ARTICLE
Compact folded metasurface spectrometer
MohammadSadegh Faraji-Dana
1
, Ehsan Arbabi
1
, Amir Arbabi
1,2
, Seyedeh Mahsa Kamali
1
,
Hyounghan Kwon
1
& Andrei Faraon
1
An optical design space that can highly bene
fi
t from the recent developments in meta-
surfaces is the folded optics architecture where light is con
fi
ned between re
fl
ective surfaces,
and the wavefront is controlled at the re
fl
ective interfaces. In this manuscript, we introduce
the concept of folded metasurface optics by demonstrating a compact spectrometer made
from a 1-mm-thick glass slab with a volume of 7 cubic millimeters. The spectrometer has a
resolution of ~1.2 nm, resolving more than 80 spectral points from 760 to 860 nm. The device
is composed of three re
fl
ective dielectric metasurfaces, all fabricated in a single lithographic
step on one side of a substrate, which simultaneously acts as the propagation space for light.
The folded metasystem design can be applied to many optical systems, such as optical signal
processors, interferometers, hyperspectral imagers, and computational optical systems,
signi
fi
cantly reducing their sizes and increasing their mechanical robustness and potential
for integration.
DOI: 10.1038/s41467-018-06495-5
OPEN
1
T. J. Watson Laboratory of Applied Physics and Kavli Nanoscience Institute, California Institute of Technology, 1200 East California Boulevard, Pa
sadena, CA
91125, USA.
2
Department of Electrical and Computer Engineering, University of Massachusetts Amherst, 151 Holdsworth Way, Amherst, MA 01003, USA.
These authors contributed equally: MohammadSadegh Faraji-Dana, Ehsan Arbabi. Correspondence and requests for materials should be addressed to
A.F. (email:
faraon@caltech.edu
)
NATURE COMMUNICATIONS
| (2018) 9:4196 | DOI: 10.1038/s41467-018-06495-5 | www.nature.com/naturecommunications
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O
ptical spectrometry is a key technique in various areas
of science and technology with a wide range of
applications
1
,
2
. This has resulted in a large demand for
spectrometers and/or spectrum analyzers with different proper-
ties (e.g., operation bandwidth, resolution, size, etc.) required
for different applications
3
–
5
. Conventional optical spectrometers
are composed of a dispersive element, such as a prism or a dif-
fraction gating, that de
fl
ects different wavelengths of light by
different angles, followed by focusing elements that focus light
incoming from different angles to different points (or lines).
As schematically shown in Fig.
1
a, the intensity at different
wavelengths can then be measured using an array of detectors.
Diffraction gratings have typically larger dispersive powers
than transparent materials, and therefore diffractive spectro-
meters generally have better resolutions
1
. The combination of
several free-space optical elements (the grating, focusing mirrors,
etc.) and the free-space propagation volume result in bulky
spectrometers. In recent years, there has been an increased
interest in high-performance compact spectrometers that can
be easily integrated into consumer electronics for various
medical and technological applications such as medical diagnosis,
material characterization, quality control, etc.
6
,
7
. As a result,
various schemes and structures have been investigated for reali-
zation of such spectrometers
7
–
16
. One class of miniaturized
spectrometers integrate a series of band-pass
fi
lters with different
center wavelengths on an array of photodetectors
8
,
17
. Although
these devices are compact and compatible with standard micro-
fabrication techniques, they have resolutions limited by achiev-
able
fi
lter quality factors, and low sensitivities caused by the
fi
ltering operation that rejects a large portion of the input power.
Spectrometers based on planar on-chip integrated photonics
provide another solution with high spectral resolution
7
,
9
–
13
.
However, the loss associated with on-chip coupling of the input
light and the reduced throughput because of the single-mode
operation
18
are still major challenges for widespread adoption in
many applications.
Another type of compact spectrometers are conceptually
similar to the conventional table-top spectrometers, however,
they use micro-optical elements to reduce size and mass
14
,
15
.
Due to the inferior quality and limited control achievable by
micro-optical elements as well as the shorter optical path lengths,
these devices usually have lower spectral resolutions. Higher
resolution has been achieved by using aberration-correcting
planar gratings
16
, however an external spherical mirror makes
the device bulky.
