ARTICLE
MEMS-tunable dielectric metasurface lens
Ehsan Arbabi
1
, Amir Arbabi
1,2
, Seyedeh Mahsa Kamali
1
, Yu Horie
1
, MohammadSadegh Faraji-Dana
1
&
Andrei Faraon
1
Varifocal lenses, conventionally implemented by changing the axial distance between mul-
tiple optical elements, have a wide range of applications in imaging and optical beam
scanning. The use of conventional bulky refractive elements makes these varifocal lenses
large, slow, and limits their tunability. Metasurfaces, a new category of lithographically
de
fi
ned diffractive devices, enable thin and lightweight optical elements with precisely
engineered phase pro
fi
les. Here we demonstrate tunable metasurface doublets, based on
microelectromechanical systems (MEMS), with more than 60 diopters (about 4%) change in
the optical power upon a 1-
μ
m movement of one metasurface, and a scanning frequency that
can potentially reach a few kHz. They can also be integrated with a third metasurface to make
compact microscopes (~1 mm thick) with a large corrected
fi
eld of view (~500
μ
mor40
degrees) and fast axial scanning for 3D imaging. This paves the way towards MEMS-
integrated metasurfaces as a platform for tunable and recon
fi
gurable optics.
DOI: 10.1038/s41467-018-03155-6
OPEN
1
T. J. Watson Laboratory of Applied Physics, 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. Correspondence and requests for
materials should be addressed to A.F. (email:
faraon@caltech.edu
)
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1
1234567890():,;
L
enses are ubiquitous optical elements present in almost all
imaging systems. Compact lenses with tunable focal/imaging
distance have many applications, and therefore several
methods have been developed to make such devices
1
–
18
.
Deformable solid and liquid-
fi
lled lenses with mechanical
1
, elec-
tromechanical
2
,
12
, electrowetting
9
,
10
, and thermal
11
tuning
mechanisms have been demonstrated. Although these devices are
more compact than regular multi-element varifocal lenses, they
are still bulky (since they are regular refractive devices), and have
low tuning speeds (ranging from a few Hz to a few tens of Hz).
Liquid crystal lenses with tunable focus
3
–
5
have higher tuning
speeds, but they suffer from polarization dependence and limited
tuning range. Freeform optical elements (e.g., Alvarez lenses) that
can tune the focal distance upon lateral displacement of the ele-
ments have also been demonstrated
13
,
14
. These devices are gen-
erally based on mechanical movement of bulky elements and are
therefore not very compact nor fast. Highly tunable diffractive
and metasurface lenses based on stretchable substrates
15
,
16
,
19
have also been demonstrated, but they have low speeds and
require a radial stretching mechanism that might increase the
total device size. Spatial light modulators (SLMs) and other types
of diffractive elements that have pixels with controllable phase
shifts have been used and proposed
17
,
18
to achieve tunable beam
steering and focusing. Liquid crystal based SLMs are polarization
dependent and have limited speed and numerical apertures, and
other proposals yet await an experimental demonstration of phase
tuning over two dimensional arrays with high ef
fi
ciency
17
,
20
.
Optical metasurfaces
21
,
22
are planar arrangements of scatterers
designed to manipulate various properties of an incident light
beam. In the optical regime, dielectric metasurfaces are very
versatile as they allow for wavefront control with high ef
fi
ciency
and subwavelength resolution. Several devices with the ability to
control the phase
23
–
37
, polarization
38
,
39
, polarization and
phase
40
, or spectral components of light through harmonic gen-
eration
41
–
43
or
fi
ltering
44
–
47
have been demonstrated. Their thin
form factor makes them suitable for development of ultrathin
conformal optical elements
48
,
49
, and their compatibility with
conventional micorfabrication techniques allows for monolithic
fabrication of optical systems consisting of multiple metasurfaces
on a single chip
50
,
51
. These characteristics (i.e., the ability to
precisely control the phase with subwavelength resolution and
high gradients, thin and light form factor, and compatibility with
microfabrication techniques) also make them very attractive for
integration with the microelectromechanical systems (MEMS)
technology to develop metasurface-based micro-opto-
electromechanical systems (MOEMS). To date, integration of
metasurfaces and MEMS devices has been limited to moving
uniform high-contrast grating mirrors to tune the resonance
wavelength of Fabry-Perot cavities
52
,
53
, or change roundtrip
propagation length of light to form spatial light modulators
54
.
In this manuscript, we propose and demonstrate a metasurface
doublet composed of a converging and a diverging metasurface
lens with an electrically tunable focal distance. The large and
opposite-sign optical powers of the two elements, as well as their
very close proximity, make it possible to achieve large tuning of
the optical power (~60 diopters, corresponding to about 4%) with
small movements of one element (~1 micron). We have devel-
oped a fabrication process for making such metasurface doublets,
and experimentally show metasurface lenses with over 60
μ
m
tuning of the effective focal length (EFL) from 565 to 629
μ
m,
corresponding to a ~180-diopter change in the optical power.
