of 9
High efficiency double-wavelength dielectric
metasurface lenses with dichroic birefringent
meta-atoms
E
HSAN
A
RBABI
, A
MIR
A
RBABI
, S
EYEDEH
M
AHSA
K
AMALI
, Y
U
H
ORIE
,
AND
A
NDREI
F
ARAON
*
T.
J.
Watson
Laboratory
of
Applied
Physics,
California
Institute
of
Technology,
1200
E.
California
Blvd.,
Pasadena,
California
91125,
USA
*
faraon@caltech.edu
Abstract:
Metasurfaces are ultrathin optical structures that manipulate optical wavefronts.
Most metasurface devices which deflect light are designed for operation at a single wavelength,
and their function changes as the wavelength is varied. Here we propose and demonstrate a
double-wavelength metasurface based on polarization dependent dielectric meta-atoms that
control the phases of two orthogonal polarizations independently. Using this platform, we design
lenses that focus light at 915 and 780 nm with perpendicular linear polarizations to the same
focal distance. Lenses with numerical apertures up to 0.7 and efficiencies from 65
%
to above
90
%
are demonstrated. In addition to the high efficiency and numerical aperture, an important
feature of this technique is that the two operation wavelengths can be chosen to be arbitrarily
close. These characteristics make these lenses especially attractive for fluorescence microscopy
applications.
© 2016 Optical Society of America
OCIS codes:
(050.6624) Subwavelength structures; (050.1965) Diffractive lenses; (220.1000) Aberration compensa-
tion; (050.2555) Form birefringence.
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Vol. 24, No. 16 | 8 Aug 2016 | OPTICS EXPRESS 18468
#267421
http://dx.doi.org/10.1364/OE.24.018468
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2016;
revised
23
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2016;
accepted
25
Jul
2016;
published
3 Aug
2016
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Metasurfaces are two-dimensional arrangements of sub-wavelength optical scatterers de-
signed to control the amplitude, phase, and polarization of light [1
8]. Among these, high
contrast dielectric metasurfaces have proven to be very versatile due to their high efficiency
and ability to control phase and polarization of light with subwavelength resolution on both
planar and non-planar surfaces in different parts of the optical spectrum [9
22]. Similar to
other diffractive optical elements, metasurfaces with deflection capabilities such as lenses and
beam deflectors suffer from chromatic aberrations [23
26], as schematically shown in Fig. 1(a).
Multi-wavelength metasurface lenses have been demonstrated using several techniques including
polarization and wavelength selectivity of plasmonic nano-scatterers [27], aperiodic arrays of
coupled dielectric resonators [25, 28], generating a hologram with the combined phase pro-
files for multiple wavelengths [29], and using metamolecules formed from combining multiple
meta-atoms [26]. However, lenses demonstrated by these methods have multiple focuses at each
wavelength [25, 27
29] or have low efficiency at least at some of the wavelengths [25
29]. In
addition, although the metamolecule technique used in [26] results in a single focus at each wave-
length, the corrected wavelengths cannot be very close. Here we demonstrate double-wavelength
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dielectric metasurface lenses that focus two wavelengths of light with perpendicular linear polar-
izations to the same focal distance, as schematically shown in Fig. 1(b) (e.g. the
x
-polarized light
at a wavelength
λ
1
and
y
-polarized light at a different wavelength
λ
2
are focused to the same
distance). We experimentally demonstrate lenses with large numerical apertures (NA values
up to 0.7) and high efficiencies at both wavelengths (
η
65%
92%
) with nearly diffraction-
limited operation. In addition to lenses, this concept can be applied to other metasurfaces to
independently control the wavefronts at two different wavelengths for orthogonal polarizations,
and provide different functionalities at those wavelengths.
(a)
(b)
(c)
(d)
Λ
Λ
2a
2b
x
y
Fused silica
α
-Si
Fig. 1. (a) Normal chromatic dispersion of a metasurface lens, resulting in different focal
distances for different wavelengths (schematically shown by red and blue rays), and (b)
schematics of a metasurface corrected to focus light with two different wavelengths and
orthogonal linear polarizations to the same focal distance. (c) An
α
-Si nano-post with
elliptical cross-section exhibiting birefringence. (d) A metasurface formed by arraying
elliptical nano-posts in a periodic lattice.
We have previously shown that metasurfaces based on amorphous silicon (
α
-Si) nano-posts
with elliptical cross sections [Fig. 1(c)] can independently control the phases of two orthogonal
polarizations at a single wavelength [12]. These metasurfaces are composed of nano-posts placed
at the vertices of a hexagonal lattice shown in Fig. 1(d). For proper choices of the lattice constant
(
0
.
5
λ
) and the height of the nano-posts (
0
.
