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MEMS-tunable metasurface lens
Ehsan Arbabi,
1
Amir Arbabi,
1, 2
Seyedeh Mahsa Kamali,
1
Yu
Horie,
1
MohammadSadegh Faraji-Dana,
1
and Andrei Faraon
1,
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
Keywords: Metasurfaces, diffractive optics, tunable lenses, nanoscale materials, MEMS, MOEMS
Corresponding author: A.F.: faraon@caltech.edu
1
arXiv:1712.06548v1 [physics.optics] 18 Dec 2017
Lenses with tunable focal length are widely used in zoom lenses and laser scanning imag-
ing systems. They are generally implemented by changing the axial distance between the
elements of a varifocal system of refractive lenses. However, conventional refractive ele-
ments are bulky and thick. Therefore tunable multi-element lenses are large, heavy, slow,
require macroscopic movements, and have limited optical power tunability. Metasurfaces,
a new category of lithographically defined diffractive devices, are on the other hand thin
and lightweight, and their phase profiles can be engineered with subwavelength resolution.
This enables agile varifocal lenses, with large tunability of the optical power even for minute
changes of the axial distance. Here, we propose and demonstrate MEMS-based tunable
metasurface doublets with more than 60 diopters (about 4
%
) change in the optical power
upon a 1-
μ
m movement of a membrane with one of the metasurface elements. Several dou-
blets can be integrated on the same chip to scan a large range of focal distances at frequencies
reaching a few kHz. The doublet can also be integrated with a third metasurface element
to make a compact microscope (
1 mm thick) with a large corrected field of view (
500
μ
m
or 40 degrees) and a fast axial scanning for 3D imaging. The results presented here pave
the way towards metasurface-based optical systems with fast, electrically tunable focal and
imaging distances. They also present an example of the potentials of integrating metasur-
faces with the well-established MEMS technology to enable a new category of micro-opto-
electromechanical systems (MOEMS) with enhanced functionalities and new applications.
Lenses are ubiquitous optical elements present in almost all imaging systems [1]. Compact
lenses with tunable focal/imaging distance have many applications, and therefore several methods
have been developed to make such devices [2–23]. Deformable solid and liquid-filled lenses with
mechanical [2] , electro-mechanical [3, 4, 14], electrowetting [11, 12], and thermal [13] 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 [5–7, 24] 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 elements have also been demonstrated [15–17]. These
devices are generally 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 [18, 19, 25] have also been demonstrated, but they have low speeds and require a radial
2
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 [20–23, 26] 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 efficiency [21, 22, 26].
Optical metasurfaces [27–29] are planar arrangements of scatterers designed to manipulate var-
ious properties of an incident light beam. In the optical regime, dielectric metasurfaces are very
versatile as they allow for wavefront control with high efficiency and subwavelength resolution.
Several devices with the ability to control the phase [30–45] polarization [46, 47], polarization
and phase [48], or spectral components of light through harmonic generation [49–51] or filter-
ing [52–55] have been demonstrated. Their thin form factor makes them suitable for development
of ultrathin conformal optical elements [56, 57], and their compatibility with conventional micor-
fabrication techniques allows for monolithic fabrication of optical systems consisting of multiple
metasurfaces on a single chip [58, 59]. These characteristics (i.e., the ability to precisely control
the phase with subwavelength resolution and high gradients, thin and light form factor, and com-
patibility 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 wave-
length of Fabry-Perot cavities [60, 61], or change roundtrip propagation length of light to form
spatial light modulators [62]. In this manuscript, we propose and demonstrate a metasurface dou-
blet 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, corre-
sponding to about 4
%
) with small movements of one element (
1 micron). We have developed a
fabrication process for making such metasurface doublets, and experimentally show metasurface
lenses with over 60
μ
m tuning of effective focal length from 565
μ
m 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 in a sam-
ple 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 [58] to
3
develop compact focus-scanning objectives with corrected monochromatic aberrations over a large
field of view. To the best of our knowledge, this is the first demonstration of MEMS-integrated
metasurface lenses with a tunable focal distance. It is worth noting that MOEMS devices with the
ability to axially scan the focus have previously been demonstrated based on integration of refrac-
tive and Fresnel microlenses with axially moving frames [8–10, 63]. 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).
