Multiwavelength
polarization
-
insensitive
lenses
based
on
dielectric
metasurfaces
with
meta-molecules:
supplementary
material
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,
CA
91125,
USA
*
Corresponding author: A.F.: faraon@caltech.edu
Published 10 June
2016
This
document
contains
supplementary
methods
and
materials
for
"Multiwavelength
polariza-
tion
-
insensitive
lenses
based
on
dielectric
metasurfaces
with
meta-molecules
,
"
http://dx.doi.org/10.1364/optica.3.000628.
©
2016
Optical
Society
of
America
http://dx.doi.org/10.1364/optica.3.000628.s001
1. S1. MATERIALS AND METHODS
Simulation
To find the transmission amplitude and phase of a multi-
element metasurface, the rigorous coupled wave analysis tech-
nique was used [
1
]. A normally incident plane wave at each
wavelength was used as the excitation, and the amplitude and
phase of the transmitted wave were extracted. Since the lattice is
subwavelength for normal incidence at both wavelengths, only
the zeroth order diffracted light is nonzero. This justifies the use
of only one transmission value at each wavelength to describe
the behavior of meta-atoms. The lattice constant was chosen as
720 nm, and the
α
-Si posts were 718-nm tall. Refractive indices
of 3.56 and 3.43 were assumed for
α
-Si at 915 nm and 1550 nm,
respectively.
The paraxial focal distance of the two lenses were calculated
to be 286
μ
m and 495
μ
m for the lenses that focus light from the
fiber to 400
μ
m and 1000
μ
m respectively, by fitting a parabola
to the phase profiles of the lenses. For a fitted parabola
y
=
α
x
2
,
the paraxial focal distance can be calculated using
f
=
2
π
/
2
αλ
.
The corresponding numerical apertures can then found to be
0.46 and 0.29 for the two lenses.
The perfect phase mask (that also served as the goal phase
profile for the designed devices) was calculated from the illu-
minating field and the aspherical desired phase profile using
the method described in supplementary information of [
2
]. The
illuminating field was calculated by propagating the output
fields of single mode fibers at each wavelength using plane
wave expansion (PWE) method up to the metasurface layer. The
perfect phase mask was then applied to the field, and the result
was propagated using the PWE method to the focal point. The
diffraction limited FWHM was then calculated from the intensity
profile at the focal plane.
Full wave simulation of a full lens was done using finite
difference time domain method (FDTD) in MEEP [
3
]. A lens
with a diameter of 75
μ
m and a focal length of 100
μ
m was
designed with the same method as the fabricated device. The
lens focuses the light emitted from a single mode fiber (with
mode diameters of 10.4
μ
m at 1550 nm and 6
μ
m at 915 nm)
placed 150
μ
m away from a 125
μ
m thick fused silica substrate
(all of the geometrical dimensions were chosen 4 times smaller
than the values for the experimentally measured device). The
distances to fibers were chosen such that more than 99% of the
total power emitted by the fiber passes through the lens aperture.
At both wavelengths, the light from the fibers was propagated
through air, air-glass interface, and through glass up to a plane
about a wavelength before the metasurface using a plane wave
expansion (PWE) code. Electric and magnetic field distributions
at this plane were used as sources for FDTD simulation of the
lenses, and fields were calculated at about a wavelength after
the metasurface using MEEP. The PWE code was used again
to further propagate these fields to the focal plane and beyond
(main text Fig. 4(d)). The focusing efficiencies were calculated by
dividing the power in a 20-
μ
m-diameter disk around the focus,
to the total power incident on the lens.
Sample fabrication
A 718-nm-thick hydrogenated
α
-Si layer was deposited on a
fused silica substrate using the plasma enhanced chemical vapor
deposition (PECVD) technique with a 5% mixture of silane in
argon at 200
◦
C. A Vistec EBPG5000+ electron beam lithogra-
phy system was used to define the metasurface pattern in the
ZEP-520A positive resist (
∼
300 nm, spin coated at 5000 rpm
for 1 min). The pattern was developed in a resist developer
for 3 minutes (ZED-N50 from Zeon Chemicals). An approxi-
mately 100-nm-thick aluminum oxide layer was deposited on
the sample using electron beam evaporation, and was lifted off
reversing the pattern. The patterned aluminum oxide hard mask
was then used to dry etch the
α
-Si layer in a 3:1 mixture of
SF
6
and
C
4
F
8
plasma. After etching, the mask was removed using a
1:1 solution of ammonium hydroxide and hydrogen peroxide at
80
◦
C.
Measurement procedure
Devices were measured using a fiber placed
∼
1100
μ
m away
from the metasurface (500
μ
m substrate thickness plus 600
μ
m
distance between the fiber and the substrate), and a custom built
microscope with
∼
100X magnification (Fig.
S1). At 915 nm,
a fiber coupled semiconductor laser with a single mode fiber
with an angled polished connector was used for illumination.
