of 35
Compact Folded Metasurface Spectrometer
MohammadSadegh Faraji-Dana,
1,
Ehsan Arbabi,
1,
Amir Arbabi,
1, 2
Seyedeh Mahsa Kamali,
1
Hyounghan Kwon,
1
and Andrei Faraon
1,
1
T. J. Watson Laboratory of Applied Physics and Kavli Nanoscience Institute,
California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125, USA
2
Department of Electrical and Computer Engineering,
University of Massachusetts Amherst,
151 Holdsworth Way, Amherst, MA 01003, USA
Keywords: Metasurfaces, Diffractive optics, Spectrometer, Nano-scale materials, Folded optics
These authors contributed equally to this work
Corresponding author: A.F.: faraon@caltech.edu
1
arXiv:1807.10985v1 [physics.optics] 29 Jul 2018
Recent advances in optical metasurfaces enable control of the wavefront, polarization
and dispersion of optical waves beyond the capabilities of conventional diffractive optics. An
optical design space that is poised to highly benefit from these developments is the folded
optics architecture where light is confined between reflective surfaces and the wavefront is
controlled at the reflective interfaces. In this manuscript we introduce the concept of folded
metasurface optics by demonstrating a compact high resolution optical 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 in a 100-nm bandwidth centered
around 810 nm. The device is composed of three different reflective dielectric metasurfaces,
all fabricated in a single lithographic step on one side of a transparent optical substrate,
which simultaneously acts as the propagation space for light. An image sensor, parallel to
the spectrometer substrate, can be directly integrated on top of it to achieve a compact mono-
lithic device including all the active and passive components. Multiple spectrometers, with
similar or different characteristics and operation bandwidths may also be integrated on the
same chip and fabricated in a batch process, significantly reducing their costs and increas-
ing their functionalities and integration potential. In addition, the folded metasystems design
can be applied to many optical systems, such as optical signal processors, interferometers,
hyperspectral imagers and computational optical systems, significantly reducing their sizes
and increasing their mechanical robustness and potential for integration.
Optical 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 properties (e.g., operation bandwidth, resolution, size, etc.) required for
different applications [3–5]. Conventional optical spectrometers are composed of a dispersive ele-
ment, such as a prism or a diffraction gating, that deflects 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 spectrometers 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 spectrome-
ters that can be easily integrated into consumer electronics for various medical and technological
2
applications such as medical diagnosis, material characterization, quality control, etc. [6, 7] . As
a result, various schemes and structures have been investigated for realization of such spectrom-
eters [7–16]. One class of miniaturized spectrometers integrate a series of band-pass filters with
different center wavelengths on an array of photodetectors [8, 17]. Although these devices are
compact and compatible with standard microfabrication techniques, they have resolutions limited
by achievable filter quality factors, and low sensitivities caused by the filtering operation that re-
jects a large portion of the input power. Spectrometers based on planar on-chip integrated photon-
ics 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 spectrome-
ters, 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 function-
alities, have attracted a great deal of interest in recent years [19–22]. Overcoming many of the
material and fundamental limitations of plasmonic metasurfaces [23], dielectric metasurfaces have
proven capable of implementing several conventional [19, 24–34] and new optical devices [35–
39] with high efficiencies. 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 techniques, which allows for integration
of multiple metasurfaces for realizing complex optical metasystems [24, 40]. Such metasystems
allow for significantly improving optical properties of metasurfaces through aberration correction
(such as lenses with diffraction limited operation over wide field of view [24]), or functionalities
fundamentally unachievable with local single-layer metasurfaces such as retroreflection [40].
Taking a different approach to device integration, here we introduce folded optical metasys-
tems 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 over a 100-nm bandwidth (more than 80 points over a
12
%
band-
3
width) in the near infrared. As schematically shown in Fig.