Dielectric metasurfaces, a new category of diffractive optical
elements with enhanced functionalities, have attracted a great
deal of interest in recent years
19
–
22
. Overcoming many of the
material and fundamental limitations of plasmonic meta-
surfaces
23
, dielectric metasurfaces have proven capable of
implementing several conventional
19
,
24
–
34
and new optical devi-
ces
35
–
39
with high ef
fi
ciencies. They enable control of phase with
subwavelength resolution and high gradients and simultaneous
control of phase and polarization
35
. A key feature of metasurfaces
is their compatibility with micro and nano-fabrication techni-
ques, which allows for integration of multiple metasurfaces for
realizing complex optical metasystems
24
,
40
. Such metasystems
allow for signi
fi
cantly improving optical properties of meta-
surfaces through aberration correction (such as lenses with dif-
fraction limited operation over wide
fi
eld of view
24
), or
functionalities fundamentally unachievable with local single-layer
metasurfaces such as retrore
fl
ection
40
.
Results
Concept and design
. Taking a different approach to device
integration, here we introduce folded optical metasystems
where multiple metasurfaces are integrated on a single substrate
that is also playing the role of propagation space for light
[Fig.
1
b]. Using this platform, we experimentally demonstrate
a compact folded optics device for spectroscopy with a 1-mm
thickness (
~
7-mm
3
volume) that provides a
~
1.2-nm resolution
Focusing
mirror
Diffraction
grating
Detector
array
Fore-optics
a
Metasurface 1
Gold mirrors
Metasurface 2
Substrate
b
Metasurface n
1
2
2
1
Detector
array
Spectrum
Wavelength
Fig. 1
Schematics of a conventional and a folded metasurface spectrometer.
a
Schematic illustration of a typical diffractive spectrometer. The main
components are comprised of the fore-optics section, diffraction grating, focusing lenses, and detector array.
b
The proposed scheme for a folded compact
spectrometer. All the dispersive and focusing optics can be implemented as re
fl
ective metasurfaces on the two sides of a single transparent substrate.
Mirrors on both sides con
fi
ne and direct light to propagate inside the substrate, and the detector can be placed directly at the output aperture of the device.
If required, transmissive metasurfaces can also be added to the input and output apertures to perform optical functions. Although the schematic here
includes metasurfaces on both sides to show the general case, the actual devices demonstrated here are designed to have metasurfaces only on one side t
o
simplify their fabrication
ARTICLE
NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-06495-5
2
NATURE COMMUNICATIONS
| (2018) 9:4196 | DOI: 10.1038/s41467-018-06495-5 | www.nature.com/naturecommunications
over a 100-nm bandwidth (more than 80 points over a
~
12%
bandwidth) in the near-infrared. As schematically shown in
Fig.
1
b, multiple re
fl
ective metasurfaces can be designed and
fabricated on the same transparent substrate to disperse and focus
light to different points on a plane parallel to the substrate. To the
best of our knowledge, this is the
fi
rst demonstration of an optical
metasystem comprising more than two metasurfaces that
implements a sophisticated optical functionality like spectro-
metry. Furthermore, the presented con
fi
guration can allow for the
integration of the detector array on top of the folded spectro-
meter, resulting in a compact monolithic device. We should note
here that it was recently demonstrated that an off-axis metasur-
face lens (i.e., a lens with an integrated blazed grating phase
pro
fi
le
41
,
42
) can disperse and focus different wavelengths to dif-
ferent points. However, there are fundamental and practical
limitations for such elements that signi
fi
cantly limits their
application as a spectrometer (which is the reason why other
types of diffractive optical elements, such as holographic optical
elements and kinoforms, that can essentially perform the same
function have not been used for this application before). Fun-
damentally, the chromatic dispersion
43
–
47
and angular response
correlation of diffractive optical elements and metasurfaces
38
,
48
limit the bandwidth and angular dispersion range where the
device can provide tight aberration-free focusing. This in turn
limits the achievable resolution and bandwidth of the device.
Moreover, the chromatic dispersion results in a focal plane almost
perpendicular to the metasurface, which will then require the
photodetector array to be placed almost normal to the metasur-
face plane
41
,
42
,
49
. In addition to the distance for the propagation
of dispersed light, this normal placement undermines the com-
pactness of the device.