Fiber tip angle was adjusted to correct for the angled connector
cut. A 100X objective lens (Olympus UMPlanFl, NA=0.95) and
a tube lens (Thorlabs AC254-200-B-ML) with a focal distance
of 20 cm were used to image intensity at planes of interest to
a CCD camera (CoolSNAP K4, Photometrics). A calibration
sample with known feature sizes was measured to find the pixel-
size transferred to the object plane. The objective was moved
with a translation stage to image different planes around the
focus. The plotted axial plane intensities are upsampled 2:1 in
the axial direction (4
μ
m adjacent measurement planes distance
to 2
μ
m) to achieve a smoother graph. For focusing efficiency
measurement at 915 nm, a 20-
μ
m-diameter pinhole was placed
in the focal plane of the metasurface lens to only let the focused
light pass through. The pinhole was made by wet etching a 20
μ
m hole in a thick layer of chrome deposited on a fused silica
substrate. A power meter (Thorlabs PM100D with photodetector
head Thorlabs S122C) was then used to measure the power after
the pinhole, and the output power of the fiber. The efficiency
was calculated as the ratio of these two powers. The reported
measured efficiency is therefore a lower bound on the actual
efficiency as it does not include reflection from the substrate, and
two reflections from the two sides of the pinhole glass substrate.
A similar setup was used for measurements at 1550: a tunable
1550 nm laser (Photonetics Tunics-Plus) was used with a single
mode fiber for illumination. The same 100X objective was used
with a 20 cm tube lens (Thorlabs AC254-200-C-ML) to image
the intensity in the object plane to a camera (Digital CamIR
1550 by Applied Scintillation Technologies). The camera has a
significantly non-uniform sensitivity for different pixels which
leads to high noise level of the images captured by the camera
(as seen in main text Fig. 4(b)). The nonphysical high frequency
noise of the images (noise with frequencies higher than twice
the free space propagation constant) was removed numerically
to reduce the noise in the axial intensity patterns. The intensity
pattern was also upsampled in the axial direction from the actual
4
μ
m distance between adjacent measurement planes, to 2
μ
m to
achieve a smoother intensity profile. To find the focused power,
the focal plane of the lens was imaged using the microscope to a
photodetector. A 2 mm iris in the image plane (corresponding
to 20
μ
m
in the object plane) was used to limit the light reaching
the photodetector. The input power was measured by imaging
the fiber facet to the photodetector using the same setup and
without the iris. The efficiency was obtained by dividing the
focused power by the input power.
2. S2. DISCUSSION OF DEFLECTION EFFICIENCY
OF BLAZED GRATINGS DESIGNED WITH THE PRO-
POSED META-MOLECULE PLATFORM
To understand the reasons behind the low efficiency of the lenses
at 915 nm, two double wavelength blazed gratings were de-
signed using the proposed meta-molecule scheme. One grating
with a small deflection angle (5 degrees) and another one with a
larger angle (20 degrees) were simulated at 915 nm using MEEP,
and power loss channels were analyzed in both cases (Fig.
S3).
Both gratings were chosen to be 2 meta-molecules wide in the
y
direction, so that periodic boundary conditions in this direc-
tion can be used in FDTD. The 5 degree grating is 322 lattice
constants long in
x
direction, while the 20 degree one is 146
lattice constants. The lengths are chosen such that the grating
phases at 915 nm and 1550 nm are both almost repeated after the
chosen lengths (Fig.
S3(a)). An x-polarized plane-wave normally
incident from the fused silica side was used as excitation in both
simulations, and the transmitted and reflected electric and mag-
netic field intensities were calculated about a wavelength apart
from the meta-molecules. The transmitted fields were further
propagated using a plane wave expansion program, and the
resulting fields in an area of length 30
μ
m around the center can
be seen in Fig.
S3(b and c) for 5 degree and 20 degree gratings,
respectively. The field distributions outside of the areas shown
here look similar to the ones shown. In both cases, a dominant
plane wave propagating in the design direction is observed,
along with some distortions. Angular distribution of power in
transmission and reflection is analyzed using the Fourier trans-
form of the fields. The resulting power distributions are shown
in Fig.
S3(d and e) for 5 degrees and 20 degrees, respectively.
While the average power transmission of meta-molecules used
in both gratings (found from the data in main text Fig. 2(e)) is
slightly above 73%, only 36% and 22% of the incident power is
directed to 5 and 20 degrees for the corresponding gratings. The
actual total transmitted powers are 56% and 50% for the 5 and 20
degree gratings, showing that an additional
∼
20% of the power
gets reflected as a result of the introduced aperiodicity. Because
of the relatively large lattice constant, even a small aperiodicity
can result in generation of propagating modes in the substrate,
thus the reflection is considerably higher for the gratings than
for a perfectly periodic lattice. From the 56% transmitted power
in the 5 degree grating, 20% is lost to diffraction to other an-
gles. From Fig.