Figure 1a 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,
x
1
μ
m, leads to a large
tuning of the focal length (
f
36
μ
m change in the front focal length from 781
μ
m to 817
μ
m
when the lens separation is changed from 10
μ
m to 9
μ
m, see Supplementary Fig. S1 for the phase
profiles and their ray tracing simulations). The membrane and glass lenses are 300
μ
m in diameter,
and have focal lengths of
120
μ
m and
-130
μ
m, respectively. The electrostatic actuation is
achieved through contacts only to the glass substrate. The capacitor plates are shown in the inset
of Fig. 1a. The contacts are configured 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 1b shows the first two mechanical resonance modes
of the membrane at
2.6 kHz (left) and
5.6 kHz (right). 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 [30, 33, 35]. These de-
vices 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 [46, 48, 64]. When only phase control is required, the nano-posts should have
a symmetric cross-section (i.e., square, circular, etc.). For fabrication considerations, we choose
nano-posts with square-shaped cross-section on a square lattice. Since both the moving and sta-
tionary 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, lat-
tice constant, and minimum and maximum post side lengths) to maximize the efficiency of high
4
NA lenses for both transverse electric (TE) and transverse magnetic (TM) polarizations [65]. The
method is based on approximating the efficiency of a lens designed with certain metasurface pa-
rameters through efficiencies 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 nm and 615 nm for the moving and stationary lenses, respectively. The lattice constant
was set to 320 nm in both cases. Figures 1c and 1d show simulated transmission amplitudes and
phases for uniform arrays of nano-posts on the membrane and the glass substrate, respectively.
Given a required phase profile, one can find the best nano-post for each site on the metasurface
using Fig. 1c or 1d [35].
A summary of the key fabrication steps for the moving and stationary lenses is schematically
depicted in Figs. 2a-2c (for more details refer to 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 followed by a 530-nm-thick
α
-Si layer was deposited on the SiNx 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 defined 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 membrane was patterned and dry etched to release the metasurface. An
optical image of the fabricated metasurface on a membrane is shown in Fig. 2a, bottom. 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. Figures 2d and 2e show scanning electron
micrographs of the fabricated metasurfaces.
The fabrication steps of the stationary metasurface are schematically shown in Fig. 2b. 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 the bottom row of Fig. 2b.
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 a UV-
5
curable epoxy (Fig. 2c). An optical image of the final device is shown in the bottom row of Fig. 2c.
Figure 3 summarizes the focusing measurement results under application of a 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 de-
tails of the measurement setup, see Methods and Supplementary Fig. S2). The simulated effective
focal length (EFL) is plotted against the distance between the two lenses in Fig. 3a, 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 to 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 distances to simultaneously image a larger range of depths. Figure 3b 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 mea-
sured focal distances in a few measurements falls within the measurement error of
5
μ
m. The
possibility of changing the applied voltage very finely, makes it possible to tune the membrane
separation and thus the optical power very finely, in the absence of external vibrations. Intensity
distributions measured in the focal plane under application of different DC voltages are shown
in Fig. 3c for device 2. As seen in Figs. 3c and 3d, the measured Airy disk radii are 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 performance 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
μ
m
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 in-
tended. 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
μ
m to 781
μ
m (or change the EFL from 560
μ
m to 681
μ
m, tuning optical
power by more than 300 diopters, or
20
%
).
Figure 3d shows the measured absolute focusing efficiency of the doublet (defined as the power
6
passing through a
20-
μ
m-diameter aperture to the total power hitting the device). The absolute
efficiency is between 40
%
and 45
%
for all applied voltage values. The high-NA (NA
0.8) singlets
used here are expected to be
75
%
efficient [65]. Because the doublet uses two of such lenses,
its efficiency is estimated to be
55
%
. Taking into account the reflections 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 airflow), we obtain a total efficiency of
50
%
which agrees well with the measured
efficiency values. We attribute the slightly lower measured efficiency to fabrication imperfections.