Arrays of these devices can be fabricated on the same chip to
allow for multiple lenses with different focal distances scanning
different depths with frequencies potentially reaching several
kHz. In addition, we show that such devices can be combined
with the recently demonstrated monolithic metasurface optical
systems design
50
to develop compact focus-scanning objectives
with corrected monochromatic aberrations over a large
fi
eld of
view. It is worth noting that MOEMS devices with the ability to
axially scan the focus have previously been demonstrated based
on integration of refractive and Fresnel microlenses with axially
moving frames
6
–
8
,
55
. However, in these devices the focal point is
scanned by the same distance that the lens is moved, and the
effective focal length (or equivalently the optical power) is not
actually tuned. Nevertheless, the concepts and techniques used in
such devices can be combined with the metasurface doublet
demonstrated here to achieve enhanced functionalities (e.g.,
enable lateral scanning of focus).
Results
Concept and design
. Figure
1
a shows a schematic of the tunable
focus doublet. The system consists of a stationary metasurface on
a glass substrate, and a moving metasurface on a SiN
x
membrane.
The membrane can be electrostatically actuated to change the
distance between the two metasurfaces. The lenses are designed
such that a small change in the distance between them,
Δ
x
~1
μ
m, leads to a large tuning of the focal length (
Δ
f
~36
μ
m change
in the front focal length from 781 to 817
μ
m when the lens
separation is changed from 10 to 9
μ
m, see Supplementary Fig.
1
for the phase pro
fi
les and their ray tracing simulations). The
membrane and glass lenses are 300
μ
m in diameter, and have
focal lengths of ~120 and ~
−
130
μ
m, respectively. The electro-
static actuation is achieved through contacts only to the glass
substrate. The capacitor plates are shown in the inset of Fig.
1
a.
The contacts are con
fi
gured to make two series capacitors. Each
capacitor has one plate on the glass substrate and another one on
the membrane, resulting in an attractive force between the
membrane and the glass substrate. Figure
1
b, c show the
fi
rst two
mechanical resonance modes of the membrane at ~2.6 and ~5.6
kHz, respectively. This limits the operation frequency of the
device to ~4 kHz to avoid unwanted excitation of the second
resonance.
The metasurfaces are based on high-contrast dielectric
transmitarrays
23
,
27
. These devices consist of arrays of high index
dielectric scatterers (nano-posts) with different shapes and sizes.
With proper design, the nano-posts enable complete control of
phase and polarization on a subwavelength scale
38
,
40
,
56
. When
only phase control is required, the nano-posts should have a
symmetric cross-section (i.e., square, circular, etc.). For fabrica-
tion considerations, we choose nano-posts with square-shaped
cross-section on a square lattice. Since both the moving and
stationary metasurface lenses have high numerical apertures (NA
~0.8), we used a recently developed technique for choosing the
metasurface parameters (i.e., amorphous silicon layer thickness,
lattice constant, and minimum and maximum post side lengths)
to maximize the ef
fi
ciency of high NA lenses for both transverse
electric (TE) and transverse magnetic (TM) polarizations
57
. The
method is based on approximating the ef
fi
ciency of a lens
designed with certain metasurface parameters through ef
fi
ciencies
of periodic gratings designed with the same parameters. Using
this method and considering the design wavelength of 915 nm,
the
α
-Si layer thicknesses were chosen to be 530 and 615 nm for
the moving and stationary lenses, respectively. The lattice
constant was set to 320 nm in both cases. Figure
1
d, e show
simulated transmission amplitudes and phases for uniform arrays
of nano-posts on the membrane and the glass substrate,
respectively. Given a required phase pro
fi
le, one can
fi
nd the
best nano-post for each site on the metasurface using Fig.
1
d, e
27
.
Device fabrication
. A summary of the key fabrication steps for
the moving and stationary lenses is schematically depicted in
ARTICLE
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Fig.
2
a
–
f (for more details see the Methods section). The moving
metasurface fabrication was started on a silicon wafer with a
~210-nm-thick low-stress SiN
x
. A 20-nm-thick SiO
2
layer fol-
lowed by a 530-nm-thick
α
-Si layer was deposited on the SiN
x
layer. The SiO
2
layer acts both as an adhesion promoter between
the SiN
x
and the
α
-Si layers, and as an etch-stop during the dry
etch process to form the metasurface. In the next step, patterns
for backside holes were de
fi
ned and transferred to an alumina
layer. This layer was then used as a hard mask to partially etch
through the silicon wafer (a ~50-
μ
m-thick layer was left to
maintain the mechanical strength of the sample during the next
steps). Alignment marks were then etched through the
α
-Si layer
for aligning the top and bottom sides. The metasurface lens was
then patterned into the
α
-Si layer. Next, the metallic contacts
were deposited and patterned. The top side of the device was
covered with a protective polymer, and the remaining part of the
wafer under the membrane was wet etched. Finally, the mem-
brane was patterned and dry etched to release the metasurface.
