of objects are correlated: cylinders focus light to a
line, spheres to a point and arbitrarily shaped objects introduce optical aberrations. Multi-
functional components with decoupled geometrical form and optical function are needed
when specific optical functionalities must be provided while the shapes are dictated by other
considerations like ergonomics, aerodynamics or aesthetics. Here we demonstrate an
approach for decoupling optical properties of objects from their physical shape using thin and
flexible dielectric metasurfaces which conform to objects’ surface and change their optical
properties. The conformal metasurfaces are composed of silicon nano-posts embedded in a
polymer substrate that locally modify near-infrared (
l
¼
915 nm) optical wavefronts. As proof
of concept, we show that cylindrical lenses covered with metasurfaces can be transformed to
function as aspherical lenses focusing light to a point. The conformal metasurface concept is
highly versatile for developing arbitrarily shaped multi-functional optical devices.
DOI: 10.1038/ncomms11618
OPEN
1
T. J. Watson Laboratory of Applied Physics, Kavli Nanoscience Institute, California Institute of Technology, 1200 E California Boulevard, Pasaden
a,
California 91125, USA. Correspondence and requests for materials should be addressed to A.F. (email: faraon@caltech.edu).
NATURE COMMUNICATIONS
| 7:11618 | DOI: 10.1038/ncomms11618 | www.nature.com/naturecommunications
1
T
he correlation between the geometry of an object and its
optical functionality
1
has introduced long-standing design
challenges to optical engineers developing multi-functional
components
2
. The traditional solution has been to compromise
and optimize the component material and geometry by
considering all the physical requirements. This was originally
studied in the context of conformal and freeform optics where
optical components with non-standard surfaces were developed
for integration of optics into flying objects with specific
aerodynamic shapes
3,4
. More recently, this issue has attracted
new attention due to its application in integration of optics into
various consumer electronic products and medical equipment
with stringent packaging and design requirements. Furthermore,
controlling optical properties of objects without physically
modifying them can enable the visual blending of an object
with its background
5–8
or changing its appearance through
generation of a holographic virtual image
9,10
. In the context of
conformal optics, the conventional solution is to stack several
bulky optical elements with non-standard surface profiles
underneath the outermost surface of the object
4
. Such solutions
usually have challenging fabrication processes requiring custom-
made fabrication equipment, are bulky and do not provide a
unified and versatile approach that can be applied to arbitrary
geometries. Conformal metasurface approach can provide a
solution for decoupling the geometric shape and optical
characteristics of arbitrary objects.
Metasurfaces are two-dimensional (2D) arrays of scatterers
rationally designed to locally modify phase and polarization of
electromagnetic waves
11–14
. They enable wafer-scale production
of lithographically defined thin diffractive optical elements using
conventional
nano-manufacturing
techniques.
These
manufacturing techniques are optimized for patterning flat
substrates and are not applicable for the direct fabrication of
metasurfaces on non-planar structures required for conformal
optics. However, the 2D nature and the minute thickness of
optical metasurfaces make them suitable for transferring to
non-planar substrates. Several different plasmonic and dielectric
metasurface platforms for optical wavefront manipulation have
been recently proposed
11–18
. Among different platforms,
dielectric metasurfaces based on high-contrast transmitarrays
are highly versatile
14,17,18
as they provide simultaneous mani-
pulation of phase and polarization of light with high efficiencies,
and can sample optical wavefronts with subwavelength spatial
resolution
14
. In these metasurfaces, each meta-atom is a high-
index nano-post acting as a short waveguide, which locally
imposes a certain phase shift and polarization rotation. Several
efforts have been made to transfer metasurfaces (mostly
plasmonic ones) to flexible substrates with the aim of tuning
their frequency response using substrate deformation
19–25
.
Plasmonic metasurfaces, however, have low efficiencies,
especially in the transmission mode, which in many situations
make them impractical.
Here, we introduce flexible metasurfaces based on a dielectric
high-contrast transmitarray platform that can be conformed to a
non-planar arbitrarily shaped object to modify its optical
properties at will. We present a general design procedure and a
high-yield fabrication process for the conformal flexible metasur-
face platform. As proof of principle, we experimentally
demonstrate flexible metasurfaces that wrap over cylindrical
surfaces and convert them to aspherical lenses.
