Multiwavelength polarization insensitive lenses based on dielectric metasurfaces with
meta-molecules
Ehsan Arbabi,
1
Amir Arbabi,
1
Seyedeh Mahsa Kamali,
1
Yu Horie,
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
Metasurfaces are nano-structured devices composed of arrays of subwavelength scatterers (or meta-atoms)
that manipulate the wavefront, polarization, or intensity of light. Like other diffractive optical devices, meta-
surfaces suffer from significant chromatic aberrations that limit their bandwidth. Here, we present a method for
designing multiwavelength metasurfaces using unit cells with multiple meta-atoms, or meta-molecules. Trans-
missive lenses with efficiencies as high as 72
%
and numerical apertures as high as 0.46 simultaneously operating
at 915 nm and 1550 nm are demonstrated. With proper scaling, these devices can be used in applications where
operation at distinct known wavelengths is required, like various fluorescence microscopy techniques.
Over the last few years, a new wave of interest has risen in
nano-structured diffractive optical elements due to advances
in nano-fabrication technology [1–7]. From the multiple de-
signs proposed so far, dielectric transmitarrays [7–9] are some
of the most versatile metasurfaces because they provide high
transmission and subwavelength spatial control of both polar-
ization and phase. Several diffractive optical elements, includ-
ing high numerical aperture lenses and simultaneous phase
and polarization controllers have recently been demonstrated
with high efficiencies [8, 9]. These devices are based on sub-
wavelength arrays of high refractive index dielectric nano-
resonators (scatterers) with different geometries, fabricated on
a planar substrate. Scatterers with various geometries impart
different phases to the transmitted light, shaping its wavefront
to the desired form.
One main drawback of almost all of metasurface devices,
particularly the ones with spatially varying phase profiles like
lenses and gratings, is their chromatic aberration: their perfor-
mance changes as the wavelength is varied [10–12]. Refrac-
tive optical elements also suffer from chromatic aberrations;
however, their chromatic aberrations, which stem from ma-
terial dispersion, are substantially smaller than those of the
diffractive elements [11, 12]. An ideal refractive lens made of
a dispersionless material will show no chromatic aberration.
On the other hand, the chromatic aberration of diffractive ele-
ments mainly comes from the geometrical arrangement of the
device. Early efforts focused on making achromatic diffrac-
tive lenses by cascading them in the form of doublets and
triplets [13–16], but it was later shown that it is fundamen-
tally impossible to make a converging achromatic lens which
has a paraxial solution (i.e. is suitable for imaging) by only us-
ing diffractive elements [17]. Although diffractive-refractive
combinations have successfully been implemented to reduce
chromatic aberrations, they are mostly useful in deep UV and
X-ray wavelengths where materials are significantly more dis-
persive [18, 19]. More recently, wavelength and polarization
selectivity of metallic meta-atoms have been used to fabricate
a Fresnel zone plate lens that operates at two distinct wave-
lengths with different orthogonal polarizations [20]. Besides
undesired multi-focus property of Fresnel zone plates and ef-
ficiency limitations of metallic metasurfaces [18, 21, 22], the
structure works only with different polarizations at the two
wavelengths. The large phase dispersion of dielectric meta-
atoms with multiple resonances has also been exploited to
compensate for the phase dispersion of metasurfaces at three
wavelengths [23, 24], but the cylindrical lens demonstrated
with this technique is polarization dependent and has low nu-
merical aperture and efficiency. Multiwavelength metasur-
faces based on elliptical apertures in metallic films are demon-
strated in [25], but they are also polarization dependent and
have a multi-focus performance. An achromatic metasurface
design is proposed in [26] based on the idea of dispersionless
meta-atoms (i.e. meta-atoms that impart constant delays). Un-
fortunately, this idea only works for metasurface lenses with
one Fresnel zone limiting the size and numerical aperture of
the lenses. For a typical lens with tens of Fresnel zones, dis-
persionless meta-atoms will not reduce the chromatic disper-
sion as we will shortly discuss. In the following we briefly
discuss the reason for chromatic dispersion of metasurface
lenses, and then propose a method for correcting this disper-
sion at distinct wavelengths. We also present experimental
results demonstrating corrected behavior of a lens realized us-
ing the proposed method.
