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SUPPLEMENTARY FIGURES
Strehl ratio (a.u.)
Incident angle (degree)
30
20
10
0
0.5
0
1
0.9
Singlet
Doublet
Supplementary Figure 1
.
Strehl ratio of the singlet and doublet metasurface lenses
. Strehl ratio is the
ratio of the volume under the 2D MTF of a lens to the volume under the 2D MTF of a diffraction limited
lens with the same NA. The red dashed line shows the Strehl ratio value of 0.9 which we have used as a
threshold for referring to the focal spot as being “nearly diffraction limited”.
2
a
b
0
1
Intensity (a.u.)
d
x
= 0
d
y
= 5
P
m
d
x
= 5
P
m
d
y
= 0
15°
-15°

=-30°
30°
d
x
= 0
d
y
= 0
Correcting
metasurface
Focusing
metasurface
d
y
d
x
θ
x
z
x
y
θ
Supplementary Figure 2
.
Effect of misalignment between the two metasurfaces
.
a
, Schematic illus-
tration of the side and the top views of the metasurface doublet lens. The misalignments along
x
and
y
directions (d
x
and d
y
) are shown in the top view illustration.
b
, Simulated focal plane intensity of the
metasurface doublet lens for different misalignments between the metasurfaces and at several different in-
cident angles
θ
. The aperture and field stops are assumed to be aligned with the metasurfaces on their
corresponding sides. Scale bar: 2
μ
m.
3
790
810
830
850
870
890
910
0
1
Power density (a. u.)
Wavelength (nm)
c
a
845
850
855
0
1
Power density (a. u.)
Wavelength (nm)
b
790
810
830
850
870
890
910
0
1
Power density (a. u.)
Wavelength (nm)
Supplementary Figure 3
.
Measured spectra of the sources used to characterize the metasurface lenses
and the miniature camera
.
a
, Measured spectrum of the laser used in the measurement of incident angle
dependent focusing of the metasurface doublet and singlet lenses (Fig. 3a). Different peaks observed in the
spectrum correspond to different Fabry-P
́
erot modes of the laser cavity.
b
, Measured spectrum of the LED
used to capture the image shown in Fig. 5c.
c
, Measured spectrum of the filtered LED used as illumination
for the images shown in Figs 4b,c,g, and 5d. The solid blue curves show the measured spectra and the
dashed red curves represent the best Gaussian function fits. The full width at half maximum (FWHM)
bandwidth values for the Gaussian fits are equal to 0.9 nm, 42.7 nm, and 9.8 nm for the spectra shown in
a
,
b
, and
c
, respectively.
4
Supplementary Figure 4
.
Image captured by the metasurface doublet lens.
Image taken using the setup
shown in Fig. 4a, but with an objective lens with higher magnification and NA (50
×
, 0.5 NA). See Methods
for the measurement details. The vignetting observed at the corners of the image is due to the limited field
of view of the objective lens used to magnify the image. Scale bar: 10
μ
m.
5
a
Image plane
Substrate
15°
30°
b
Substrate
Cover glass
Image sensor
15°
30°
Metasurface Doublet Lens II
Metasurface Doublet Lens I
Supplementary Figure 5
.
Image-space telecentricity of the metasurface doublet lenses. a
, Ray diagram
for the metasurface doublet lens I (designed for focusing in air), and
b
, the metasurface doublet lens II
(designed for focusing through the cover glass). The correcting and focusing metasurfaces (not shown) are
assumed to be patterned on the left and right sides of the substrates, respectively. The chief rays are nearly
normal to the image planes (i.e. the lenses are telecentric in the image space), and the angular distributions
of the focused rays are independent of the incident angle. Scale bars: 400
μ
m.
6
FWHM (nm)
0
400
800
1200
0
0.5
1
Frequency (cycles per mm)
MTF (a.u.)
0
10
20
40
Supplementary Figure 6
.
Simulated modulation transfer function for the metasurface doublet lens
at the incident angle of 15
. The solid and dashed lines show the modulation transfer function in the
tangential plane (along
x
in Fig. 5a) and sagittal plane (along
y
in Fig. 5a), respectively.
7
a
400
0
20
10
0
400
200
200
Radial coordinate (
P
m)
Phase (rad.)
800
0
800
400
400
Radial coordinate (
P
m)
Phase (rad.)
0
1000
2000
3000
b
c
400
0
200
100
0
400
200
200
Radial coordinate (
P
m)
Phase (rad.)
800
0
800
400
400
Radial coordinate (
P
m)
Phase (rad.)
0
1000
2000
3000
d
Supplementary Figure 7
.
Phase profiles of the metasurfaces composing the doublet lenses. a
, Phase
profile of the correcting and
b
, focusing metasurfaces of the doublet lens I (designed for focusing in air).
c
, and
d
, similar plots as
a
and
b
but for the metasurface doublet lens II which is designed for focusing
through the cover glass of a CMOS image sensor (as shown in Figs 4f,g).
8
SUPPLEMENTARY TABLES
Supplementary Table 1
|
Phase profile parameters for the metasurface doublet lens I
Metasurface
R
(
μ
m)
a
1
a
2
a
3
a
4
a
5
Correcting Metasurface
400
-71.86
57.90
9.62
1.30
0.66
Focusing Metasurface
800
-3285.68
-31.88
33.77
-8.41
1.51
Supplementary Table 2
|
Phase profile parameters for the metasurface doublet lens II
Metasurface
R
(
μ
m)
a
1
a
2
a
3
a
4
a
5
Correcting Metasurface
400
-225.92
31.29
3.84
0.49
0.34
Focusing Metasurface
700
-2559.04
11.57
0.83
-3.58
1.94
9
SUPPLEMENTARY NOTE 1: IMAGING BANDWIDTH OF METASURFACE LENSES
Here we discuss the relation between the numerical aperture (NA), focal length and bandwidth
of a metasurface lens. We consider a metasurface lens with the focal length of
f
which is designed
for operation at the wavelength
λ
, and is placed at the distance
f
from an image sensor. The
metasurface lens focuses light with the wavelength of
λ
+ ∆
λ
to the distance of
f
f
from the
metasurface lens. Because of the phase jumps at the zone boundaries of the metasurface lens, the
fractional change in the focal length is equal to the fractional change in the wavelength [1], that is
f
f
=
λ
λ
.
(1)
As
λ
increases the focal plane of the lens moves further away from the image sensor and the
size of the spot recorded by the image sensor increases. As a quantitative measure, we define the
bandwidth of the metasurface lens as the wavelength change
λ
that increases the diameter of
the recorded spot by a factor of
2
compared to its value at
λ
. With this definition, the distance
between the image sensor and the focal plane at the wavelength of
λ
+ ∆
λ
is equal to the Rayleigh
range
z
0
of the focused light (i.e.
f
=
z
0
). The Rayleigh range is given by
z
0
=
πw
2
0
λ
,
(2)
where
w
0
is the
1
/
e
2
focal spot radius and is inversely proportional to the NA of the metasurface
lens
w
0
=
λ
2
ln(2)NA
.
(3)
Therefore, the fractional bandwidth of the metasurface lens is given by
λ
λ
=
πw
2
0
λf
=
π
4ln(2)
λ
f
NA
2
,
(4)
and is proportional to
λ/
(
f
NA
2
)
.
SUPPLEMENTARY REFERENCES
[1] Arbabi, E., Arbabi, A., Kamali, S. M., Horie, Y. & Faraon, A. Multiwavelength polarization insensitive
lenses based on dielectric metasurfaces with meta-molecules.
Optica
3
(2016).
10