1
b, multiple reflective 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 first
demonstration of an optical metasystem comprising more than two metasurfaces that implements
a sophisticated optical functionality like spectrometry. Furthermore, the presented configuration
can allow for the integration of the detector array on top of the folded spectrometer, resulting in a
compact monolithic device. We should note here that it was recently demonstrated that an off-axis
metasurface lens (i.e., a lens with an integrated blazed grating phase profile [41, 42]) can disperse
and focus different wavelengths to different points. However, there are fundamental and practical
limitations for such elements that significantly 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 applica-
tion before). Fundamentally, 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 achiev-
able 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 metasurface plane [41, 42, 49]. In addition to the distance for the
propagation of dispersed light, this normal placement undermines the compactness 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 first
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 fo-
cusing over a wide field 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 configuration, 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 configu-
ration, allows for the focal plane to be parallel to the substrate. This makes the integration of the
4
spectrometer and the detector array much simpler, results in a more compact and mechanically ro-
bust device, and allows for direct integration into consumer electronic products like smartphones.
The optimized phase profiles for the two surfaces are shown in Fig.
2
a, right (see Supplementary
Table I 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 show-
ing negligible geometric aberrations. The spot diagrams are plotted only at three wavelengths, but
the small effect of optical aberrations was confirmed for all wavelengths in the 760 nm-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 nm, 810 nm, and 860 nm are plotted in the same panel, showing
two resolvable peaks.
To implement the reflective metasurfaces, we used a structure similar to the reflective elements
in [40]. Each of the meta-atoms, shown schematically in Fig.
3
a, consists of an
α
-Si nano-post
with a rectangular cross section, capped by a 2-
μ
m-thick SU-8 layer and backed by a gold mir-
ror. The post height and lattice constant were chosen to be 395 nm and 246 nm, respectively, to
achieve full 2
π
phase coverage while minimizing variation of the reflection phase derivative across
the band (Supplementary Fig.
S1
). Minimizing the phase derivative variation will mitigate the re-
duction of device efficiency over the bandwidth of interest [47] by decreasing the wavelength
dependence of the phase profiles (Supplementary Fig.
S2
). In addition, since the two focusing
metasurfaces are working under an oblique illumination (
θ
33.9
), the nano-posts were chosen
to have a rectangular cross-section to minimize the difference in reflection amplitude and phase for
the transverse electric (TE) and transverse magnetic (TM) polarizations (for the oblique incident
angle of
33
.
9
at 810 nm). Reflection coefficients are found through simulating a uniform array of
nano-posts under oblique illumination (
θ
33.9
) with TE and TM polarized light [Fig.
3
a, right].
The simulated reflection phase as a function of the nano-posts side lengths are shown in Fig.
3
b.
The black triangles highlight the path through the
D
x
-
D
y
plane along which the reflection phase
for the TE and TM polarizations is almost equal. In addition, as shown in Supplementary Fig.
S2
having almost the same reflection phases for the TE and TM polarizations holds true for the whole
desired 760nm-860 nm bandwidth. The nanopost dimensions calculated from this path were used
to implement the two focusing metasurfaces.
5
The blazed grating has a periodic phase profile (with a period of 1
μ
m) that deflects normally
incident light to a large angle inside the substrate. With a proper choice of the lattice constant
(250 nm, in our case), its structure can also be periodic. This different structure and operation
require a different design approach. The periodicity of the grating allows for its efficient full-
wave simulation which can be used to optimize its operation over the bandwidth of interest. A
starting point for the optimization was chosen using the recently developed high-NA lens design
method [50], and the structure was then optimized using the particle swarm optimization algo-
rithm to simultaneously maximize deflection efficiency at a few wavelengths in the band for both
polarizations (see Supplementary Section
S1
and Fig.
S3
for details).