An optical image of the fabricated metasurface on a membrane is
shown in Fig.
2
b. Due to the residual stress in the membranes, the
beams are slightly bent such that the central part of the lens is
about 6 to 8
μ
m above the surface of the wafer.
The fabrication steps of the stationary metasurface are
schematically shown in Fig.
2
c. A 615-nm-thick layer of
α
-Si
was deposited on a glass substrate. The metasurface pattern was
generated and etched through the layer, followed by deposition
and patterning of the contacts. An optical image of a completed
metasurface on the glass substrate is shown in Fig.
2
d. Finally, a
20
μ
m spacer layer was spin coated and patterned on the glass
substrate (to achieve a ~12
μ
m distance between the lenses), and
the two chips were aligned and bonded with an ultraviolet (UV)
curable epoxy (Fig.
2
e). An optical image of the
fi
nal device is
shown in Fig.
2
f. Figure
2
g, h show scanning electron
micrographs of the fabricated metasurfaces.
Experimental doublet characterization results
. Figure
3
sum-
marizes the focusing measurement results under application of a
direct-current (DC) voltage. For these measurements, the device
was illuminated with a collimated beam from a 915-nm diode
laser, and the focal plane intensity patterns were imaged using a
custom-built microscope (for details of the measurement setup,
see Methods section and Supplementary Fig.
2
). The simulated
EFL is plotted against the distance between the two lenses in
Fig.
3
a, along with the measured values for multiple devices with
different initial separations between the membrane and the glass
substrate. In all measurements, these separations were extracted
by comparing the measured focal distances to their simulated
values. We should note that devices 2 and 3 are on the same chip,
and devices 4
–
8 are on another chip. This shows the potential of
the proposed structure for integrating multiple devices on the
same chip with the ability to scan different ranges of focal dis-
tances to simultaneously image a larger range of depths. Figure
3
b
shows the measured front focal length (i.e., the physical distance
between the focus and the stationary lens), and the extracted lens
separation for device 2 versus the applied DC voltage, indicating
that the optical power changes by more than 180 diopters when
applying 80 V. The difference between the measured focal dis-
tances in a few measurements falls within the measurement error
of ~5
μ
m. The possibility of changing the applied voltage very
fi
nely, makes it possible to tune the membrane separation and
thus the optical power very
fi
nely, in the absence of external
vibrations. Intensity distributions measured in the focal plane
under application of different DC voltages are shown in Fig.
3
c
for device 2. As seen in Fig.
3
c, d, the measured Airy disk radii are
Δ
x
Δ
f
a
0
1
0
1
100
200
Post width (nm)
|
t
|
∠
t
/2
π
|
t
|
∠
t
/2
π
SiN
x
t
E
-Si
E
d
Post width (nm)
0
1
80
180
t
E
-Si
FS
E
e
b
c
Transmission (a.u.)
Displacement (a.u.)
Transmission (a.u.)
Fig. 1
Schematic illustration of the tunable doublet and design graphs.
a
Schematic illustration of the proposed tunable lens, comprised of a stationary lens
on a substrate, and a moving lens on a membrane. With the correct design, a small change in the distance between the two lenses (
Δ
x
~1
μ
m) results in a
large change in the focal distance (
Δ
f
~35
μ
m). (Insets: schematics of the moving and stationary lenses showing the electrostatic actuation contacts.)
b
The
fi
rst and
c
second mechanical resonances of the membrane at frequencies of ~2.6 and ~5.6 kHz, respectively. The scale bars are 100
μ
m.
d
Simulated
transmission amplitude and phase for a uniform array of
α
-Si nano-posts on a ~213-nm-thick SiN
x
membrane versus the nano-post width. The nano-posts
are 530 nm tall and are placed on the vertices of a square lattice with a lattice constant of 320 nm.
e
Simulated transmission amplitude and phase for a
uniform array of
α
-Si nano-posts on a glass substrate versus the nano-post width. The nano-posts are 615 nm tall and are placed on the vertices of a square
lattice with a lattice constant of 320 nm. FS: Fused silica
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3
smaller than 1.1 times their corresponding theoretical values. The
observed aberrations are caused by the mechanical deformation
of the moving lens resulting from the residual stress in the SiN
x
layer. The metasurface lenses are designed for optimal perfor-
mance when their separation changes from 12 to 6
μ
m. As a result
of this change, the effective focal length should be tuned from 627
to 824
μ
m. The achieved initial distance between the metasurfaces
is slightly different from the design value (~15
μ
m instead of ~12
μ
m) because the spacer layer was slightly thicker than intended.
Besides, in order to avoid the pull-in instability (which would
destroy the device), we stayed away from higher voltage values
than 80 V in this sample. In principle, one should be able to
decrease the lens separation in device 2 from 15
μ
m to about 10
μ
m, and thus increase the front focal distance from 635 to 781
μ
m
(or change the EFL from 560 to 681
μ
m, tuning optical power by
more than 300 diopters, or ~20%).