In diffractive lenses, chromatic dispersion mainly manifests
itself through a significant change of focal length as a func-
tion of wavelength [18]. This change is schematically shown
in Fig. 1a, along with a metasurface lens corrected to have
the same focal distance at a few wavelengths. To better un-
derstand the underlying reasons for this chromatic dispersion,
we consider a hypothetical aspherical metasurface lens. The
lens is composed of different meta-atoms which locally mod-
ify the phase of the transmitted light to generate the desired
wavefront. We assume that the meta-atoms are dispersionless
in the sense that their associated phase changes with wave-
length as
φ
(
λ
) = 2
πL/λ
like a piece of dielectric with a con-
stant refractive index. Here
λ
is the wavelength and
L
is an
effective parameter associated with the meta-atoms that con-
trols the phase (
L
can be an actual physical parameter or a
function of physical parameters of the meta-atoms). We as-
sume that the full 2
π
phase needed for the lens is covered
using different meta-atoms with different values of
L
. The
lens is designed to focus light at
λ
0
(Fig. 1b) to a focal dis-
tance
f
0
, and it’s phase profile in all Fresnel zones matches
the ideal phase profile at this wavelength. Because of the spe-
arXiv:1601.05847v1 [physics.optics] 22 Jan 2016
2
a
1
1.1
0.9
1.1
λ
0
1.05
λ
0
λ
0
0.95
λ
0
0.9
λ
0
0.5
1
0
z/f
0
c
z
y
f
0
b
0
5
10
ρ [
a.u.
]
-4
-2
0
φ(ρ, λ)
/2
π
Ideal phase
λ
0
Ideal phase
λ
1
Actual phase
λ
0
Actual phase
λ
1
0
5
10
L
ρ [
a.u.
]
Intensity [a.u.]
FIG. 1.
Chromatic dispersion of metasurface lenses. a
, Schematic illustration of a typical metasurface lens focusing light of different
wavelengths to different focal distances (top), and a metasurface lens corrected to focus light at specific different wavelengths to the same focal
distance (bottom).
b
, The phase profile of a hypothetical aspherical metasurface lens at the design wavelength
λ
0
and a different wavelength
λ
1
as a function of the distance to the center of the lens (
ρ
). (Inset) Plot of the parameter of the meta-atoms controlling phase (named
L
).
c
,
Intensity of light at different wavelengths in the axial plane after passing through the lens showing considerable chromatic dispersion rising
from phase jumps at the boundaries between different Fresnel zones.
cific wavelength dependence of the dispersionless meta-atoms
(i.e. proportionality to 1/
λ
), at a different wavelength (
λ
1
) the
phase profile of the lens in the first Fresnel zone follows the
desired ideal profile needed to maintain the same focal dis-
tance (Fig. 1b). However, outside the first Fresnel zone, the
actual phase profile of the lens deviates substantially from the
desired phase profile. Due to the jumps at the boundaries be-
tween the Fresnel zones, the actual phase of the lens at
λ
1
is
closer to the ideal phase profile at
λ
0
than the desired phase
profile at
λ
1
. In the inset of Fig. 1b the effective meta-atom
parameter
L
is plotted as a function of distance to the center
of the lens
ρ
. The jumps in
L
coincide with the jumps in the
phase profile at
λ
1
. In Fig. 1c, the simulated intensity profile
of the same hypothetical lens is plotted at a few wavelengths
close to
λ
0
. The focal distance changes approximately propor-
tional to
1
/λ
. This wavelength dependence is also observed in
Fresnel zone plates [18], and for lenses with wavelength inde-
pendent phase profiles [11, 12] (the
1
/λ
dependence is exact
in the paraxial limit, and approximate in general). This behav-
ior confirms the previous observation that the phase profile of
the lens at other wavelengths approximately follows the phase
profile at the design wavelength. Therefore, the chromatic dis-
persion of metasurface lenses mainly stems from wrapping the
phase, and the dependence of the phase on only one effective
parameter (e.g.