The device was fabricated using conventional micro- and nano-fabrication techniques. First,
a 395-nm-thick layer of
α
-Si was deposited on a 1-mm-thick fused silica substrate. All metasur-
faces were then patterned using electron beam lithography in a single step, followed by a pattern
inversion through the lift-off and dry etching processes. The metasurfaces were capped by a
2-
μ
m-thick SU-8 layer, and a 100-nm-thick gold layer was deposited as the reflector. A second
reflective gold layer was deposited on the second side of the substrate. Both the input and output
apertures (with diameters of 790
μ
m and 978
μ
m, respectively) were defined using photolithog-
raphy and lift-off. An optical microscope image of the three metasurfaces, along with a scanning
electron micrograph of a part of the fabricated device are shown in Fig.
4
a.
To experimentally characterize the spectrometer, a normally incident collimated beam from a
tunable continuous wave laser was shinned on the input aperture of the device. A custom-built
microscope was used to image the focal plane of the spectrometer,
200
μ
m outside its output
aperture (see Supplementary Section S1 and Fig.
S5
for details of the measurement setup). The
input wavelength was tuned from 760 nm to 860 nm in steps of 10 nm, and the resulting intensity
distributions were imaged using the microscope. The resulting one-dimensional intensity profiles
are plotted in Fig.
4
b for TE (left) and TM (right) polarizations. The intensity profiles were mea-
sured over the whole 1.2-mm length of the y-direction in the focal plane (as shown in Fig.
4
b,
inset) at each wavelength. The background intensity is beyond visibility in the linear scale profiles
plotted here for all wavelengths (see Supplementary Figs. S6 and S7 for two-dimensional and
logarithmic-scale plots of the intensity distribution, respectively). Figure
4
d shows the measured
intensity profiles for three sets of close wavelengths, separated by 1.25 nm. The insets show the
corresponding two-dimensional intensity distribution profiles. For all three wavelengths, and for
both polarizations the two peaks are resolvable. The experimentally obtained spectral resolution
6
is plotted in Supplementary Fig.
S8
versus the wavelength. The average resolution for both po-
larizations is
1.2 nm, which is slightly worse than the theoretically predicted value (
1.1 nm).
We attribute the difference mostly to practical imperfections such as the substrate having an ac-
tual thickness different from the design value and thickness variation. In addition the metasurface
phases are slightly different from the designed profiles due to fabrication imperfections. The angu-
lar sensitivity/tolerance of the device was also measured with respect to polar and azimuthal angle
deviations from 0 incidence angle, in the
x
-
z
and
y
-
z
planes, using the setup shown in Supplemen-
tary Fig.
S9
c). In the
y
-
z
plane the maximum tilt angle to maintain the same 1.25 nm resolution is
±
0.15
, while in the
x
-
z
plane the device has a
±
1
degree acceptance angle. The measurement
results in Fig.
S9
match well with the predictions from ray-tracing simulations.
The measured and calculated focusing efficiencies are plotted in Fig.
4
c. The focusing effi-
ciency, defined as the power passing through a
30-
μm
diameter pinhole around the focus divided
by the total power hitting the input aperture, was measured using the setup shown in Supplemen-
tary Fig.
S5
. For both polarizations, the average measured efficiency is about 25
%
. As seen from
the measured efficiency curves, the optimization of the blazed grating efficiency versus wavelength
and the choice of the design parameters to minimize variations in the phase-dispersion for the dou-
blet metasurface lens, have resulted in a smooth measured efficiency. An estimate for the expected
efficiency (shown as simulated efficiency in Fig.
4
c ) is calculated by multiplying the deflection
efficiency of the grating, the efficiency of seven reflections off the gold mirrors, the input and
output aperture transmission efficiencies, and the average reflectivities of the uniform nano-post
arrays (as an estimate for the two focusing metasurface efficiencies). It is worth noting that consid-
ering only the reflection losses at the interfaces (nine reflective ones, and two transmissive ones)
reduces the efficiency to about 48
%
, showing a close to 50
%
efficiency for the three metasurfaces
combined. We attribute the remaining difference between the measured and estimated values to
fabrication imperfections (e.g., higher loss for the actual gold mirrors, and imperfect fabrication
of the metasurfaces), the lower efficiency of the metasurfaces compared to the average reflectivity
of uniform arrays, and to the minor difference from the designed value of the metasurface phase
profiles at wavelengths other than the center frequency.