6
λ
), the phase of light for two linear polarizations
oriented along the nano-post axes can be controlled independently by changing the ellipse
diameters [12]. We have also demonstrated broadband operation of non-deflecting metasurfaces
(e.g. spatially varying wave plates) composed of elliptical nano-posts [30], but the approach is
not applicable to the metasurfaces operating based on light deflection (e.g. lenses). Here we show
that the two control parameters (i.e. the axis lengths) of nano-posts with elliptical cross-sections
can be utilized to independently control the wavefronts of optical waves with two different
wavelengths and orthogonal polarizations. For instance, the phase profile of the device can be
independently controlled for
x
-polarized light at a wavelength
λ
1
, and for
y
-polarized light at a
different wavelength
λ
2
. The behavior of the device for cross polarized light (e.g.
y
-polarized
light at
λ
1
) will be governed through the regular chromatic dispersion of diffractive devices (see
for instance [23, 26]).
Figures 2(a) and 2(b) show simulated transmission amplitude (top) and phase (bottom) at
915 and 780 nm for
x
and
y
-polarized light, respectively (ellipse diameters
2
a
and
2
b
and the
axis directions are shown in Fig. 1(d)). Here, the meta-atoms are assumed to be 553 nm tall,
the lattice constant is 500 nm, and the wavelengths are chosen to match available laser sources
in our lab. Rigorous coupled wave analysis (RCWA) was used for the simulations [31]. The
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nano-posts operate as truncated multimode optical waveguides with multiple resonances around
the operation wavelengths [11, 19, 32]. The ellipticity, results in an effective birefringence and
a phase difference for light polarized along the two axes of the ellipse [12]. Therefore, the
two ellipse diameters provide two phase control parameters that enable independent control of
phase for light polarized along the two axes [12]. Figure 2 shows that the independent phase
control is possible even if the two orthogonal polarizations of light have different wavelengths.
Using the simulated transmission amplitude and phase data, we find the corresponding ellipse
diameters that provide any desired phase pairs at both wavelengths,
φ
1
and
φ
2
, while keeping
both transmission amplitudes high. To simultaneously achieve the desired phases and high
transmission amplitudes at both wavelengths, we minimize the total complex amplitude error
defined as
ε
=
|
exp
(
i
φ
1
)
t
1
|
2
+
|
exp
(
i
φ
2
)
t
2
|
2
. Here
φ
1
and
φ
2
are the desired phases at the
two wavelengths, and
t
1
and
t
2
are complex transmissions of nano-posts at the two wavelengths
for the corresponding orthogonal linear polarizations. The corresponding values of the chosen
diameters are plotted in Fig. 2(c) as functions of the phases at the two wavelengths. As Fig. 2(c)
shows, the axis length
2
a
dominantly controls the phase of
x
-polarized light, and the phase of
y
-polarized light is mostly controlled by the axis length
2
b
. Amplitudes and phases of these
chosen nano-posts are plotted in Figs. 2(d) and 2(e), showing that this independent phase control
is achieved with very high accuracy and high transmission. Using this independent control, any
two arbitrary phase profiles for orthogonal linearly polarized light at the two wavelengths can be
realized.
We designed, fabricated, and characterized five lenses with the same diameter of 200
μ
m
and numerical apertures ranging from 0.12 to 0.7 that simultaneously work at 915 and 780 nm,
for
x
and
y
-polarized light, respectively. The fabrication process was similar to [12]: a 553 nm
α
-Si layer was deposited on a fused silica substrate using plasma enhanced vapor deposition.
The metasurface pattern was generated with an electron beam lithography system. A
70 nm
aluminum oxide layer was deposited using electron beam evaporation, and was lifted off, leaving
a hard mask defining the nano-posts. The hard mask was used to etch the
α
-Si layer in a dry
etching step, and was then removed. Scanning electron microscope images of the fabricated
devices are shown in Fig. 3.
