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Highly tunable elastic dielectric metasurface lenses
Seyedeh Mahsa Kamali,
1
Ehsan Arbabi,
1
Amir Arbabi,
1
Yu Horie,
1
and Andrei Faraon
1,
1
T. J. Watson Laboratory of Applied Physics and Kavli Nanoscience Institute,
California Institute of Technology, 1200 E California Blvd., Pasadena, CA 91125, USA
Dielectric metasurfaces are two-dimensional structures composed of nano-scatterers that manipulate phase
and polarization of optical waves with subwavelength spatial resolution, enabling ultra-thin components for
free-space optics. While high performance devices with various functionalities, including some that are diffi-
cult to achieve using conventional optical setups have been shown, most demonstrated components have a fixed
functionality. Here we demonstrate highly tunable metasurface devices based on subwavelength thick silicon
nano-posts encapsulated in a thin transparent elastic polymer. As proof of concept, we demonstrate a metasur-
face microlens operating at 915 nm, with focal distance tuning from 600
μ
m to 1400
μ
m through radial strain,
while maintaining a diffraction limited focus and a focusing efficiency above 50
%
. The demonstrated tunable
metasurface concept is highly versatile for developing ultra-slim, multi-functional and tunable optical devices
with widespread applications ranging from consumer electronics to medical devices and optical communica-
tions.
Metasurfaces are composed of a large number of discrete
nano-scatterers (meta-atoms) that locally modify phase and
polarization of light with subwavelength spatial resolution.
The meta-atoms can be defined lithographically, thus provid-
ing a way to mass-produce thin optical elements [1–4] that
could directly replace traditional bulk optical components or
provide novel functionalities [4, 5]. The two dimensional na-
ture and the subwavelength thickness of metasurfaces make
them suitable for tunable and reconfigurable optical elements.
Some efforts have recently been focused on developing tun-
able and reconfigurable metasurfaces using different stimuli
for tuning the meta-atoms. Examples include frequency re-
sponse tuning using substrate deformation [6, 7], refractive
index tuning via thermo-optic effects [8, 9], phase change ma-
terials [10, 11], and electrically driven carrier accumulation
[12, 13].
Stretchable substrates have been used to demonstrate tun-
able diffractive and plasmonic metasurface components [14–
16], but they have exhibited low tunability, poor efficiency,
polarization dependent operation, or significant optical aber-
rations.
Here we present mechanically tunable dielectric
metasurfaces based on elastic substrates, simultaneously pro-
viding a high tuning range, polarization independence, high
efficiency, and diffraction limited performance. As a proof of
principle, we experimentally demonstrate an aspherical mi-
crolens with over 130
%
focal distance tuning (from 600
μ
m
to 1400
μ
m) while keeping high efficiency and diffraction lim-
ited focusing.
Figure 1(a) shows a schematic of a metasurface microlens
encapsulated in an elastic substrate with radius
r
and focal
distance
f
. The phase profile of the lens has the following
form, and is drawn in Fig. 1(c) (solid blue curve):
φ
(
ρ,λ
) =
2
π
λ
(
ρ
2
+
f
2
f
)
(1)
where
ρ
is the distance to the center of the lens. Equation
(1) in the paraxial approximation (
ρ

f
) reduces to
(c)
ρ
Phase
ρ
0
(1+
є
)
ρ
0
φ
0
φ(ρ,λ)
φ
'
(ρ,λ)
(a)
(b)
f
r
d
a-Si
PDMS
(1+
є
)
2
f
(1+
є
)r
d/
(1+
є
)
2
FIG. 1. Principle of tunable elastic metasurface lenses. (a) A side
view schematic illustration of a dielectric metasurface microlens with
focal distance of
f
encapsulated in a low index elastic membrane. (b)
By stretching the metasurface microlens with a stretch ratio of
1 +

,
its focal distance changes by
(1 +

)
2
, providing a large tunability.
The membrane thickness decreases according to its Poisson ratio (
ν
),
considered to be 0.5 here. (c) Phase of the metasurface microlens
before (solid blue curve) and after (solid red curve) stretching. a-Si:
amorphous silicon, PDMS: Polydimethylsiloxane.
φ
(
ρ,λ
)
πρ
2
λf
(2)
By uniformly stretching the substrate with a stretch ratio of
1 +

, and assuming that the local phase transformation does
not depend on the substrate deformation, the phase initially
applied at radius
ρ
is now applied at radius
ρ
(1 +

)
; therefore,
the under strain phase profile becomes
φ
(
ρ,λ
) =
πρ
2
/
(
λ
(1+

)
2
f
)
(shown in Fig. 1(c), solid red curve). This indicates that
by stretching the elastic metasurface microlens with stretching
ratio of
1 +

the focal length scales by a factor of
(1 +

)
2
, as
arXiv:1604.03597v1 [physics.optics] 12 Apr 2016