L
) whose value undergoes sudden changes at
the zone boundaries. As we show in the following, using two
parameters to control metasurface phase at two wavelengths
can resolve this issue, and enable lenses with the same focal
lengths at two different wavelengths.
The metasurface platform we use in this work is based on
amorphous silicon (a-Si) nano-posts on a fused silica substrate
(Fig. 2a). The nano-posts are placed on the vertices of a
hexagonal lattice, and locally sample the phase to generate
the desired phase profile [8]. For a fixed height, the trans-
mission phase of a nano-post can be controlled by varying its
diameter. The posts height can be chosen such that at a cer-
3
|t|Ee
i
φ
a-Si
Fused Silica
E
c
D
2
D
1
a/2
a
a
b
Top view
a-Si
a
D
2
[nm]
D
1
[nm]
|t
1
| at
1550nm
100
100
200
300
500
d
0.5
1
0
Transmission amplitude
φ
1
at 1550nm
100
100
200
300
500
D
1
[nm]
D
2
[nm]
π
2π
0
Phase
[
Rad
]
0.5
1
0
Transmission amplitude
|t
2
| at
915nm
100
100
200
300
500
D
1
[nm]
D
2
[nm]
e
φ
2
at 915nm
100
100
200
300
500
D
1
[nm]
D
2
[nm]
π
2π
0
Phase
[
Rad
]
D
2
915 nm phase,
φ
2
[Rad]
1550 nm phase,
φ
1
[Rad]
0
0
π
−π
π
−π
250
500
0
Diameter [nm]
D
1
915 nm phase,
φ
2
[Rad]
1550 nm phase,
φ
1
[Rad]
0
0
π
−π
π
−π
f
|t
2
|
915 nm phase,
φ
2
[Rad]
1550 nm phase,
φ
1
[Rad]
0
0
π
−π
π
−π
0.5
1
0
Transmission amplitude
|t
1
|
915 nm phase,
φ
2
[Rad]
1550 nm phase,
φ
1
[Rad]
0
0
π
−π
π
−π
g
FIG. 2.
Meta-molecule design and its transmission characteristics. a
, The single scattering element composed of an a-Si nano-post on
a fused silica substrate.
b
, The unit cell composed of four scattering elements that provide more control parameters for the scattering phase
(left). The meta-molecules are placed on a hexagonal lattice with lattice constant
a
(middle). Top view of a single meta-molecule (right).
c
,
Schematic of the structure simulated for finding the transmission coefficient of the metasurface.
d
and
e
, Transmission amplitude (top) and
phase (bottom) as a function of the two diameters in the unit cell for 1550 nm and 915 nm.
f
, Selected values of
D
1
(top) and
D
2
(bottom) as
functions of phases at 1550 nm (
φ
1
) and 950 nm (
φ
2
).
tain wavelength the whole 2
π
phase shift is covered, while
keeping the transmission amplitude high. To design a meta-
surface that works at two different wavelengths, a unit cell
consisting of four different nano-posts (Fig. 2b) was cho-
sen because it has more parameters to control the phases at
two wavelengths almost independently. As molecules con-
sisting of multiple atoms form the units for more complex
materials, we call these unit cells with multiple meta-atoms
meta-molecules
. The meta-molecules can also form a peri-
odic lattice (in this case hexagonal), and effectively sample
the desired phase profiles simultaneously at two wavelengths.