Figure
3
d shows the measured absolute focusing ef
fi
ciency of
the doublet (de
fi
ned as the power passing through a ~20-
μ
m
diameter aperture to the total power hitting the device). The
absolute ef
fi
ciency is between 40 and 45% for all applied voltage
values. The high-NA (NA ~0.8) singlets used here are expected to
be ~75% ef
fi
cient
57
. Because the doublet uses two of such lenses,
its ef
fi
ciency is estimated to be ~55%. Taking into account the
re
fl
ections at the three air-glass interfaces (a glass wafer is used to
cap the backside of the membrane to fully isolate it from the
environment air
fl
ow), we obtain a total ef
fi
ciency of ~50% which
agrees well with the measured ef
fi
ciency values. We attribute the
slightly lower measured ef
fi
ciency to fabrication imperfections. It
is foreseeable that the ef
fi
ciency can be signi
fi
cantly improved
with better optimization and design processes
35
, use of anti-
re
fl
ection coatings to reduce re
fl
ection losses, and optimizing the
fabrication process.
The frequency response of the doublet is measured and plotted
in Fig.
3
e (see Supplementary Note
1
and Supplementary Fig.
2
for details of frequency response measurement). The frequency
response transfer function is de
fi
ned as the membrane displace-
ment at frequency
f
, normalized to its value under the same
voltage applied in DC. The black dashed line shows the
−
3-dB
line, showing a ~230 Hz bandwidth for the device. The red and
blue dashed lines show second order system
fi
ts (i.e.,
H
ð
f
Þ¼
1
1
ib
=
ffiffiffiffiffi
mk
p
ðÞ
f
=
f
0
ðÞ
f
=
f
0
ðÞ
2
, where
f
0
is the resonance frequency
for the
fi
rst mode,
b
is a damping factor, and
m
and
k
are the
oscillator mass and spring constant, respectively), indicating that
the
fi
t follows the measurement well for
b
¼
20
ffiffiffiffiffiffiffi
mk
p
. This
corresponds to a highly overdamped system with a damping ratio
(
b
=
2
ffiffiffiffiffiffiffi
mk
p
) of ~10. Under the atmosphere pressure the dominant
loss mechanism is the air damping
58
. If the damping is reduced
by about 20 times by reducing the air pressure inside the lens
packaging (i.e.,
b
=
2
ffiffiffiffiffiffiffi
mk
p
0
:
5), then the frequency response will
follow the blue dashed line in Fig.
3
e, with a 3-dB bandwidth
reaching 4 kHz. This would correspond to a quality factor of ~1
ace
g
h
b
d
f
: c-Si
: Au
: FS
: SiN
x
: SiO
2
: SU-8
:
-Si
Fig. 2
Fabrication process summary.
a
Simpli
fi
ed fabrication process of a lens on a membrane: a SiO
2
spacer layer and an
α
-Si layer are deposited on a Si
substrate with a pre-deposited SiN
x
layer. The backside of the substrate is partially etched, and alignment marks are etched into the
α
-Si layer. The lens is
patterned and etched into the
α
-Si layer, and gold contacts are evaporated on the membrane. The remaining substrate thickness is etched and the
membrane is released. c-Si: crystalline silicon; FS: fused silica.
b
An optical microscope image of a fabricated lens on a membrane.
c
Simpli
fi
ed fabrication
process of the lens on the glass substrate: an
α
-Si layer is deposited on a glass substrate and patterned to form the lens. Gold contacts are evaporated and
patterned to from the contacts.
d
An optical microscope image of the fabricated lens on the glass substrate.
e
Schematics of the bonding process: an SU-8
spacer layer is patterned on the glass substrate, the two chips are aligned and bonded.
f
A microscope image of the
fi
nal device.
g
Scanning electron
micrograph of the lens on the membrane, and
h
nano-posts that form the lens. Scale bars are 100
μ
min
b
,
d
,
f
, and
g
, and 1
μ
min
h
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for the mechanical resonator, which should be feasible by reducing
air damping. In addition, at such a low quality factor, oscillation
and long settling times should not be an issue. Vacuum packaging
could be done through bonding the backside glass substrate (the
one with no metasurface) and the silicon chip carrying the
membrane in a vacuum chamber with controllable pressure.
Imaging with electrical focusing
. The tunable doublet can be
used for imaging with electrically controlled focusing. To
demonstrate this, we formed an imaging setup using the doublet
and a refractive lens. The setup is schematically shown in Fig.
4
a.
A transmissive object was placed in front of the imaging system.
A 1.8-mm diameter pinhole was placed in front of the aspheric
lens to reduce the aperture and increase contrast. The system
images the object to a plane ~130
μ
m outside the stationary lens
substrate. Since this image is very small and close to the lens, we
used a custom-built microscope (×55 magni
fi
cation) to re-image
it onto the camera. The results are summarized in Fig.