Results
Conformal metasurfaces platform
. Figure 1a shows a schematic
illustration of a non-planar arbitrarily shaped transparent object
wrapped by a flexible metasurface based on this platform. The
metasurface layer is composed of an array of dissimilar cylindrical
amorphous silicon (a-Si) nano-posts with different diameters
placed on a subwavelength periodic hexagonal lattice and
embedded in polydimethylsiloxane (PDMS) as a flexible substrate
(Fig. 1a, inset). The arbitrary shape of the object’s surface distorts
the wavefront of the transmitted light in an undesirable way
(Fig. 1b). By conforming the metasurface onto the object’s
outermost surface, the distortion can be compensated and the
wavefront of the transmitted light can be shaped to a desired
form, similar to phase-compensating antenna arrays used in the
microwave regime
26
. For example, the metasurface can be
designed to correct the distortions introduced by the arbitrarily
shaped object and make it act similar to an aspherical lens that
focuses light to a point as schematically shown in Fig. 1c.
Operation principle and design procedure
. The desired phase
profile of the conformal metasurface is found with the knowledge
of the geometry of the transparent object over which it is wrap-
ped, and the desired optical response. First, the object without the
metasurface is considered, and the phase profile of the optical
waves transmitted through the object is computed along the
surface of the object. For objects with dimensions significantly
larger than the optical wavelengths, this phase profile can be
found using ray optics approximation and by computing the
optical path length and the corresponding optical path difference
(OPD) of the rays passing through different points along the
outermost surface of the object with respect to the chief ray.
Then, using a similar OPD-based approach, the phase profile
required to achieve the desired specific functionality is obtained
along the surface of the object. For example, if we want the object
to focus light to a point, a converging spherical wavefront is
desired, which is sampled along the arbitrary surface of the object.
The metasurface layer, when wrapped on the surface of the object,
should locally impose an additional optical phase shift equal to
the difference between the original phase of the object and the
desired phase profile. Therefore, the desired metasurface phase
profile is expressed as a function of two coordinate values
defining the non-planar surface of the object. To obtain the
appropriate phase profile of the metasurface before its transfer to
the non-planar surface, an appropriate coordinate transformation
should be applied. For example, if the flexible substrate of the
metasurface is under no stress after being mounted on the object’s
surface, then the appropriate coordinate transformation con-
serves length along the surface of the object.
Using this design procedure, we computed two sets of
conformal metasurface phase profiles for both a convex and a
concave cylindrical glass. The metasurfaces modify the wave-
fronts of the cylindrical objects to make them behave as
aspherical lenses. Figures 2a and 2d show the OPD of the rays
passing through the convex and concave cylinders at their top
surfaces, respectively. Considering the desired converging sphe-
rical wavefronts, the desired OPDs of the rays at the surfaces of
the convex and concave cylinders are calculated and shown in
Figs 2c and 2f, respectively. The differences between the OPDs of
the convex and concave cylindrical objects and their correspond-
ing converging spherical phase profiles are shown in Figs 2b and
2e, respectively. The conformal metasurfaces should impose
phase shifts equivalent to these OPDs at the operation wavelength
(see the ‘Methods’ section for simulation details). Since the
cylindrical surfaces are isometric with a plane, the metasurfaces
can be mounted on them under negligible stress. Therefore, only
a simple geometric transformation (
XY
to
SY
in Fig. 2a) is used to
map the coordinates on a cylinder surface to a plane.
The optical coupling among the nano-posts is weak in the
high-contrast transmitarray metasurface platform, and each
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nano-post scatters light almost independent of its neighbouring
nano-posts. The weak coupling is due to the high-index contrast
between the nano-posts and their surroundings, and it is
manifested in the localization of the optical energy inside the
nano-posts and the weak dependence of the transmission of the
nano-post arrays to their spacing (that is, lattice constant) as has
been previously discussed
17
in more detail. This simplifies the
design by allowing to directly relate the local transmission
coefficient to the diameter of the nano-post at each unit cell
of the metasurface. Figure 2g shows the simulated intensity
transmission coefficient and phase of the transmission coefficient
for periodic arrays of 720-nm tall nano-posts embedded in PDMS
with diameters ranging from 100 to 275 nm (see the ‘Methods’
section for simulation details). The nano-posts are arranged in a
hexagonal lattice with 550 nm lattice constant, and the simulation
wavelength is 915 nm. Refractive indices of a-Si and PDMS are
3.56 and 1.41 at the simulation wavelength, respectively. The
whole 0 to 2
p
-phase range can be covered by changing the nano-
post diameters while keeping the intensity transmission
coefficient above 91%. These results are obtained assuming
normal incidence.