Figure 4 shows schematics of the measurement setups used to characterize the devices. A
custom built microscope with a
100
×
magnification, shown schematically in Fig. 4(a), was
used to perform the intensity distribution measurements. Figure 5 summarizes the measurement
results for the five lenses. Axial and focal plane intensities are plotted in Figs. 5(a) and 5(b) for
780 and 915 nm, respectively. At both wavelengths and for all lenses, one single focus is observed
close to the designed distances of 100, 200, 400, 600, and 800
μ
m. As denoted by Fig. 5(c),
all lenses have a nearly diffraction limited focus (measured FWHMs at both wavelengths and
for all NA values are less than 7
%
larger than their diffraction limited values). The measured
FWHMs in the axial plane are plotted in Fig. 5(d), along with the theoretical values calculated
from
2
π
w
2
/
λ
, with
w
denoting the diffraction limited transverse FWHM. Efficiency was defined
as the measured power in focus, divided by the total power incident on the lens. The setup
used to measure the efficiencies is schematically shown in Fig. 4(b). Since the diameter of the
collimated beam (
2.3 mm, using the
1
/
e
2
intensity definition) is much larger than the size
of the metasurface lenses, for efficiency measurements the beam was partially focused using a
lens with a focal distance of 200 mm to have a diameter of
134
μ
m at the metasurface lenses
(such that 99
%
of the beam power passes through the lens aperture). The radius of curvature
of the beam at the metasurfaces is
16 mm, which is much larger than the focal distances of
the metasurface lenses, making the curvature of the beam almost negligible. The measured
efficiencies are plotted in Fig. 5(e) for both wavelengths, and are seen to be above 65
%
for all
NAs at both wavelengths. Similar to our previous works [11], efficiency generally decreases with
increasing NA. A set of fabricated pinholes were used to filter out-of-focus light for efficiency
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(a)
|t
1
| at
915 nm
φ
1
at 915 nm
0.5
1
0
Transmission amplitude
π
0
Phase
[
Rad
]
2b [nm]
2a [nm]
100
100
400
400
2b [nm]
2a [nm]
100
100
400
400
2b [nm]
2a [nm]
φ
2
at 780 nm
|t
2
| at
780 nm
100
100
400
400
(b)
0.5
1
0
Transmission amplitude
π
0
Phase
[
Rad
]
2b [nm]
2a [nm]
100
100
400
400
780 nm phase,
φ
2
[Rad]
915 nm phase,
φ
1
[Rad]
0
0
π
−π
π
−π
(c)
2a [nm]
780 nm phase,
φ
2
[Rad]
915 nm phase,
φ
1
[Rad]
0
0
π
−π
π
−π
2b [nm]
200
400
0
Axis length [nm]
|t
1
| at
915 nm
0.5
1
0
Transmission amplitude
0.5
1
0
Transmission amplitude
|t
2
| at
780 nm
desired phase at 780 nm [Rad]
desired phase at 915 nm [Rad]
0
0
π
−π
π
−π
(d)
desired phase at 780 nm [Rad]
desired phase at 915 nm [Rad]
0
0
π
−π
π
−π
0
−π
π
Phase
[
Rad
]
0
−π
π
Phase
[
Rad
]
phase obtained for
915 nm
phase obtained for
780 nm
desired phase at 780 nm [Rad]
desired phase at 915 nm [Rad]
0
0
π
−π
π
−π
(e)
desired phase at 780 nm [Rad]
desired phase at 915 nm [Rad]
0
0
π
−π
π
−π
Fig. 2. (a) Transmission amplitude (top) and phase (bottom) of the meatasurface at 915 nm
for
x
-polarized light versus ellipse diameters. (b) The same plots as (a), but for
y
-polarized
light at 780 nm. (c) Optimal values of diameters 2
a
and 2
b
that provide phase pairs
(
φ
1
,
φ
2
)
for complete phase coverage at the two wavelengths. (d) Transmission amplitude, and (e)
phase at both wavelengths for the corresponding optimal diameters shown in (c).
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(b)
500 nm
(a)
2
μ
m
Fig. 3. (a) Scanning electron micrograph of a fabricated device viewed normally, and (b) at
a tilt angle.
Objective lens
Tube lens
Camera
Device
Polarizer
(a)
Laser
Collimator
Polarization
controller
Device
Pinhole
(b)
Optical power meter
Polarizer
Laser
Collimator
Polarization
controller
Fig. 4. (a) Schematic of the measurement setup used for measuring intensity profiles, and
(b) focusing efficiencies.
measurements. Diameters of the used pinholes were 6, 6, 10, 15, and 20
μ
m for different lenses
in decreasing NA order. We attribute the lower efficiency at 780 nm to higher sensitivity of its
phase to fabrication errors.
We
have
also
characterized
the
operation
of
the
devices
under
illumination
with
cross-polarized
light
(i.e.
y
-polarized
light
at
915
nm,
and
x
-polarized
light
at
780
nm).
In
cross-polarized
operation,
the
devices
also
exhibit
Fresnel
phase
zones
but
these
zones
are
not
optimized
for
focusing
to
a
tight
spot.
Indeed,
the
cross-polarization
measurement
results
summarized
in
Fig.
6
show
that
the
devices
focus
cross-polarized
light
as
well,
but
with
lower
efficiency,
higher
distortions,
and
to
focal
distances
different
from
the
corresponding
copolarized
values.
It
is
worth
noting
that
these
devices
operate
as
diffractive
lenses
with
different
phase
profiles
for
x
and
y
-polarized
light.
Also,
for
each
polarization
they
follow
the
regular
chromatic
dispersion
of
diffractive
lenses,
and
therefore
their
focal
distance
changes
with
wavelength
proportional
to
1
/
λ
[23,
24,
26].
Since
cross-polarized
light
is
focused
to
a
different
focal
distance,
it
can
be
considered
as
loss
when
the
device
focuses
unpolarized
light.
When
the
devices
are
used
for
imaging
applications,
the
excitation
and
the
collected
paths
need
to
be
passed
through
polarizers.
Otherwise,
the
image
will
exhibit
elevated
background
and/or
imaging
artifacts
depending
on
the
exact lens design.
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