4
b. When
the object is
p
~ 15 mm away and no voltage is applied, the image
is out of focus. If the applied voltage is increased to 85 V in the
same con
fi
guration, the image comes to focus. Changing the
object distance to
p
~ 9.2 mm, the voltage should also be changed
to 60 V to keep the image in focus. At 0 V, the object should be
moved to
p
~ 4 mm to be in focus, and applying 85 V to the
doublet will result in a completely out of focus image in this
con
fi
guration. As observed here, by moving the membrane only
about 4
μ
m, the overall system EFL changes from 44 to 122 mm, a
ratio of about 1:2.8. This is an example of the importance of the
large absolute optical power tunability of the metasurface doublet,
especially when it is integrated into a system with a comparably
small overall optical power. It also allows for changing the object
distance from 4 to 15 mm by electrically controlled refocusing.
Electrically tunable compact microscope
. To further demon-
strate the capabilities of this platform, we use it to design a 1-mm-
thick electrically tunable microscope. The structure is schemati-
cally shown in Fig.
5
a, and is a metasurface triplet composed of a
tunable doublet (with an optical design different from the fabri-
cated one), and an additional metasurface lens. The lenses, from
left to right are 540, 560, and 400
μ
m in diameter. They have focal
lengths of about
−
290, 275, and 1470
μ
m. The glass substrate is 1-
mm thick, and the image plane is located 14 mm behind the third
lens. The stop aperture is located at the plane of the right-most
lens, and has the same diameter of 400
μ
m. By moving the
membrane and changing the separation
d
from 13 to 5
μ
m, the
object plane distance
D
changes from 622 to 784
μ
m. The triplet
can be optimized to correct for monochromatic aberrations
50
to
keep the focus close to the diffraction limit over a large
fi
eld of
view (see Supplementary Fig.
1
for phase pro
fi
les, and Supple-
mentary Table
2
for the corresponding coef
fi
cients). Here, we
have optimized the phase pro
fi
les to keep the focus almost dif-
fraction limited in a ~500
μ
m diameter
fi
eld of view (corre-
sponding to a ~40-degree
fi
eld of view in the
D
=
700
μ
m case).
Spot diagrams of point sources at 0, 125, and 250
μ
m distances
from the optical axis are shown in Fig.
5
b, demonstrating a
diffraction-limited behavior. The spot diagrams are ray optics
11
13
15
0
80
640
680
d
(
μ
m)
720
40
Voltage (V)
b
d
600
800
400
EFL (
μ
m)
d
(
μ
m)
10
20
30
Simulation
a
Device 1
Device 2
Device 3
Device 4
Device 8
Device 7
Device 6
Device 5
v
= 0 V,
f
= 635
μ
m
v
= 60 V,
f
= 664
μ
m
v
= 70 V,
f
= 682
μ
m
v
= 80 V,
f
= 717
μ
m
c
e
Frequency (Hz)
1 2 5 10
100
1000
10,000
–10
0
–20
Transfer function (dB)
f
(
μ
m)
640
680
720
0
0.5
1
Normalized Airy radius
Efficiency
Efficiency / r
–
A
(a.u.)
Measured
b
=20
√
mk
b
=
√
mk
1
0
Intensity (a.u.)
f
(
μ
m)
Fig. 3
Focusing measurement results of the tunable doublet.
a
Simulated EFL versus the distance between lenses, along with measured EFL values for 8
devices under different applied voltages. Different devices have different initial lens separations, resulting in different focal distances unde
r no applied
voltage.
b
Measured front focal length versus the applied DC voltage for device 2 of panel
a
. The separation values between the moving and stationary
lenses are also plotted.
c
Intensity distributions in the focal plane of the doublet lens at different actuation voltages. The scale bars are 2
μ
m.
d
Measured
Airy radii (normalized to their corresponding diffraction-limited values),
r
̄
A
, and measured absolute focusing ef
fi
ciency of the tunable doublet.
e
Measured
frequency response of the system, along with second order transfer functions with two values of the damping factor (
b
) equal to 20
ffiffiffiffiffiffi
mk
p
and
ffiffiffiffiffiffi
mk
p
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5
Objective lens
Doublet
Lens
1.3 mm
Tube lens
Filter
Camera
a
b
v
p
= 4 mm,
v
=85 V
p
= 4 mm,
v
=0 V
p
= 9.2 mm,
v
= 60 V
p
= 15 mm,
v
= 85 V
p
= 15 mm,
v
=0 V
p
Fig. 4
Imaging with the tunable doublet.
a
Schematic illustration of the imaging setup using a regular glass lens and the tunable doublet. The image formed
by the doublet is magni
fi
ed and re-imaged using a custom-built microscope with a ×55 magni
fi
cation onto an image sensor.