To get more insight into the operation mechanism, each nano-
post can be considered as a truncated circular cross-sectional
waveguide
27
. Because of the truncation of both ends, the nano-
post supports multiple low-quality factor Fabry–Perot resonances
which interfere and lead to high transmission of the nano-post
array (see Supplementary Note 1 and Supplementary Fig. 1). We
also note that in contrast to Huygens’ metasurfaces, where only
a-Si
PDMS
Al
2
O
3
Y
a
X
Y
bc
X
Z
Figure 1 | Conformal optics with optical dielectric metasurfaces.
(
a
) A schematic illustration of a dielectric metasurface layer conformed to the surface of
a transparent object with arbitrary geometry. (Inset) The building block of the metasurface structure: an amorphous silicon (a-Si) nano-post on a th
in layer
of aluminium oxide (Al
2
O
3
) embedded in a low-index flexible substrate (PDMS for instance). (
b
) Side view of the arbitrarily shaped object showing how the
object refracts light according to its geometry and generates an undesirable wavefront. (
c
) The same object with a thin dielectric metasurface layer
conformed to its surface to change its optical response to a desired one.
X
Y
Z
S
S
(mm)
0 0.25
–0.25
S
(mm)
0 0.25
–0.25
S
(mm)
0 0.25
–0.25
Y
(mm)
Y
(mm)
0.25
0
–0.25
Y
(mm)
0.25
–0.25
Y
(mm)
0.25
–0.25
–45
–90
0
OPD (
μ
m)
OPD (
μ
m)
X
Y
Z
S
X
Y
Z
S
X
Y
Z
S
X
Y
Z
S
X
Y
Z
S
S
(mm)
0
0.5
–0.5
S
(mm)
0
0.5
–0.5
S
(mm)
00.5
–0.5
0.5
00
–0.5
Y
(mm)
0.5
–0.5
0
Y
(mm)
0.5
–0.5
100
150
200
250
0.0
1
0.5

/(2
π
)
Post diameter (nm)
a-Si
E
0
–150
120
t
Ee
i

t
2
Al
2
O
3
a
d
b
e
c
f
g
PDMS
Figure 2 | Design procedure of conformal metasurfaces.
(
a
) The OPD (in
m
m) of the rays passing through a converging cylindrical object. (
b
) The
difference OPD needed at the surface of the convex cylindrical object compensated by the conformal metasurface. (
c
) Desired OPD at the surface of the
object which is provided by the object and conformal metasurface combination. (
d
f
) show similar plots for a diverging cylinder. ‘
S
’ is the arch length on the
cylinder surface in a plane perpendicular to the
y
-axis. (
g
) Simulated intensity transmission and phase of the transmission coefficient for a periodic array of
amorphous silicon (a-Si) nano-posts embedded in PDMS as shown in the inset. The nano-posts are composed of 720 nm a-Si on 100 nm aluminium oxide
(Al
2
O
3
), and are arranged in a hexagonal lattice. The simulation wavelength is 915 nm. This graph is used to relate the phase-shift values (and the
respective OPDs) needed at different points on the conformal metasurface to the nano-post diameters. See the ‘Methods’ section for simulation detai
ls.
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3
two resonant modes are used (one with a significant electric
dipole and one with significant magnetic dipole)
28
, the resonant
modes of the nano-posts contain dipole, quadrupole and higher-
order electric and magnetic multipoles in their multipole
expansion. Although the modal expansion approach provides
some intuitive understanding of the operation principle, it does
not offer guidelines for designing of the nano-post arrays.
Moreover, an effective medium method does not capture the
underlying physics of the periodic structures that support more
than one propagating mode
18,27,29
. Therefore it is not applicable
to most of the nano-posts widths we used in designing the
metasurface, because a periodic array of nano-posts with
diameters
4
180 nm would be multimode. Considering these,
and the limited number of design parameters (that is, nano-post
height and the lattice constant), we prefer the direct approach of
finding the transmission of the nano-post arrays (as shown in
Fig. 2g) over the modal expansion technique.