It is foreseeable that the efficiency can be significantly improved with better optimization and
design processes [43], use of anti-reflection coatings to reduce reflection losses, and optimizing
the fabrication process.
The frequency response of the doublet is measured and plotted in Fig. 3e (see Supplementary
Section S1 and Figure S2 for details of frequency response measurement). The frequency response
transfer function is defined as the membrane’s displacement 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
fits (i.e.,
H
(
f
)
=
1
1
i
(
b
/
mk
)(
f
/
f
0
)−(
f
/
f
0
)
2
, where
f
0
is the resonance frequency for the first mode,
b
is a damping factor, and
m
and
k
are the oscillator mass and spring constant, respectively),
indicating that the fit follows the measurement well for
b
=
20
mk
. This corresponds to a highly
overdamped system with a damping ratio (
b
/
2
mk
) of
10. Under the atmosphere pressure the
dominant loss mechanism is the air damping [66]. If the damping is reduced by about 20 times
by reducing the air pressure inside the lens packaging (i.e.,
b
/
2
mk
0
.
5
), then the frequency
response will follow the blue dashed line in Fig. 3e, with a 3-dB bandwidth reaching 4 kHz. This
would correspond to a quality factor of
1 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.
The tunable doublet can be used for imaging with electrically controlled focusing. To demon-
strate this, we formed an imaging setup using the doublet and a refractive lens. The setup is
schematically shown in Fig. 4a. 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
7
substrate. Since this image is very small and close to the lens, we used a custom-built microscope
(
×
55 magnification) to re-image it onto the camera. The results are summarized in Fig. 4b. 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 configuration, 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 configuration. As observed here, by
moving the membrane only about 4
μ
m, the object distance can be moved from 4 mm to 15 mm
(corresponding to the overall EFL of the system changing from 44 mm 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.
To further demonstrate the capabilities of this platform, we use it to design a 1-mm-thick elec-
trically tunable microscope. The structure is schematically shown in Fig. 5a, and is a metasurface
triplet composed of a tunable doublet (with an optical design different from the fabricated one),
and an additional metasurface lens. The lenses, from left to right are 540
μ
m, 560
μ
m, and 400
μ
m
in diameter. They have focal lengths of about -290
μ
m, 275
μ
m, 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
μ
m to 5
μ
m, the object plane distance
D
changes from 622
μ
m to 784
μ
m. The triplet can be optimized to correct for monochromatic
aberrations [58] to keep the focus close to the diffraction limit over a large field of view (see
Supplementary Fig. S1 for phase profiles, and Table S2 for the corresponding coefficients). Here,
we have optimized the phase profiles to keep the focus almost diffraction limited in a
500
μ
m
diameter field of view (corresponding to a
40-degree field 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. 5b, demonstrating a diffraction limited behavior. The spot diagrams are ray-optics 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 5c 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 significantly larger than the focal
8
lengths of the membrane and first glass lenses, similar to the fabricated doublet. As a result, the
object space NA is about 0.16, corresponding to an imaging resolution of
3.5
μ
m. Considering
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 magnification of the system also changes
from 11.3 (for
d
=5
μ
m) to 10.3 (for
d
=13
μ
m).
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 demonstrated [67, 68]. In addition,
the electrostatic forces and the mechanical resonance frequencies can be engineered by appropriate
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 rel-
atively high sensitivity to the membrane bending, and to misalignment between the two lenses
(see Supplementary Fig. S3 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 misalign-
ment between the two lenses should be better than 2
μ
m. Based on 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 a 2-
μ
m resolution is not a
challenge.
Similar to other diffractive and metasurface optical devices, the lenses demonstrated here suf-
fer from chromatic aberrations [69–72]. The exact “acceptable” operation bandwidth of the lens
depends on the effective focal length, the numerical aperture, and a criterion for “acceptability”.
Using the criterion given in [58] 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 operation bandwidth is given by
λ
=
2
.
27
λ
2
/(
f
NA
2
)≈
50
nm.
