Experimental demonstration of rotational
varifocal moiré metalens∗

Kentaro Iwami,

Chikara Ogawa, Tomoyasu Nagase, and Satoshi Ikezawa

Department of Mechanical Systems Engineering,Tokyo University of Agriculture and Technology, Koganei, Tokyo 1848588 Japan
E-mail: k_iwami@cc.tuat.ac.jp

Phone: +81 (0)42 3887658. Fax: +81 (0)42 3887657

Abstract
This paper reports experimental demonstration of moiré metalens with a wide focal length tunability from negative to positive through mutual angle rotation at awavelength of 900 nm. The moiré metalens was developed using high-index contrast
transmit array meta-atoms composed of amorphous silicon octagonal pillars designed
to have polarization insensitivity and full 2π phase coverage. The designed moiré metalens was fabricated on a glass substrate using simple a-Si sputter deposition, electron
beam lithography through character projection, metal mask lift-o, and reactive-ion
silicon etching. The moiré metalens has focal length tunability ranges from −∞ to1.73 mm, and from 1.73 mm to ∞, corresponding to an optical power in the range−578 − 578 m−1 at a mutual rotation between ±90◦ . Our results reveal a proof of concept for focal length tuning with mutual rotation of lens components based on moiré
lens conguration at optical frequencies.

1Keywords
dielectric metasurfaces, varifocal metalens, moiré lens, amorphous silicon, waveguides

Introduction
Metasurfaces, a planar branch of metamaterials, have attracted signicant attention because they can tailor optical wavefront by arranging subwavelength patterns (meta-atoms)
on surfaces. 13 They can demonstrate unique optical properties that cannot be achieved
with natural materials and have high anity for micro/nanofabrication methods, including
lithography, deposition, and etching. Therefore, metasurfaces have opened many researchelds and have several applications, including lenses, 46 retarders and waveplates, 710 vector
beam converters, 1113 color lters, 1416 and holography. 1720 It should be emphasized thatmechanical deformation or change of mutual geometric position of metasurfaces oer novel
functionalities and tunability for their optical properties. Recongurable metasurfaces havebeen studied based on this idea, including tunable transmittance, 21 color tuning, 22 and active
phase shifters. 23,24
Metasurface lenses, or metalens, has attracted considerable attention owing to their thinness and lightweight. The recent development of lossless dielectric metalens 5,6,25 have also
stimulated the attention in this eld. Tunable focal length, or varifocal lens, are a promising and expected functionality of metalens. Similar to conventional refractive lens doublet,the longitudinal motion of lens along with the optical axis have been demonstrated basedon micro-electromechanical actuators. 26 However, the eect of the pull-in instability of theelectrostatic parallel plates actuator limits the travel range of metalens, 27,28 resulting in anarrow tunable range for the focal length.
Since metalens has a high degree of design freedom, it is not necessary to make thetuning method for the focal length similar to conventional refractive lenses. It is desirable tostudy how diractive optical element (DOE) techniques or diractive lenses can be applied2

to metalens. In fact, a DOE-inspired tunable metalens, the Alvalez metalens, has been
experimentally demonstrated with focal length tuning based on the lateral movement of apair of lenses. 2931 However, the lateral motion of Alvarez lenses limits the eective area ofthe lenses. Furthermore, the reported focal length range of mechanically tunable metalens
is limited to the positive region.
Moiré lenses are a pair of axially asymmetric lenses that achieve tunable focal lengthwith mutual rotation, as presented in Fig. 1(a). 32,33 They oer a wide range of focal lengths
from negative to positive and has been realized using DOE. 34 Moiré metalens has also beenstudied using numerical simulations, 35,36 and has been demonstrated in the microwave frequency band quite recently. 37 However, the demonstration at optical frequencies has notbeen reported yet due to the diculty of fabricating at such frequencies.
In this paper, we experimentally demonstrate tunable focal length using moiré metalens at
the near infrared frequency band using polarization-insensitive meta-atoms based on highindex contrast transmit arrays (HCTAs), which are made of amorphous silicon (a-Si) in
this case. We designed a-Si octagonal pillars with polarization insensitivity and full 2πphase coverage at a wavelength of 900 nm. The metalens were designed to satisfy the phase
distribution of moiré metalens, as detailed below, by hexagonally mapping the corresponding
pillars to each lattice points. The metalens was fabricated on a silicon substrate using simple
a-Si sputter deposition, electron beam lithography through character projection, metal mask
lift-o, and reactive-ion etching (RIE) of silicon. The fabricated metalens exhibited focal
length tunability at the ranges from −∞ to 1.73 mm and from +1.73 mm to +∞ at a mutual
rotation of ±90◦ at 900 nm. The results reported here reveal a proof of concept for focal
length tuning with mutual rotation of lens components based on moiré lens conguration
at optical frequencies, and thus paving way for applications in optical frequencies, includingnear infrared, visible, and ultraviolet wavelengths.