The lattice is subwavelength at both wavelengths of interest;
therefore, the non-zero diffraction orders are not excited. In
general, the four nano-posts can each have different diameters
and distances from each other. However, to make the design
process more tractable, we choose three of the four nano-posts
with the same diameter
D
1
and the fourth post with diameter
D
2
, and place them in the centers of the hexagons at a distance
a/
2
(as shown in Fig. 2b). Therefore, each meta-molecule has
two parameters,
D
1
and
D
2
, to control the phases at two wave-
lengths. For this demonstration, we choose two wavelengths
of 1550 nm and 915 nm, because of the availability of lasers
at these wavelengths. A periodic array of meta-molecules
was simulated to find the transmission amplitude and phase
as shown in Fig. 2c (see methods for simulation details). The
simulated transmission amplitude and phase for 1550 nm (
|
t
1
|
and
φ
1
) and 915 nm (
|
t
2
|
and
φ
2
) are plotted as functions of
D
1
and
D
2
in Fig. 2d and 2e. In these simulations the lattice
constant (
a
) was set to 720 nm and the posts were 718 nm
tall. Since the two wavelengths are not close, the ranges of
D
1
and
D
2
must be very different in order to properly control
the phases at 1550 nm and 915 nm. For each desired com-
bination of the phases
φ
1
and
φ
2
in the
(
−
π,π
)
range at the
two wavelengths, there is a corresponding
D
1
and
D
2
pair
that minimizes the total transmission error which is defined
as
=
|
exp(
iφ
1
)
−
t
1
|
2
+
|
exp(
iφ
2
)
−
t
2
|
2
. These pairs are
plotted in Fig. 2f as a function of
φ
1
and
φ
2
. Using the com-
plex transmission coefficients (i.e.
t
1
and
t
2
) in error calcula-
tions results in automatically avoiding resonance areas where
the phase might be close to the desired value, but transmis-
sion is low. The corresponding transmission amplitudes for
the chosen meta-molecules are plotted in Fig. 2g, and show
this automatic avoidance of low transmission meta-molecules.
In the lens design process, the desired transmission phases of
the lens are sampled at the lattice points at both wavelengths
resulting in a
(
φ
1
,φ
2
)
pair at each lattice site. Using the plots
4
in Fig. 2f, values of the two post diameters are found for each
lattice point. Geometrically, the values of the two diameters
are limited by
D
1
+
D
2
< a
. Besides, we set a minimum
value of 50 nm for the gaps between the posts to facilitate the
metasurface fabrication.
A double wavelength aspherical lens was designed using
the proposed platform to operate at both 1550 nm and 915
nm. The lens has a diameter of 300
μ
m and focuses the light
emitted from single mode fibers at each wavelength to a focal
plane 400
μ
m away from the lens surface (the corresponding
paraxial focal distance is 286
μ
m, thus the numerical aperture
is 0.46). The lens was fabricated using standard nanofabrica-
tion techniques: a 718-nm-thick layer of a-Si was deposited
on a fused silica substrate, the lens pattern was generated us-
ing electron beam lithography and transferred to the a-Si layer
using aluminum oxide as a hard mask (see methods for more
details on fabrication). Optical and scanning electron micro-
scope images of the lens and nano-posts are shown in Fig.
3. For characterization, the fabricated metasurface lens was
illuminated by light emitted from the end facet of a single
mode fiber, and the transmitted light intensity was imaged at
different distances from the lens using a custom built micro-
scope (see methods and Supplementary Information Fig. S1
for measurement details). Measurement results for both wave-
lengths are plotted in Fig. 4a-4d. Figures 4a and 4b show the
intensity profiles in the focal plane measured at 915 nm and
1550 nm, respectively. The measured full width at half maxi-
mum (FWHM) is 1.9
μ
m at 915 nm, and 2.9
μ
m at 1550 nm.
The intensity measured at the two axial plane cross sections
are plotted in Fig. 4c and 4d for the two wavelengths. A nearly
diffraction limited focus is observed in the measurements, and
no other secondary focal points with comparable intensity is
seen. To confirm the diffraction limited behavior, a perfect
phase mask was simulated using the same illumination as the
measurements. The simulated FWHM’s were 1.6
μ
m and 2.75
μ
m for 915 nm and 1550 nm respectively (see methods for
details on the simulation). Focusing efficiencies of 22
%
and
65
%
were measured for 915 nm and 1550 nm, respectively.