Low sensitivity to the incident angle is a necessary property for
a conformal metasurface since the incident angle would be
varying across the metasurface when it is wrapped over a
non-planar object. For the metasurface platform considered here,
the transmission coefficient of transverse electric (TE) polarized
light is weakly dependent on the incidence angle, and transmis-
sion coefficient of transverse magnetic (TM) polarized light shows
some angle-dependent resonances (Supplementary Note 2 and
Supplementary Fig. 2). These resonances introduce a small-phase
error and lower transmission, but as we experimentally show,
they only slightly reduce the metasurface efficiency for TM
polarization. For very steep angles, the metasurface efficiency
decreases as analysed in our previous work
17
. The general
metasurface design procedure is as follows. First, the coordinate-
transformed desired metasurface phase was sampled at the lattice
sites of the periodic hexagonal lattice. Then, the diameter of the
nano-post at each site was obtained using the corresponding
sampled phase value at that site and the phase-diameter relation
shown in Fig. 2g. To ensure a one-to-one relationship between
the phase and nano-post diameters, and to keep the transmission
high, nano-post diameters corresponding to the sharp resonances
in Fig. 2g were not used. Using this procedure, metasurfaces with
phase profiles shown in Figs 2b and 2e were designed to be
conformed to convex and concave cylindrical objects,
respectively. These metasurfaces modify the optical response of
the cylinders such that they behave as aspherical lenses and focus
light to single points (see the ‘Methods’ section for the details of
designed lenses and cylindrical surfaces).
Fabrication and characterization of conformal metasurfaces
.
Figure 3a schematically illustrates the key steps in fabricating
thin, flexible and conformable metasurfaces. A germanium
sacrificial layer is deposited on a silicon wafer and then an a-Si
layer is deposited over the germanium (Fig. 3a (i)). The a-Si layer
is patterned using electron-beam lithography followed by dry
etching using an alumina hard mask (Fig. 3a (ii)). The sample is
subsequently spin coated with two layers of PDMS (a diluted thin
layer followed by a thicker layer (Fig. 3a (iii)). Then, the sample is
immersed in a diluted ammonia solution which dissolves the
germanium layer and releases the flexible metasurface with
minimal degradation of the metasurface and the PDMS layer
(Fig. 3a (iv)). A scanning electron microscope image of the
fabricated device before spin coating the PDMS layer is shown in
Fig. 3b. Optical images of metasurfaces conformed to the convex
and concave glass cylinders are shown in Fig. 3c. The whole
fabrication process has a near-unity yield, with almost all of the
metasurfaces retaining a large majority of the nano-posts
(Supplementary Note 3 and Supplementary Fig. 3). Moreover, it
does not degrade the optical quality of the metasurface layer. The
optical quality of the flexible metasurface layer was tested by
transferring a flat metasurface lens to a flat substrate. See
Supplementary Fig. 4 for the measurement results and focusing
efficiency of the transferred flat metasurface lens. To demonstrate
the capabilities of this platform, two different conformal meta-
surfaces operating at the near-infrared wavelength of 915 nm
were fabricated and characterized. The first 1-mm-diameter
metasurface conforms to a converging cylindrical lens with a
radius of 4.13 mm. The cylinder by itself focuses light to a line
8.1 mm away from its surface (Fig. 4a). The presence of the
metasurface modifies the cylinder to behave as an aspherical lens
focusing light to a point 3.5 mm away from the surface of the
cylinder (Fig. 4a). The second device is a 2-mm-diameter meta-
surface conforming to a diverging glass cylinder with a radius of
6.48 mm and a focal length of

12.7 mm (Fig. 4b). With the
metasurface on top, the concave cylinder focuses light to a point
8 mm away from the cylinder surface (Fig. 4b).
The devices were characterized under 915 nm collimated laser
beam illumination by recording intensity profiles at different
planes parallel to their focal planes. Figure 4 also shows the
measured intensity profiles. The focal-plane intensity profiles are
shown as insets. A tight focus is observed at the designed focal
length. Focusing efficiencies of 56 and 52% under TE illumination
(that is, electrical field parallel to the cylinder axis) were measured
for the two devices, respectively. The focusing efficiency is defined
as the ratio of the power focused by the device to the incident
power on the device (see the ‘Methods’ section for the
measurement details). Under TM illumination, numerical
estimations based on the angular response of a uniform array
shown in Supplementary Fig. 2 indicate a slight degradation of
the device performance for larger angles between the metasurface
and the incident beam. The devices were measured with TM
input beam polarizations and, as expected, showed similar
behaviour as under TE illumination with focusing efficiencies of
56 and 50%. The difference in TE and TM polarization
efficiencies increases as the incidence angle becomes steeper
(Supplementary Fig. 5); the focus pattern, however, remains
almost the same under both polarizations (Supplementary Fig. 6).