S3(b and c) we can see there are distortions in
the transmitted field. These distortions, mainly due to the low
transmission amplitude of some of the meta-molecules and their
phase errors result in the transmitted power being diffracted to
other angles. Besides, it is seen that power loss to other angles
both in reflection and transmission is higher for larger grating
angles. This is due to the need for finer sampling of the wave
front for waves with steeper angles. The lower efficiency for
gratings with larger angles results in lower efficiency of lenses
with higher numerical apertures which need bending light with
larger angles.
2
Objective lens
Tube lens
Camera
Device
(a)
Laser
Device
Pinhole
(b)
Laser
Optical power meter
Objective lens
Mirror
Tube lens
Camera
Device
(c)
Laser
Optical power meter
Iris
Fig. S1.
Measurement setups. (a) The measurement setup used to capture the focus pattern and the intensity distribution in differ-
ent planes around focus. The laser source, fibers, tube lens, and camera were different in 915 nm and 1550 nm measurements. (b)
The measurement setup for measuring the efficiency of the lenses at 915 nm using a 20
μ
m pinhole in the focal plane. (c), The setup
for measuring focusing efficiency of the lens at 1550 nm using a 2 mm iris in the image plane of a
∼
100X microscope.
3
y[
μ
m]
x[
μ
m]
y[
μ
m]
x[
μ
m]
z[
μ
m]
z[
μ
m]
z[
μ
m]
y[
μ
m]
x[
μ
m]
-20
20
-20
20
-20
20
-20
20
-20
20
-20
20
600
1000
50
250
(g)
(h)
(c)
(d)
0.5
1
0
Intensity [a.u.]
5
μ
m
(b)
x
y
5
μ
m
(f)
x
y
(a)
x
y
2
μ
m
(e)
x
y
2
μ
m
600
1000
z
y
z
x
z
x
z
x
z
y
z
y
z[
μ
m]
y[
μ
m]
x[
μ
m]
-20
20
-20
20
50
250
z
x
z
y
Fig. S2.
Measurement and simulation results for the lenses with a lower NA. (a) and (b) Measured intensity in the focal plane of a
double wavelength lens (1000
μ
m focal length, 300
μ
m diameter) at 915 nm (a) and 1550 nm (b). At 915 nm the lens actually focuses
the light 980
μ
m away from its surface, so the focal spot shown here is imaged at
≈
980
μ
m away from the surface. The error in
focal distance is probably due to the approximation made in the mode diameter of the fiber (see Fig. S1), which affects the focusing
distance of a low NA lens more than that of a high NA lens. (c) Intensity measured in the axial planes of the lens for 915 nm. (d)
The same axial plots for 1550 nm. (e) and (f) Simulated focal plane intensity of a lens with the same numerical aperture as the one
shown in (a–d) but with a dimeter of 75
μ
m at wavelengths of 915 nm (e), and 1550 nm (f). (g) and (h) Simulated intensity profiles
in the axial planes at 915 nm and 1550 nm, respectively, calculated for the same lens described in (e).
4
(d)
(e)
-5-10-15
0
0
1
5
10
15
Power [a.u.]
angle [degrees]
(b)
0
5
-5
-10
0
5
10
x [
μ
m]
z [
μ
m]
(c)
-5
-10
0
0
5
5
10
x [
μ
m]
z [
μ
m]
-20-40-60
0
0
1
20
40
60
Power [a.u.]
angle [degrees]
(a)
PBC
PBC
PBC
Transmission
Reflection
Transmission
Reflection
0
1
-1
Electric Field [a.u.]
0
1
-1
Electric Field [a.u.]
Fig. S3.
Double wavelengths blazed gratings based on the proposed meta-molecule design. (a) Schematic of the simulated grating.
The 5 degree grating is 322 meta-molecules long, while the 20 degree one is 146 meta-molecules long. Periodic Boundary Condi-
tions (PBC) was used in side boundaries and PML was used to terminate the simulation domain in top and bottom directions. (b)
and (c) Real part of the electric field a few wavelengths after the 5 degree (b) and 20 degree (c) gratings. (d) and (e) Distribution of
transmitted and reflected power in different angles for the 5 degree (d) and 20 degree (e) gratings.
5
REFERENCES
1.
V. Liu and S. Fan, “S4 : A free electromagnetic solver for
layered periodic structures,” Comput. Phys. Commun.
183
,
2233–2244 (2012).
2.
A. Arbabi, Y. Horie, A. J. Ball, M. Bagheri, and A. Faraon,
“Subwavelength-thick lenses with high numerical apertures
and large efficiency based on high-contrast transmitarrays,”
Nat. Commun.
6
(2015).
3.
A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D.
Joannopoulos, and S. G. Johnson, “Meep: A flexible free-
software package for electromagnetic simulations by the fdtd
method,” Comput. Phys. Commun.
181
, 687–702 (2010).
6