Focusing efficiency is defined as the ratio of the power passing
through a 20-
μ
m-diameter disk around the focus to the total
power incident on the lens. Anther lens with a longer focal
distance of 1000
μ
m (thus a lower NA of 0.29) was fabricated
and measured with the same platform and method. Measure-
ment results for those devices are presented in Supplementary
Information Fig. S2. Slightly higher focusing efficiencies of
25
%
and 72
%
were measured at 915 nm and 1550 nm for
those devices. For comparison, a lens designed with the same
method and based on the same metasurface platform is simu-
lated using finite difference time domain (FDTD) method with
a freely available software (MEEP) [27]. To reduce the com-
putational cost, the simulated lens is four times smaller and
focuses the light at 100
μ
m distance. Because of the equal nu-
merical apertures of the simulated and fabricated devices, the
focal intensity distributions and the focal depths are compara-
ble. The simulation results are shown in Fig. 4e-4h. Figures
4e and 4f show the simulated focal plane intensity of the lens
at 915 nm and 1550 nm, respectively. The simulated FWHM
is 1.9
μ
m at 915 nm and 3
μ
m at 1550 nm, both of which are in
accordance with their corresponding measured values. Also,
the simulated intensity distributions in the axial cross section
planes, which are shown in Fig. 4g and 4h, demonstrate only
one strong focal point. The focusing efficiency was found to
be 32
%
at 915 nm, and 73
%
at 1550 nm. We attribute the
difference in the simulated and measured efficiencies to fabri-
cation imperfections and measurement artifacts (see methods
for details about measurements).
The efficiency at 915 nm is found to be lower than what ex-
pected both in measurement and FDTD simulation. While the
average power transmission of the selected meta-molecules is
about 73
%
as calculated from Fig. 2g, the simulated focus-
ing efficiency is about 32
%
. To better understand the reasons
for this difference, two blazed gratings with different angles
were designed and simulated for both wavelengths using the
same meta-molecules (see Supplementary Information Sec-
tion 1 and Fig. S3). It is observed that for the gratings (that
are aperiodic), a significant portion of the power is diffracted
to other angles both in reflection and transmission. Besides,
the power lost into diffractions to other angles is higher for
the grating with larger deflection angle. The main reason for
the large power loss to other angles is the the relatively large
lattice constant. The chosen lattice constant of
a
=
720 nm
is just slightly smaller than 727 nm, the lattice constant at
which the first order diffracted light starts to propagate in the
glass substrate for a perfectly periodic structure. Thus, even
a small deviation from perfect periodicity can result in light
diffracted to propagating orders. Besides, the lower transmis-
sion of some meta-molecules reduces the purity of the plane
wave wavefronts diffracted to the design angle. Furthermore,
the desired phase profile of high numerical aperture lenses
cannot be sampled at high enough resolution using large lat-
tice constants. Therefore, as shown in this work, a lens with
a lower numerical aperture has a higher efficiency. There are
a few methods to increase the efficiency of the lenses at 915
nm: The lattice constant is bound by the geometrical and fab-
rication constraint:
D
1
+
D
2
+ 50nm
< a
, hence the smallest
value of
D
1
+
D
2
that gives full phase coverage at the longer
wavelength sets the lower bound for the lattice constant. This
limit can usually be decreased by using taller posts, however,
that would result in a high sensitivity to fabrication errors at
the shorter wavelength. Thus, a compromise should be made
here, and higher efficiency designs might be possible by more
optimum selections of the posts height and the lattice constant.
The lattice constant can also be smaller if less than the full 2
π
phase shift is used at 1550 nm (thus lower efficiency at 1550
nm). In addition, as explained earlier, in minimizing the to-
tal transmission error equal weights are used for 915 nm and
1550 nm. A higher weight for 915 nm might result in higher
efficiency at this wavelength, probably at the expense of 1550
nm efficiency. For instance, if we optimize the lens only for
operation at 915 nm, devices with efficiencies as high as 80
%
are possible [8].
The approach presented here cannot be directly used to cor-