b
Imaging results, showing the
tuning of the imaging distance of the doublet and glass lens combination with applied voltage. By applying 85 V across the device, the imaging distance
p
increases from 4 to 15 mm. The scale bars are 10
μ
m
a
c
b
D
d
X
x
14 mm
x
=0
μ
m
x
= 125
μ
m
x
= 250
μ
m
X
= 0 mm
X
= 1.376 mm
X
= 2.752 mm
100
μ
m
d
=5
μ
m,
D
= 784
μ
m
d
=9
μ
m,
D
= 700
μ
m
d
=13
μ
m,
D
= 622
μ
m
Fig. 5
Tunable focus metasurface microscope.
a
Schematic illustration of a metasurface triplet operating as a compact electrically tunable microscope. The
metasurfaces have diameters of 540, 560, and 400
μ
m from the left to the right, respectively, and the glass substrate is 1 mm thick. Moving the membrane
by about 8
μ
m moves the object plane more than 160
μ
m.
b
Ray optics simulation of spot diagrams of the microscope for the case of
d
=
9
μ
m. The inset
shows a schematic of the triplet, the locations of the point source in the object plane and the image plane. The phase pro
fi
les of the metasurfaces are
designed to keep the focus almost diffraction limited for a 500-
μ
m-diameter
fi
eld of view when d is changed from 5 to 13
μ
m. The system has a
magni
fi
cation close to 11 and a numerical aperture of 0.16 when
d
=
9
μ
m.
c
Image simulation results using the triplet for different values of
d
and
D
. The
scale bars are 50
μ
m in the zoomed-out images, and 5
μ
m in the zoomed-in areas
ARTICLE
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simulation results from a point source at their corresponding
distances from the optical axis. The red circles show the
diffraction-limited Airy disks for different cases, with ~40-
μ
m
radii. Figure
5
c shows the image formation simulation results for
the system at three different values of
d
(and
D
). The insets show
that the system can resolve the ~3.5
μ
m line-space in an object.
The effective focal length for the whole system is ~1160
μ
m (for
d
=
9
μ
m case), which is signi
fi
cantly larger than the focal lengths
of the membrane and
fi
rst glass lenses, similar to the fabricated
doublet. As a result, the object space NA is about 0.16, corre-
sponding to a resolution of ~3.5
μ
m at the object plane. Con-
sidering the 14-mm distance between the image plane and the
backside aperture, the image space NA is ~0.014 which results in
an Airy radius of about 40
μ
m in the image plane. As the effective
focal length of the system changes with tuning
d
, the total mag-
ni
fi
cation of the system also changes from 11.3 (for
d
=
5
μ
m) to
10.3 (for
d
=
13
μ
m).
Discussion
The lenses demonstrated here have small sub-millimeter aperture
sizes suitable for applications in ultra-compact optical systems. In
principle, the lenses can have centimeter-scale apertures as silicon
nitride membranes at these scales have already been demon-
strated
59
,
60
. In addition, the electrostatic forces and the
mechanical resonance frequencies can be engineered by appro-
priate choice of the electrostatic actuation plate areas, membrane
thickness, and mechanical beam design.
The high optical power of the elements, and the small aperture
of the doublet result in a relatively high sensitivity to the mem-
brane bending, and to misalignment between the two lenses (see
Supplementary Fig.
3
for modulation transfer function and Strehl
ratio simulation results). We estimate the radius of curvature of
the measured membranes to be ~20 mm, using mechanical
simulations of the structure and the observed ~6-
μ
m distance
between the center of the lens and the surface of the wafer. This
would result in a Strehl ratio slightly larger than 0.95. A Strehl
ratio of 0.9 (as an acceptability criterion) corresponds to a radius
of curvature of ~15 mm. If the membrane curvature is larger than
this and known a priori, the lens design can be optimized to
include the effects of the bending. In addition, to have a Strehl
ratio better than 0.9, the misalignment between the two lenses
should be better than 2
μ
m. On the basis of the symmetric
measured focal spots, we estimate the misalignment in the
doublets to be smaller than this limit. Considering the high
alignment precision achievable with industrial aligners, achieving
a2-
μ
m resolution is not a challenge.
Similar to other diffractive and metasurface optical devices, the
lenses demonstrated here suffer from chromatic aberrations
61
–
63
.
The exact
“
acceptable
”
operation bandwidth of the lens depends
on the effective focal length, the numerical aperture, and a cri-
terion for
“
acceptability
”
. Using the criterion given in
50
that is
based on the focal spot area increasing to twice its value at the
center wavelength, and assuming an effective focal length of ~600
μ
m (corresponding to a numerical aperture of 0.24), the opera-
tion bandwidth is given by
Δ
λ
=
2.27
λ
2
/(
f
NA
2
)
≈
50 nm. To make
multiwavelength tunable doublets, many of the recently demon-
strated approaches for making multiwavelength metasurfaces can
be directly applied
56
,
64
–
66
. In addition, the recently introduced
concept of phase-dispersion control
67
–
69
can be used to increase
the operation bandwidth of the metasurface lenses by correcting
the chromatic aberrations over a continuous bandwidth.