3

Design and Fabrication of Moiré MetalensFigure 1 presents a schematic diagram of moiré metalens. It consists of two metalenses,
as shown in Fig. 1(a), and their total focal length can be tuned by mutual rotation fromnegative to positive. Each of the moiré metalens pair is designed with transmission function
distributions in polar coordinates (r, ϕ): 32
T1 (r, ϕ) = exp iround(ar2 )ϕ
T2 (r, ϕ) = exp −iround(ar2 )ϕ(1)

where a is a constant. The phase distribution of the rst lens T1 is presented in Fig. 1(b).
With mutual rotation angle of θ, the joint transmission function can be expressed as:Tjoint = T1 (r, ϕ)T2 (r, ϕ − θ) = exp iround(ar2 )θ .

(2)

This equation is similar to that for spherical lenses under paraxial approximation, T =exp(iπr2 /f λ), where f and λ represent the focal length and the wavelength, respectively.
Therefore, by adjusting the constant a to satisfy equation f −1 = aθλ/π , the optical powerf −1 becomes proportional to θ. Note that the round function is used to avoid the sectoringeect. 32
Figures 1(ce) presents the phase distributions of the second metalens with mutual rotation angles of +30◦ , +60◦ , and 60◦ , respectively, together with the total phase distributions
superimposed with the rst metalens (Fig. 1(b)). Positive rotation angles create total phase
distribution similar to convex Fresnel lenses, whereas and larger rotation angles give rise tohigher phase gradient, which corresponds to short focal length and higher optical power, aspresented in Figs. 1(c) and (d). In contrast, as presented in Fig. 1(e), a negative rotation
angle creates concave-like phase distribution. We show that adopting moiré metalens leads
to focal lengths with a wide tuning range from negative to positive.

4

(a)

Figure 1: Principle of moiré metalens. (a) Schematic drawing of working principle. (b) Phase
distribution of one of two lenses. (ce) Phase distributions of second lens and combined moiré
metalens for various mutual rotation angles θ for focal length, f tuning. Note that the samecolor legends are used throughout (be).

5

We adopted a-Si octagonal pillar HCTAs as polarization-insensitive meta-atoms. 25 Electromagnetic simulation was conducted using the commercially available nite element software, COMSOL Multiphysics ver. 5.1 (COMSOL Inc., USA), as presented in Fig. 2. A
schematic diagram of the simulation setup is presented in Figure 2(a). An octagonal pillar
with a period of 400 nm was situated on the silica glass substrate, with air as the surrounding
medium (not shown). X -polarized light at a wavelength of 900 nm was incident from theglass bottom side, whereas the transmittance and phase delay of the pillar was evaluated at
the output port (air side). The perfect electric conductor (PEC) boundary condition wasapplied to the ±x boundaries, whereas the Froquet periodic condition was applied to otherboundaries. An a-Si material parameter was used as an Si pillar. 38
Figure 2(b) presents the results of parameter sweep for transmittance and phase/2π ,which is obtained by changing the pillar width and height in 10-nm steps. We found thatthe region around height> 380 nm achieves both high transmittance and full 2π phase
coverage. Figure 2(c) presents the x−component of electric eld, Ex distribution at a pillar
height of 400 nm, and widths of 90, 240, and 300 nm, respectively. It is clearly shown thatthe phase dierence between the 240, 300, and 90 nm pillars at the output port (top of
the image) correspond to π and 2π , respectively. Therefore, considering fabrication process
limitations for high-aspect-ratio structures, we adopted pillars with 400-nm height as a meta
atoms.
We used these octagonal pillars as meta-atoms to design moiré metalens with a diameterof 2 mm with maximum optical powers of f −1 = ±(1.73 mm)−1 at a mutual rotation angleof θ = ±90◦ . This corresponds to a maximum numerical aperture (NA) of 0.5 for the moiré
metalens. We prepared a GDSII CAD le of the moiré metalens by mapping pillars withcorresponding phase delays satisfying the phase distribution described by T1 of equation 1
to each hexagonal lattice point with the pitch of 400 nm using a Python library Gdspy.
We fabricated a metalens on a quartz glass substrate, sputter-depositing an amorphoussilicon lm with a thickness of 400 nm. A lens pattern with a diameter of 2 mm was drawn by6

(a)Transmitted
light

Pillar width
Octagonal
a-Si pillar

Pillar heightGlass
substrate
Incident light(x-pol.)
(b)

(c)

90 nm

240 nm

300 nmEx(a. u.)