To demonstrate that the metasurface spectrometer actually has the ability to measure dense
optical spectra, we use it to measure the transmission spectra of two different samples. First, we
measured the spectrum of a wideband source (a super-continuum laser source, filtered with an
840-nm short-pass filter), both with the metasurface spectrometer (MS) and a commercial optical
7
spectrum analyzer (OSA). By dividing the spectra measured by the two devices, we extract the
required calibration curve that accounts for the variation of the metasurface spectrometer as well
as the non-uniformities in the responsivity of the optical setup used to image the focal plane (i.e.,
the objective lens and the camera, as well as the optical fiber used to couple the signal to the OSA).
The measured spectra and the extracted calibration curve are plotted in Fig.
5
a. Next, we used this
calibration curve to measure the transmission spectrum of a band-pass filter with a nominal 10-nm
full width at half maximum bandwidth and centered at 800 nm. The measured spectrum along
with the transmission spectrum obtained from the filter datasheet are plotted in Fig.
5
b, showing
a good agreement. Finally, we used the metasurface spectrometer to measure the optical depth
of a Nd:YVO
4
crystal sample. The spectrum measured with the metasurface spectrometer (after
calibration) is compared with the transmission spectrum of the same sample measured with the
OSA in Fig.
5
c. Dividing the spectrum without and with the sample, we have extracted the optical
depth of the sample which is plotted in Fig.
5
d. A good agreement is observed between the two
measurement results. It is worth noting that the Nd:YVO
4
crystal sample was cut though the
z-plane, resulting in an equal absorption spectrum for the two polarizations. Therefore, we can
assume that all spectral measurements were done with the same state of input polarization. This
justifies the use of only one calibration curve for all the measurements.
The measured efficiency of the spectrometer demonstrated here is about 25
%
. This value can
be significantly increased to about 70
%
by using mirrors with higher reflectivity (e.g., DBRs or
high contrast grating mirrors [51, 52]), and anti-reflection coatings on the input and output aper-
tures. In addition, more advanced optimization techniques [53] could be exploited to optimize the
diffraction grating to achieve high efficiency and polarization insensitivity. Implementing these
changes and optimizing the fabrication process, one can expect to achieve efficiencies exceeding
70
%
for the spectrometer.
The metasurface spectrometers are fabricated in a batch process, and therefore many of them
can be fabricated on the same chip, even covering multiple operation bandwidths. This can drasti-
cally reduce the price of these devices, allowing for their integration into various types of systems
for different applications. In addition, the demonstrated structure is compatible with many of the
techniques developed for the design of multi-wavelength metasurfaces [46, 54], and therefore one
might be able to combine different optical bandwidths into the same device (e.g., using a grating
that deflects to the right at one bandwidth, and to the left at the other), resulting in compact devices
with enhanced functionalities.
8
The optical throughput (etendue) is a fundamental property of any optical system, setting an
upper limit on the ability of the system to accept light from spatially incoherent sources. It can
be estimated as the product of the physical aperture size and the acceptance solid angle of the
system. Furthermore, the total etendue of a system is limited by the element with the lowest
etendue. To calculate the throughput of the metasurface spectrometer, we have performed sim-
ulations and measurements to characterize its acceptance angle. According to the measurement
results in Supplementary Fig.
S9
the acceptance angle of the system is about 2 degrees in the
horizontal direction, and 0.3 degrees in the vertical direction. Given this and the input aperture di-
mensions, the optical throughput of our device is calculated to be
90
Sr
(
μm
)
2
. For comparison,
the etendue of optical systems operating around 1
μ
m that utilize single-mode input channels (i.e.,
most optical spectrometers based on integrated optics platforms) is around
1
Sr
(
μm
)
2
. Further-
more, the demonstrated spectrometer is optimized for maximum sensitivity and not throughput.