Here we introduced a category of MOEMS devices based on
combining metasurface optics with the MEMS technology. To
showcase the capabilities of the proposed platform, we experi-
mentally demonstrated tunable lenses with over 180 diopters
change in the optical power, and measured focusing ef
fi
ciencies
exceeding 40%. In principle, the optical power tunability could be
increased to above 300 diopters for the presented design. We
demonstrated how such tunable lenses can be used in optical
systems to provide high-speed electrical focusing and scanning of
the imaging distance. The potentials of the introduced technology
go well beyond what we have demonstrated here, and the devices
can be designed to enable compact fast-scanning endoscopes,
fi
ber-tip-mounted confocal microscopes, etc. In principle, meta-
surfaces can replace many of the refractive and diffractive micro-
optical elements used in conventional MOEMS devices to make
them more compact, increase their operation speed, and enhance
their capabilities.
Methods
Simulation
. The optimized phase pro
fi
les (for both the fabricated doublet and the
triplet shown in Fig.
5
) were obtained using Zemax OpticStudio. The phase pro
fi
les
are de
fi
ned as even-order polynomials of the radial coordinate
r
according to
φ
ð
r
Þ¼
P
2
n
a
2
n
r
=
R
0
ðÞ
2
n
, where
R
0
is a normalization radius and
a
2
n
are the
coef
fi
cients (see Supplementary Fig.
1
and Supplementary Table
1
for the phase
pro
fi
les and the optimized coef
fi
cients). This was done through simultaneously
minimizing the root mean square radius of the focal spot for several con
fi
gurations
(i.e., different lens separations, and, in the case of the triplet, the lateral source
position). The image formation simulations (for Fig.
5
) were done using the
extended scene simulations of Zemax OpticStudio and took into account the
aberrations and limitations resulting from diffraction.
Mechanical simulation of the MEMS structure was performed in COMSOL
Multiphysics to
fi
nd the resonances of the structure. The metallic contacts and the
α
-Si metasurface were treated as additional masses on the membrane. The Young
modulus of SiN
x
was assumed to be 250 GPa and its Poisson ratio was set to be
0.23. The following densities were used for different materials: 3100 kg m
−
3
for
SiN
x
, 2320 kg m
−
3
for
α
-Si, and 19,300 kg m
−
3
for gold. To account for the fact
that the whole metasurface volume is not
fi
lled with
α
-Si, an average
fi
ll factor of
0.5 was used.
Transmission amplitudes and phases of the metasurface structures on both
fused silica and silicon nitride were computed through rigorous coupled-wave
analysis
70
. The transmission values were calculated by illuminating a uniform array
of nano-posts with a normally incident plane wave at 915 nm wavelength and
fi
nding the amplitude and phase of the transmitted zeroth-order wave right above
the nano-posts. The subwavelength lattice ensures that this single number is
adequate to describe the optical behavior of a uniform array. The following
refractive indices were used in the simulations: 3.5596 for
α
-Si, 2.1 for SiN
x
, 1.4515
for fused silica. The lattice constant was 320 nm in both cases, and the
α
-Si
thickness was 530 nm for the moving, and 615 nm for the stationary lens.
Device fabrication
. Fabrication of the stationary lenses was started by depositing a
615-nm-thick layer of
α
-Si on a 500-
μ
m-thick fused silica substrate through a
plasma enhanced chemical vapor deposition (PECVD) process. The metasurface
pattern was written on a ~300-nm-thick layer of ZEP520A positive electron resist
with a Vistec EBPG5000
+
electron beam lithography system. After development of
the resist, a 70-nm-thick alumina layer was evaporated on the sample that was used
as a hard mask. The pattern was then transformed to the
α
-Si layer via a dry etch
process. The metallic contacts
’
pattern was de
fi
ned using photolithography on AZ
5214 E photoresist which was used as a negative resist. A ~10-nm-thick layer of Cr,
followed by a ~100-nm-thick Au layer was evaporated onto the sample, and a lift-
off process transferred the photoresist pattern to the metal layer. Finally, a ~20-
μ
m-
thick layer of SU-8 2015 was spin coated on the sample and patterned to function
as a spacer.