Figure 2: COMSOL simulation of a-Si octagonal pillar meta-atom. (a) Calculation model.
(b) Parameter mapping of transmittance and phase/2π , sweeping pillar height, and width.
(c) Electric eld (Ex ) distribution of a-Si octagonal pillars with widths of 90, 240, and 300
nm, respectively.

7electron beam lithography using character projection (CP) (Advantest F7000-S, Advantest,
Japan), employing dedicated octagonal stencil masks to achieve high-throughput drawing.
The GDSII CAD le descried above was converted into a CP shot data with proximity eect
compensation. After the resist development, an aluminum mask was patterned on the a-Si
lm through lift-o process. Si pillars were formed by RIE. Finally, the aluminum mask wasremoved using a solution of phosphoric, nitric, and acetic acids mixture.

Results and Discussion(a)(c)
Metalens(b)(d)

Transmittance

Phase

Figure 3: Fabricated metalens. (a) Photograph of the fabricated lenses on a 2-cm-squareglass substrate. The nine circles represent 2-mm-diameter metalenses. Blue-indicated square
patterns are pillar arrays with constant widths for transmission property measurements.
(b) Transmission properties at a wavelength of 900 nm. The dots indicate measurement
results, whereas the lines indicate COMSOL simulation. Blue and orange correspond totransmittance and phase/2π , respectively. (c) SEM images of the lens and (d) its close-up
to the center, observed with 45◦ tilting angles.
Figure 3 represents (a) a photograph of the fabricated lenses on a 2-cm-square glass
substrate, (b) transmission properties, and scanning electron microscope (SEM) images (cd). In Fig. 3(a), the nine circles are 2-mm-diameter metalenses. Blue-indicated square
patterns are pillar arrays with constant widths for transmission property measurements.

8

Figure 3(b) presents the transmission properties of the pillars as a function of pillar width ata wavelength of 900 nm. The dots indicate the measurement results, and the lines represent
COMSOL simulation results. Blue and orange correspond to transmittance and phase/2π ,respectively. The data points in Fig. 3(b) are based on the measured widths of pillars.
The phase delays of the pillars were measured by the interference method, 39 using a laser
diode and a microspectroscopic system (Techno Synergy, DF-1037). Figure 3(c) presents theSEM image of the lens, and 3(d) shows its close-up to the center, which is observed at 45◦
angles. We fabricated width-distributed pillars. However, the pillars are cylindrical insteadof octagonal due to fabrication limitations.
The phase delay rapidly increases for both the simulation and experiment as the width
increases, as presented in Fig. 3(b). Though the experimental transmittance is lower thanthat of the simulation, the position of the dips is similar. The disparity between the experiment and simulation can be attributed to fabrication error, including the rounded shape of
the pillar top presented in 3(d).
Figure 4 presents the experimental setup for focal length measurement. The opticalsystem is presented in Fig. 4(a). It uses tungsten halogen white light as a source. The
incident light passes through a band pass lter (#65-184, Edmund Optics USA, OD = 4,center wavelength = 904 nm, FWHM = 10 nm) and a test target (USAF 1951). We prepared
the moiré metalens sample by assembling two metalens pieces fabricated using the abovementioned process. The latter lens was ipped upside down along the horizontal axis tosatisfy the phase distribution of T2 in equation 1. These lenses are aligned carefully underthe microscope observation, and adhered using a tape with certain mutual rotation angles

θ. The transmitted image of a USAF target captured using a CMOS camera (DCC1545M,
Thorlab Co., USA) with a 20× objective lens and iris.
Figure 4(b) presents images captured without the moiré metalens and focused onto thetest target. A bright part due to the light source can be seen at the center. Figure 4(c)presents the image focused on the moiré metalens doublet. The lens diameter of 2 mm was
9(a)Halogen
BPF
Test Metalens
lamp (λ=904 nm) target (doublet)

l

OBJ
(20㽢)
Iris

x
WD

(b)
CMOS
Camera(c)(d)θ = 30 deg

1 mm

Figure 4: Experimental setup for focal length measurement. (a) Optical system. (b) Image
focused on the target without moiré metalens, showing the iris circle. (c) Image focused on
the moiré metalens and (d) its magnied version. Mutual rotation angle can be determinedfrom the image.