The corresponding measured full width at half maximum
(FWHM) of the focal spots are
B
3.5 and 5
m
m and are
comparable to the diffraction-limited FWHM of 3.2 and
3.7
m
m, respectively. Slight aberrations observed in the focal-
plane intensity profiles are mostly due to imperfections in the
alignment of the metasurface to the non-planar substrates.
Reduction of efficiency in conformal metasurfaces compared
with the transferred flat metasurfaces (Supplementary Fig. 4) is
mostly due to the imperfections in the alignment, slight
movements of the nano-posts within the flexible substrate during
the substrate handling, and the difference between the actual
non-planar substrate profile and the profile assumed for design.
Discussion
Although here we have used cylindrical substrates as proof of
principle, this platform is not limited to surfaces that can be
projected to a plane using isometric transformations. Conformal
metasurfaces can be designed for other types of objects
(for instance spheres where the metasurface needs to be stretched
for conforming) with a similar method. High stretchability and
flexibility of thin PDMS layers (
B
50
m
m) make them suitable for
conforming to non-isometric surfaces. In such cases, however, a
mechanical analysis of the metasurface deformation upon
mounting on the object should be carried out. The coordinate
transformation that projects the conformal lattice to the planar
one should also account for this deformation. Besides, in the case
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of objects with steep angles (where the incident collimated beam
is far from normal to the metasurface at some points), further
considerations should be taken in choosing the lattice constant to
avoid excitation of higher-order diffractions. Moreover, since the
design procedure is local (that is, each nano-post at each lattice
site is chosen independently), the incident angle of the beam at
each lattice point can be taken into account in designing the
respective nano-post.
Conformal dielectric metasurfaces operate based on spatially
varying nano-structured diffractive scatterers. The behaviour of
the device is wavelength dependent because both the optical
response of the scatterers and their arrangement is optimized for
a given wavelength. The performance of the proposed devices has
a wavelength dependence similar to other high-contrast transmi-
tarray lenses recently demonstrated
17
, where good performance is
maintained over a bandwidth of a few per cent around the design
wavelength.
The proposed platform is relatively robust to systematic and
random errors. Fabrication errors do not affect the device
functionality and only reduce its efficiency (5 nm error in nano-
post diameters results in
B
3% reduction of efficiency
14
).
Alignment imperfections (extra stretch or angular rotation)
results in focal distance mismatch between the non-planar
object and the metasurface. Microlens focal distance has second-
order dependence on the substrate stretch ratio. For instance,
for the devices shown in Fig. 4, having 1% strain in the flexible
metasurface results in a 2% error in focal distance and a 1 degree
rotation misalignment results in 0.06% mismatch between the
horizontal and vertical focal distances. Also, fractional
wavelength error is equal to the fractional error of the focal
distance
17
(that is, 1% error in wavelength results in 1% error in
the focal distance of the flexible metasurface).
The developed fabrication process has a near-unity yield and
we are able to transfer almost all (larger than 99.5%) of the nano-
posts into the PDMS with good accuracy. Nevertheless, the
proposed platform is very robust to the fabrication deficiencies;
various imperfections including deviations between designed and
fabricated nano-post sizes (
B
5 nm in the diameter and (or)
height of the nano-posts), rough side walls, and missing nano-
posts only result in small reductions in the efficiency of the
device, and does not alter the functionality significantly.
In conclusion, we demonstrated flexible dielectric metasurfaces
and showed their applications for conformal optics. As proof of
concept, the optical properties of glass cylinders have been
changed to behave like aspherical lenses focusing light to a point.
The design paradigm can be applied to any other system where
conformal optical design is required. In addition, flexible
electronics is a well-established field of research, with the aim
of transferring conventional systems to flexible and non-planar
substrates. Very promising results have been achieved during the
last decade with various applications in wearable electronics,
electronic skins and medical devices
30–32
. The flexible
and conformal metasurface platform proposed here can be
merged with conformal electronics leading to versatile flexible
optoelectronic technologies.
Methods
Design procedure
.