The moving lens fabrication started with a silicon wafer with ~450-nm-thick
low-stress low-pressure chemical vapor SiN
x
deposited on both sides. The device
side was etched down to about 213 nm with a dry etch process. A ~20-nm-thick
SiO
2
layer, followed by a ~530-nm-thick
α
-Si layer was deposited on the sample
with a PECVD process. Through hole patterns were de
fi
ned on the backside of the
sample using the AZ 5214 E photoresist, and a lift-off process was performed to
transfer the pattern to a ~200-nm-thick alumina layer that was used as a hard
mask. The holes were partially etched through the wafer with a Bosch process
(leaving a ~50-
μ
m-thick silicon layer to provide mechanical support for the
membrane in the following steps). Alignment marks (for aligning the lenses to the
backside holes) were patterned and etched into the
α
-Si layer using a backside-
aligned photolithography process. A process similar to the one used for the
stationary lenses was performed to fabricate the metasurfaces and the metallic
contacts. The top side (with the metasurfaces and contacts) was then covered with
a protective polymer coating (ProTEK PSB, Brewer Science) layer, and the
remaining ~50-
μ
m-thick silicon layer was etched in a 3:1 water-diluted potassium
hydroxide solution at 80 °C. The membrane pattern was de
fi
ned on the sample
using photolithography with AZ nLOf 2020 photoresist, and was etched through
the SiN
x
membrane to release the membrane. The photoresist was then removed in
NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-03155-6
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7
an oxygen plasma. A fused silica piece was bonded to the backside of the
membrane sample using a UV-curable epoxy (NOA 89, Norland Products) to
isolate the membranes from ambient air
fl
ow. At the end, the moving and stationary
samples were aligned and bonded using an MA6/BA6 aligner (Suss MicroTec). A
UV-curable epoxy was used to bond the two samples. Using this technique, an
alignment precision of a few microns is feasible.
Measurement procedure
. The doublet characterization setup is schematically
shown in Supplementary Fig.
2
a. A collimated beam from a
fi
ber coupled 915-nm
diode laser connected to a
fi
ber collimation package (F240FC-B, Thorlabs) was
used to illuminate the doublet from the membrane side. A custom-built micro-
scope consisting of a ×50 objective (Olympus LCPlanFL N, NA
=
0.7) and a tube
lens with a 20-cm focal length was used to image the focal plane of the doublet to a
charge-coupled device camera (CoolSNAP K4, Photometrics). An air coplanar
probe (ACP40 GSG 500, Cascade Microtech) was used to apply a voltage to the
doublet. For measuring the frequency response, square pulses with different base
frequencies were applied to the probe (CFG250 function generator, Tektronix). The
change in the optical power passing through a 50-
μ
m pinhole in the image plane
(equivalent to a ~1-
μ
m pinhole in the focal plane) was then measured with a fast
detector (PDA36A, Thorlabs) connected to an oscilloscope. The frequency
response was then extracted through Fourier transforming the input voltage and
the resulting change in the output power (see Supplementary Note
1
for more
details).
The ef
fi
ciency was calculated through measuring the power passing through a
~1-mm iris in the image plane (corresponding to a ~20-
μ
m pinhole in the focal
plane) and dividing it by the total power before the doublet. To make sure that the
total beam power was incident on the doublet, the beam was partially focused by a
lens with a 10-cm focal length. The distance between the lens and the doublet was
adjusted such that the beam had a ~100-
μ
m full-width at half-maximum (FWHM)
at the place of the doublet (i.e., one third of the doublet diameter). This way, more
than 99% of the power is expected to hit the doublet area.
The imaging experiments in Fig.
4
were also performed using a similar setup.
For imaging, a 910-nm LED (LED910E, Thorlabs) was used as an illumination. To
reduce the effects of chromatic dispersion, a bandpass
fi
lter (FB910-10, 910-nm
center wavelength, 10-nm FWHM) was placed in front of the camera. A negative
1951 USAF Resolution target (R1DS1N, Thorlabs) was used as an imaging object.
A4-
f
system consisting the doublet and a glass lens with focal length of 8 mm
(ACL12708U-B, Thorlabs) was used to form images of the resolution target at
different distances. To reduce the aperture size and increase contrast, a 1.8-mm-
diameter aperture (AP1.5, Thorlabs) was placed at a ~1.3-mm distance in front of
the refractive lens. The distance between the backside of the refractive lens and the
doublet was ~4.5 mm. The resulting image was magni
fi
ed and re-imaged onto the
camera with the same microscope used for the focal spot characterization.
Data availability
. The data that support the
fi
ndings of this study are available
from the corresponding author upon request.
Received: 18 August 2017 Accepted: 24 January 2018
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Acknowledgements
This work was supported by National Science Foundation award 1512266 and Samsung
Electronics. A.A. and Y.H. were also supported by DARPA, and S.M.K. was supported as
part of the Department of Energy (DOE)
“
Light-Material Interactions in Energy Con-
version
”
, Energy Frontier Research Center under grant no. DE-SC0001293. The device
nanofabrication was performed at the Kavli Nanoscience Institute at Caltech.
Author contributions
A.A., A.F., and E.A. conceived the experiment. E.A., A.A., S.M.K., and Y.H. fabricated the
samples. E.A., A.A., S.M.K., and M.F. performed the simulations, measurements, and
analyzed the data. E.A., A.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
https://doi.org/10.1038/s41467-
018-03155-6
.
Competing interests:
The authors declare no competing
fi
nancial interests.
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© The Author(s) 2018
NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-03155-6
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NATURE COMMUNICATIONS
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DOI: 10.1038/s41467-018-03155-6
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