10

almost equivalent to the opening of the iris. Figure 4(d) presents the magnied image of (c).
The mutual rotation angle of θ = 30 deg. are clearly seen.
Using the metalens position x from the image plane and target position l as shown in
4(a) under the certain mutual rotation angle θ, the focal length f (θ) of the moiré metalens
was calculated using the following equation,

1
1
1
=
+ .
f (θ)
l−x x

(3)

Figure 5 presents (a) the measurement results for focal length and (be) typical imaging
results. In Fig. 5(a), the circle markers indicate the experimental results obtained from the
setup presented in Fig. 4. The dashed curve indicates the designed characteristics, f =π/(aλθ). Note that the standard deviation of the data points is lower than the diameter of
each marker. The experimental results are consistent with the design, and we demonstrated
focal length tuning from negative to positive; (b) and (c) present captured images at nominal
rotation angles of −60◦ and +60◦ , respectively; (d) and (e) present magnied images of (b)and (c). Inversed real images are presented in (c) and (e), which correspond to the positive
focal length. In contrast, straight virtual images are presented in (b) and (d), corresponding
to the negative focal length.
Our results reveal a wide range of tunability, and this is the rst report on the focal
length tuning from negative to positive. In fact, metalens can be tuned both as a convex andconcave lens. Though we adopted alignment and adhesion processes in this paper, MEMSactuated rotational stages have been reported, whereas microrotational varifocal metalens
can be realized by proper integration with actuators. In this work, we employed a 2-mmdiameter lens, which can be extended to a cm-scale in principle due to the high throughputof CP-based EB lithography.
In conclusion, we experimentally demonstrated a rotational varifocal metalens or moiré
metalens. The metalens was designed using polarization-insensitive a-Si HCTAs as meta-

11

(a)

(b)

(c)

(d)

(e)

Figure 5: (a) Measurement results for focal length and (be) typical imaging results . In(a), the circle markers indicate the experimental results obtained from the setup presented
in Fig. 4. The dashed curve indicates the designed characteristics f = π/(aλθ). (b) and (c)present captured images at the nominal rotation angles of −60◦ and +60◦ , respectively, and(d) and (e) present their magnied images. Inversed real images are presented in (c) and(e), whereas straight virtual images are presented in (b) and (d).

12

atoms. We investigated the fabricated metalens at a wavelength of 900 nm and demonstrated
focal length tuning at the ranges from −∞ to −1.73 mm and from +1.73 mm to +∞ at amutual rotation between ±90◦ , which corresponds to an optical power tuning between ±578
m−1 .

Author Information
Corresponding Author
E-mail: k_iwami@cc.tuat.ac.jp (K. Iwami)

ORCID
Kentaro Iwami: 0000-0002-4458-5704
Satoshi Ikezawa: 0000-0001-6184-7123

Author Contributions
K. I. conceived the idea of moiré metalens, performed COMSOL simulation, and supervised
the project. K. I. and C. O. designed and fabricated the moiré metalens. K. I. and T. N.
performed measurements of phase delay of Si pillars. C. O. and S. I. performed measurementsof focal length. K. I. wrote the initial draft of the manuscript. All authors analyzed anddiscussed the results and contributed to writing the manuscript. All authors have given
approval to the nal version of the manuscript.

Notes
The authors declare no competing nancial interest.

13

Acknowledgement
This research was supported by Japanese Society for the Promotion of Science (JSPS) Grantin-Aid for Scientic Research (KAKENHI) B Grant Number JP17H02754, Nanotechnology
Platform site at the University of Tokyo, which is supported by the Ministry of Education,
Culture, Sports, Science and Technology (MEXT), Japan. The authors thank Prof. Yoshio
Mita, and Dr. Eric Lebrasseur for their help about electron beam lithography and reactive
ion etching, and Prof. Kuniaki Konishi for his help about ellipsometry. The numericalcalculations were carried out on the TSUBAME3.0 supercomputer at Tokyo Institute ofTechnology.

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