The optical path length and the corresponding OPD of light
passing through the cylinders were computed using the ray optics approximation.
For simulations, the convex and concave cylinders were assumed to have radii of
Ge
a-Si
Al
2
O
3
a
(i)
(ii)
(iii)
(iv)
PDMS
b
c
Si
Figure 3 | Overview of the fabrication process and images of the fabricated metasurfaces.
(
a
) Steps involved in the fabrication of conformal
metasurfaces: (i) Germanium (Ge) and amorphous silicon (a-Si) are deposited on a silicon wafer. (ii) a-Si nano-posts are patterned and dry etched usi
ng an
aluminium oxide hard mask. (iii) PDMS is spin coated on the substrate. (iv) The sacrificial Ge layer is dissolved to release the nano-posts which are
embedded in the flexible PDMS layer. (
b
) A scanning electron microscope image of the silicon nano-posts with the aluminium oxide mask before spin
coating PDMS. Scale bar, 1
m
m. (
c
) Optical images of two flexible metasurfaces conformed to a convex glass cylinder (left) and a concave glass cylinder
(right). In both cases, the metasurfaces make cylinders behave like converging aspherical lenses. Scale bar, 2 mm.
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5
4.13 and 6.48 mm, respectively, and a refractive index of 1.507. The PDMS layer
was modelled as a 50-
m
m-thick layer with a refractive index of 1.41. In both cases,
the object OPDs were calculated at the outermost surface of the PDMS, considering
light propagation through the PDMS layer and refraction at the glass-PDMS
interface. The desired OPDs were also calculated at the same surfaces, assuming
focal distances of 3.5 and 8 mm for the convex and concave lenses, respectively.
Two different metasurfaces of diameters 1 and 2 mm were designed for the convex
and concave cylinders to impose the phase shifts equivalent to the difference of the
cylinders’ and the desired OPDs.
The planar periodic metasurfaces were simulated using the rigorous coupled
wave analysis technique to find the complex transmission coefficients
corresponding to all nano-post diameters for normal incident plane waves
(Fig. 2g)
33
. The lattice constant is chosen such that the array is non-diffractive at
the simulation wavelength. Simulation results shown in Supplementary Fig. 2 were
also obtained using the rigorous coupled wave analysis technique. All of the
simulations and calculations were performed at the wavelength of 915 nm.
Sample fabrication
.
A 300-nm-thick germanium sacrificial layer was deposited by
electron-beam evaporation on a silicon wafer, and 720 nm hydrogenated a-Si was
deposited on the germanium layer using plasma-enhanced chemical vapour
deposition with a 5% mixture of silane in argon at 200
°
C. The refractive index of
the a-Si layer was measured using variable-angle spectroscopic ellipsometry and
was found to be 3.56 at the wavelength of 915 nm. The metasurface pattern was
defined in ZEP-520A positive resist (
B
300 nm, spin coated at 5,000 r.p.m. for
1 min) using a Vistec EBPG5000
þ
electron-beam lithography system. The pattern
was developed in a resist developer (ZED-N50 from Zeon Chemicals). After
developing the resist, the pattern was transferred into a
B
100-nm-thick alumi-
nium oxide layer deposited by electron-beam evaporation through a lift-off process.
The patterned aluminium oxide served as a hard mask for dry etching of the a-Si
layer in a mixture of SF
6
and C
4
F
8
plasma. The PDMS polymer (RTV-615 A and B
mixed with a 10:1 mass ratio) was diluted in toluene in a 2:3 weight ratio as a
thinner. The mixture was spin coated at 3,000 r.p.m. for 1 min on the fabricated
metasurface to fill the gaps between the nano-posts and to form a thin PDMS film
(Supplementary Fig. 3). The sample was degassed and cured for
4
30 min. The
second layer of PDMS without a thinner was spin coated on the sample to form a
B
50-
m
m-thick PDMS film (spin coated at 1,000 r.p.m. for 1 min). The sample was
degassed and cured for
4
1 h. Finally, immersion in a 1:1:30 mixture of ammonium
hydroxide, hydrogen peroxide and deionized water at room temperature removed
the sacrificial germanium layer releasing the PDMS substrate and the embedded
nano-posts (
B
1 day). The released metasurface is then mounted manually
on the cylinders (Edmund Optics 43–856 and 47–748). To compensate for the
misalignment of the substrate and metasurface, multiple lenses with slightly
different rotations were fabricated in each sample (Fig. 3c). This way, the best-
aligned microlens should have a rotation error of less than or equal to one degree
(the rotation step between two successive metasurface lenses).