To make multiwavelength tunable doublets, many of the recently demonstrated approaches for
making multiwavelength metasurfaces can be directly applied [64, 73–76]. In addition, the re-
9
cently introduced concept of phase-dispersion control [77–79] can be used to increase the opera-
tion bandwidth of the metasurface lenses by correcting the chromatic aberrations over a continuous
bandwidth.
Here we introduced a new 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 efficiencies 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,
fiber-tip-mounted confocal microscopes, etc. In principle, metasurfaces 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.
10
METHODS
Simulation
The optimized phase profiles (for both the fabricated doublet and the triplet shown in Fig. 5)
were obtained using Zemax OpticStudio (see Supplementary Fig. S1 and Table S1 for the phase
profiles). This was done through simultaneously minimizing the root mean square radius of the
focal spot for several configurations (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 limi-
tations resulting from diffraction.
Mechanical simulation of the MEMS structure was performed in COMSOL Multiphysics to
find 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 19300 kg/m
3
for gold. To account for the fact that
the whole metasurface volume is not filled with
α
-Si, an average fill 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 [80]. The transmission
values were calculated by illuminating a uniform array of nano-posts with a normally incident
plane wave at 915 nm wavelength and finding 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.
Sample 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 devel-
opment 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
11
contacts’ pattern was defined 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
LPCVD 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 defined 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 station-
ary 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 defined 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 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 airflow. 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. S2. A col-
limated beam from a fiber coupled 915-nm diode laser connected to a fiber collimation package
(F240FC-B, Thorlabs) was used to illuminate the doublet from the membrane side. A custom-built
microscope 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 CCD camera (CoolSNAP
12
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 Section 1 for more
details).
The efficiency 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 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 chro-
matic dispersion, a bandpass filter (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. A 4-
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 magnified and re-imaged onto the camera with the same microscope used for the focal spot
characterization.
13
ACKNOWLEDGEMENT
This work was supported by National Science Foundation award 1512266 and Samsung Elec-
tronics. 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 Conversion", Energy Fron-
tier 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.
14
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20
FIGURES
'
x
'
f
a
0
1
100
200
Post width [nm]
|t|
‘
t/2
S
SiN
x
tE
D
-Si
E
c
Post width [nm]
|t|
‘
t/2
S
0
1
80
180
tE
D
-Si
FS
E
d
b
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 (
x
1
μ
m) results in a
large change in the focal distance (
f
35
μ
m). (Insets: schematics of the moving and stationary lenses
showing the electrostatic actuation contacts.) (
b
) The first two mechanical resonances of the membrane at
frequencies of
2.6 kHz (left) and
5.6 kHz (right). The scale bars are 100
μ
m. (
c
) 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. (
d
) 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.
21
a
b
c
d
e
FIG. 2
Fabrication process summary.
(
a
) Simplified 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 LPCVD 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. An optical microscope image of a
fabricated lens on a membrane is shown at the bottom. (
b
) Simplified 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. An optical micorscope image of the fabricated
lens is shown at the bottom. (
c
) Schematics of the bonding process: an SU-8 spacer layer is patterned on
the glass substrate, the two chips are aligned and bonded. A microscope image of the final device is shown
at the bottom. (
d
) Scanning electron micrograph of the lens on the membrane, and (
e
) nano-posts that form
the lens. Scale bars are 100
μ
m in
a–d
, and 1
μ
m in
e
.
22
11
13
15
0
80
640
680
f
[
P
m]
d
[
P
m]
720
40
Voltage [V]
b
f [
P
m]
640
680
720
0
0.5
1
d
normalized Airy radius
efficiency
600
800
400
EFL [
P
m]
d
[
P
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
P
m
v
=60 V,
f
=664
P
m
v
=70 V,
f
=682
P
m
v
=80 V,
f
=717
P
m
c
e
frequency [Hz]
1 2
5 10
100
1000
10000
-10
0
-20
Transfer function [dB]
Measured
b
=20
—
mk
b
=
—
mk
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 under 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 radius (normalized to their corresponding diffraction limited values), and measured absolute focusing
efficiency 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
mk
and
mk
.
23