Figure
2
a shows the ray-tracing simulations of the designed
spectrometer. The device consists of three metasurfaces, all
patterned on one side of a 1-mm-thick fused silica substrate. The
fi
rst metasurface is a periodic blazed grating with a period of 1
μ
m
that disperses different wavelengths of a collimated input light to
different angles, centered around 33.9° at 810 nm. The second
and third metasurfaces focus light coming from different angles
(corresponding to various input wavelengths) to different points
on the focal plane. We have recently demonstrated a metasurface
doublet capable of correcting monochromatic aberrations to
achieve near-diffraction-limited focusing over a wide
fi
eld of
view
24
. The second and third metasurfaces here essentially work
similar to the mentioned doublet, with the difference of working
off-axis and being designed in a folded con
fi
guration, such that
the focal plane for our desired bandwidth is parallel to the
substrate. To simplify the device characterization, the focal plane
was designed to be located 200
μ
m outside the substrate. The
asymmetric design of the focusing metasurfaces in an off-axis
doublet con
fi
guration, allows for the focal plane to be parallel to
the substrate. This makes the integration of the spectrometer and
the detector array much simpler, results in a more compact and
mechanically robust device, and allows for direct integration into
consumer electronic products like smartphones. The optimized
phase pro
fi
les for the two surfaces are shown in Fig.
2
a, right (see
Supplementary Table 1 for the analytical expression of the phase).
Simulated spot diagrams of the spectrometer are plotted in Fig.
2
b
for three wavelengths at the center and the two ends of the
bandwidth showing negligible geometric aberrations. The spot
diagrams are plotted only at three wavelengths, but the small
effect of optical aberrations was con
fi
rmed for all wavelengths in
the 760
–
860 nm bandwidth. As a result, the spectral resolution of
the device can be calculated using the diffraction limited Airy
radius and the lateral displacement of the focus by changing the
wavelength. The calculated resolution is plotted in Fig.
2
c,
showing a theoretical value of better than 1.1 nm across the band.
Point spread functions (PSFs) calculated for input beams
containing two wavelengths 1.1 nm apart, and centered at 760,
810, and 860 nm are plotted in Fig.
2
d, showing two resolvable
peaks.
To implement the re
fl
ective metasurfaces, we used a structure
similar to the re
fl
ective elements in ref.
40
. Each of the meta-
bc
860
760
Wavelength [nm]
1.00
1.05
Resolution [nm]
1.10
810
760 nm
–0.5
0.5
0
x
[mm]
y
[mm]
–0.5
0
0.5
0
2
π
y
[mm]
0
2
π
0
0.5
-0.5
0
0.5
–0.5
810 nm
860 nm
0
1
Grating
a
200
μ
m
1 mm
760 nm
860 nm
810 nm
Focal
plane
Phase [rad]
Phase [rad]
x
[mm]
760 nm
810 nm
860 nm
Intensity [a.u]
x
z
y
d
Fig. 2
Ray-optics design and simulation results of the folded spectrometer.
a
Ray-tracing simulation results of the folded spectrometer, shown at three
wavelengths in the center and two ends of the band. The system consists of a blazed grating that disperses light to different angles, followed by two
metasurfaces optimized to focus light for various angles (corresponding to different input wavelengths). The grating has a period of 1
μ
m, and the
optimized phase pro
fi
les for the two metasurfaces are shown on the right.
b
Simulated spot diagrams for three wavelengths: center and the two ends of the
band. The scale bars are 5
μ
m.
c
Spectral resolution of the spectrometer, which is calculated from simulated Airy disk radii and the lateral displacement
of the focus with wavelength.
d
Simulated intensity distribution for two wavelengths separated by 1.1 nm around three different center wavelengths of
760, 810, and 860 nm. The intensity distributions show that wavelengths separated by 1.1 nm are theoretically resolvable. The scale bars are 20
μ
m
NATURE COMMUNICATIONS | DOI: 10.1038/s41467-018-06495-5
ARTICLE
NATURE COMMUNICATIONS
| (2018) 9:4196 | DOI: 10.1038/s41467-018-06495-5 | www.nature.com/naturecommunications
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