Measurement procedure
.
Devices were characterized using the setups shown
schematically in Supplementary Fig. 7. A 915-nm fibre-coupled semiconductor laser
60
40
20
0
–20
–40
–60
–10
10
0
–10
0
10
X
(
μ
m)
120
80
40
0
–40
–80
–120
–10
10
0
–10
0
10
X
(
μ
m)
Y
(
μ
m)
Y
(
μ
m)
Z
(
μ
m)
8.1 mm
X
Z
Y
Z
3.5 mm
3.5 mm
X
Y
X
Y
12.7 mm
X
Z
8 mm
8 mm
Y
Z
0
0.5
1
0
0.5
1
Intensity (a.u.)
Intensity (a.u.)
Z
(
μ
m)
a
b
Figure 4 | Measurement results of conformal dielectric metasurfaces.
(
a
) A converging cylindrical lens with a radius of 4.13 mm and a focal distance of
8.1 mm is optically modified using a conformal metasurface with a diameter of 1 mm. The cylinder plus the metasurface combination behaves as an
aspherical lens with a focal length of 3.5 mm. The coordinate system is the same as in Fig. 2. (
b
) A different metasurface is mounted on a concave glass
cylinder with a radius of 6.48 mm and a focal distance of

12.7 mm, which makes it focus to a spot 8 mm away from its surface (as an aspherical lens).
Schematic illustrations (side and top views) are shown on the left, and intensities at planes parallel to the focal plane and at different distances fr
om it are
shown on the right. Intensities at the focal plane are depicted in the insets. Measurements are performed at the wavelength of 915 nm. For the
measurement details see the ‘Methods’ section. Scale bar, 5
m
m.
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NATURE COMMUNICATIONS | DOI: 10.1038/ncomms11618
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NATURE COMMUNICATIONS
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was used as the source and a fibre collimation package (Thorlabs F220APC-780)
was used to collimate the beam. Intensity at different planes was captured by using
a

50 objective lens (Olympus LMPlanFL N, NA
¼
0.5), a tube lens (Thorlabs
LB1945-B) with focal distance of 20 cm, and a camera (CoolSNAP K4 from
Photometrics) as shown in Supplementary Fig. 7a. Moreover, neutral density filters
(Thorlabs ND filters, B coated) were used to adjust the light intensity and decrease
the background noise captured by the camera. The overall microscope magnifi-
cation was measured by imaging a calibration sample with known feature sizes. To
measure the efficiencies, an additional lens (Thorlabs LB1945-B with focal length of
20 cm) was used to partially focus the collimated beam, so that
4
99% of the beam
power falls inside the device under test. The beam radius was adjusted by changing
the distance between the lens and the sample. A 15-
m
m-diameter pinhole
(approximately three times the measured FWHM) was placed at the focal plane of
the sample to only allow the light focused inside the pinhole area to pass through.
The focusing efficiency was then determined as the ratio of measured optical power
after the pinhole (that is, the power in focus) to the measured power right before
the sample (the incident power). The measurement setup used for efficiency
characterization is shown in Supplementary Fig. 7b. For polarization sensitivity
measurement, a polarizer (Thorlabs LPNIR050-MP) was added before the sample
to set the polarization state of the incident beam.
The data that support the findings of this study are available from the
corresponding author on request.
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Acknowledgements
This work was supported by the DOE ‘Light-Material Interactions 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. and E.A.
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.
Author contributions
S.M.K., A.A. and A.F. conceived the experiments. S.M.K., A.A., E.A and Y.H. performed
the simulations and fabricated the devices. S.M.K., A.A and E.A. performed the
measurements, and analysed the data. S.M.K., A.A., E.A. and A.F. co-wrote the
manuscript. All authors discussed the results and commented on the manuscript.
Additional information
Supplementary Information
accompanies this paper at http://www.nature.com/
naturecommunications
Competing financial interests:
The authors declare no competing financial interests.
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How to cite this article:
Kamali, S. M.
et al.
Decoupling optical function and geometrical
form using conformal flexible dielectric metasurfaces.
Nat. Commun.
7:11618
doi: 10.1038/ncomms11618 (2016).
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