In the format provided by the authors and unedited.
© 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.
SUPPLEMENTARY INFORMATION
DOI: 10.1038/NPHOTON.2017.96
NATURE PHOTONICS
|
www.nature.com/naturephotonics
1
PlanarMetasurfaceRetroreflector
Amir Arbabi,
1
Ehsan Arbabi,
1
Yu Horie,
1
Seyedeh Mahsa Kamali,
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
1
Planar metasurface retroreflector
SUPPLEMENTARY FIGURES
0
Incident angle (degree)
10
30
20
40
50
0
0.05
0.10
0.15
RMS wavefront error (wavelength)
a
b
T
=0°
10°
20°
30°
40°
50°
Metasurface I
Metasurface II
400
P
m
Fused silica
Supplementary Figure 1
|
Simulation results of the planar retroreflector
.
a
, Ray diagram for
different incident angles. The incident rays (green) are not shown outside the substrate so that the
reflected rays (dark blue) are seen more clearly.
b
, Root mean square (RMS) wavefront error of
the retroreflected light as a function of the incident angle.
2
0
Radial coordinate (
P
m)
Phase (rad.)
0
500
1000
200
200
Metasurface I
Metasurface II
Supplementary Figure 2
|
Phase profiles of the metasurfaces composing the planar
retroreflector
. Optimized phase profiles of the metasurfaces that minimize the average RMS
wavefront error (see Supplementary Fig. 1).
3
400
P
m
10°
15°
20°
25°
5°
T
=0°
30°
35°
40°
50°
45°
55°
4GƀGEVCPEG
0
1
Supplementary Figure 3
|
Extended reflectance measurement results.
The results are the
same as the ones shown in Fig. 4a, but are presented here in 5
◦
steps.
4
L
1
Iris
Object
T
BS
Camera
L
2
f
2
850 nm
LED
f
3
Filter
f
3
f
2
f
1
f
1
L
3
Backside gold
10°
T
=0°
20°
30°
40°
1 mm
Supplementary Figure 4
|
Retroreflected images captured using a lens with long depth of
focus.
Schematic of the measurement setup (left), and images of the object in the backside gold
mirror and in the retroreflector for different retroreflector rotation angles (right). The setup is
similar to the one shown in Fig. 5a, except for the objective lens replaced with a low numerical
aperture lens, and a lager object. The numerical aperture of L
1
is 0.08 and its depth of focus is
approximately 130
μ
m. The relatively long depth of focus of L
1
allows for simultaneously
observing both the retroreflected and reflected images of the object in the
θ
= 0
image (i.e.
normal incidence). The faint images observed in the background for 10
◦
to 40
◦
are due to
undesirable reflection from the output side of the beam splitter cube and they exist even when the
device is removed from the setup. BS: beam splitter cube, L: lens. The focal lengths of lenses L
1
and L
2
are
f
1
=3 cm and
f
2
=20 cm, respectively. The diameter of the iris aperture is set to 5 mm.
5
Refractive index
Extinction coefficient
Supplementary Figure 5
|
Refractive index of amorphous silicon.
Measured refractive index
and extinction coefficient of amorphous silicon deposited at 200
◦
C using plasma enhanced
chemical vapor deposition. The index values are measured using a variable angle spectroscopic
ellipsometer.
6
b
845
850
855
0
1
Power density (a. u.)
Wavelength (nm)
a
790
810
830
850
870
890
910
0
1
Power density (a. u.)
Wavelength (nm)
Supplementary Figure 6
|
Spectra of sources used for the retroreflector characterization. a
,
Measured spectrum of the LED used in the measurement shown in Fig. 4a.
b
, Measured
spectrum of the laser used in retroreflection efficiency measurement (Fig. 4b). The full width at
half maximum bandwidth values for the best Gaussian fits to the spectra shown in (
a
) and (
b
) are
42.7 nm and 0.9 nm, respectively.
7
SUPPLEMENTARY TABLES
Supplementary Table 1
|
Phase profile parameters for the metasurfaces composing the
retroreflector
Metasurface
R
(
μ
m)
a
1
a
2
a
3
a
4
a
5
a
6
a
7
Metasurface I
250
-669.15 33.67
0.32
6.61
-3.77
1.11
-0.12
Metasurface II
300
-903.33 -9.03
6.47
-2.85
0.67
-0.08
0.00
8
SUPPLEMENTARY VIDEO LEGENDS
Supplementary Video 1
|
Reflectance of the retroreflector.
Measured reflectance of the
metasurface retroreflector as the angle between the retroreflector normal and the incident light (
θ
)
is increased from 0
◦
to 55
◦
.
9