To show that the achieved throughput here does not denote an upper limit for the etendue of a
folded metasurface spectrometer with similar characteristics (i.e., resolution, bandwidth, etc.), we
have designed a second device with a throughput of
13000
Sr
(
μm
)
2
(see Supplementary section
S2
and Fig.
S10
for design details and simulation results). Table I provides a comparison of the
optical throughput of several compact spectrometers from recent literature. According to this ta-
ble, the spectrometers designed using the folded metasurface platform can collect 2 to 4 orders of
magnitude more light compared to on-chip spectrometers that are based on single/few-mode input
waveguides, resulting in a much higher sensitivity.
TABLE I
Comparison of different spectrometers in terms of throughput (Etendue) and their
dimensions
Spectrometer
Etendue [
Sr
(
μm
)
2
]
Size (dimensions)
[11]
<
0.5
50
μm
×
100
μm
×
thickness
[55]
0.8
16
mm
×
7
mm
×
15
μm
This work
90
1
mm
×
1
mm
×
7
mm
[15]
8250
20
.
1
mm
×
12
.
5
mm
×
10
.
1
mm
Extension in Fig.
S10
13000
2
mm
×
2
.
5
mm
×
8
mm
The development of thin and compact optical elements and systems has been a key promise
of optical metasurfaces. Although many optical devices have been developed in thin and com-
pact form factors using metasurfaces, significantly reducing the volume of optical systems using
metasurfaces has not been previously demonstrated due to the requirement of the free-space prop-
agation in many systems (e.g., imaging systems, spectrometers, etc.). The folded metasystem
9
configuration introduced here can significantly reduce the size of many of these optical systems
using the substrate as the propagation space for light. Based on this configuration, we demon-
strated a 1-mm-thick spectrometer with a 7-mm
3
volume, reduced by a factor of ten compared to
the same system implemented in an unfolded scheme (twenty times reduction, if the same system
was designed in air). The spectrometer has a resolution of
1.2 nm over a 100-nm bandwidth
(
>
12
%
) in the near infrared. Using this design, multiple spectrometers can be fabricated on the
same chip and in the same process, significantly reducing the costs and enabling integration of
spectrometers covering multiple optical bands into consumer electronics. Moreover, by improving
the angular response of the current device one can design a compact hyperspectral imager capable
of simultaneous one-dimensional imaging and spectroscopy. In a broader sense, we expect that
the proposed platform will also be used for on-chip interferometers, imaging systems, and other
devices performing complex transformations of the field.
10
ACKNOWLEDGEMENT
This work was supported by Samsung Electronics. M.F. was partly supported by The Natu-
ral Sciences and Engineering Research Council of Canada (NSERC). S.M.K.is supported as part
of the Department of Energy (DOE) “Light-Material Interactions in Energy Conversion” Energy
Frontier Research Center under grant no. de-sc0001293. The device nano-fabrication was per-
formed at the Kavli Nanoscience Institute at Caltech. Authors would like to thank Dr. Tian Zhong
for providing the Nd:YVO
4
sample, and Dr. Seunghoon Han and Dr. Duhyun Lee for useful
discussions.
11
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FIGURES
Focusing
mirror
Diffraction
grating
Detector
array
Fore-optics
(a)
Metasurface 1
Gold mirrors
Metasurface 2
Substrate
(b)
Metasurface n
λ
2
λ
1
λ
λ
1
λ
2
Detector
array
Spectrum
Wavelength
Figure 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 reflective
metasurfaces on the two sides of a single transparent substrate. Mirrors on both sides confine and direct
light to propagate inside the substrate, and the detector can be directly 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 to simplify their
fabrication.
16