of 6
Wide bandwidth and high resolution planar filter array based on
DBR-metasurface-DBR structures
Yu Horie, Amir Arbabi, Ehsan Arbabi, Seyedeh Mahsa Kamali, and Andrei Faraon
T. J. Watson Laboratory of Applied Physics, California Institute of Technology,
1200 E. California Blvd., Pasadena, CA 91125, USA
We propose and experimentally demonstrate a planar array of optical bandpass filters composed of
low loss dielectric metasurface layers sandwiched between two distributed Bragg reflectors (DBRs).
The two DBRs form a Fabry-P ́erot resonator whose center wavelength is controlled by the design of
the transmissive metasurface layer which functions as a phase shifting element. We demonstrate an
array of bandpass filters with spatially varying center wavelengths covering a wide range of operation
wavelengths of 250 nm around
λ
= 1550 nm (∆
λ/λ
= 16%). The center wavelengths of each filter are
independently controlled only by changing the in-plane geometry of the sandwiched metasurfaces,
and the experimentally measured quality factors are larger than 700. The demonstrated filter
array can be directly integrated on top of photodetector arrays to realize on-chip high-resolution
spectrometers with free-space coupling.
I. INTRODUCTION
Spectroscopy is an essential tool in bio-chemical sens-
ing applications, material characterization, and multiple
areas of scientific research. Modern spectrometers based
on diffraction gratings are widely used because they can
achieve a high resolving power and high sensitivity. For
multiple applications, including those related to sensors
located on handheld devices and low cost portable point-
of-care diagnostics [1], there is a continuous interest in
miniaturizing spectrometers. However, conventional high
resolution diffraction grating based spectrometers are in-
evitably bulky as the resolution of the spectrometer scales
inversely with optical path length, and thus are not suit-
able for miniaturization. For this purpose, several inte-
grated optics approaches have been explored [2–4], such
as on-chip frequency filtering based on micro-resonators
[5], integrated diffraction gratings [6], and arrayed waveg-
uide gratings [7]. However, in many applications the opti-
cal signals of interest are freely propagating, and the low
coupling efficiency from free-space to on-chip waveguides
limits the sensitivity of this type of spectrometers. An
attractive design for a free-space coupled spectrometer is
to use an array of bandpass optical filters in conjunction
with a photodetector array [8, 9]. One can obtain the
spectral information by measuring intensities of the fil-
tered light within a specific range of wavelengths at each
detector, and more importantly the resolving power of
the spectrometer is only limited by the resolution of the
filters. The most common way to design a high-resolution
optical filter is to form a Fabry-P ́erot (FP) resonator
using a pair of broadband high reflectivity mirrors [9].
The FP cavity length can be varied in a discrete form
through multiple etching steps, or in a continuous form
by using an angled surface. The latter creates optical
filters with spatially varying center wavelength, named
wedge filters, that are manufacturable by linearly vary-
ing the cavity thicknesses of the FP resonator [10], and
are commercially available [11]. However, the angle of
the wedge limits the quality factor of the FP cavities and
in turn the resolution of the filters due to the non-normal
reflection on the angled surface. Gray-scale lithography
enables a spatially varying cavity thicknesses in a more
controlled manner [12], but the technology is expensive
and not readily available.
In this article, we propose and experimentally demon-
strate a new method to effectively vary the central wave-
lengths of a FP filter set by inserting a transmissive di-
electric metasurface as a phase shifting element between
two high reflectivity mirrors, enabling independent and
precise control of the filter’s passbands. Metasurfaces
are two dimensional arrays of subwavelength structures
capable of controlling the phase, amplitude, and polar-
ization of light [13–15]. One particularly interesting class
of metasurfaces are based on high index nano-posts sur-
rounded by a low index medium, which allow both high
transmission as well as phase control capability by de-
signing the geometry of the nano-posts. So far, vari-
ous diffractive optical elements such as high performance
flat lenses [16–18] or birefringent optical elements [19]
have been demonstrated. Unlike plasmonic metasurfaces
which inevitably suffer from optical loss [20], the loss-
less nature of dielectric metasurfaces is suitable for res-
onant applications. As schematically shown in Fig. 1,
the dielectric metasurface layers are incorporated in ver-
tical FP resonators with relatively high quality factors.
By incorporating transmissive metasurfaces with differ-
ent geometries into the cavity of a set of FP filters, the
round-trip phase inside the cavity is drastically modified.
Thus, the resonance wavelength (
i.e.
the filter passband)
can be tuned without changing the physical distance be-
tween the two mirrors. Similar concepts for implementa-
tion of arrays of FP filters have been previously studied.
Walls et al. have demonstrated FP filter arrays using
metallic mirrors and effective index medium created by
subwavelength patterning [21]. Filter arrays composed
of dielectric mirrors and 1D subwavelength gratings have
arXiv:1604.03167v1 [physics.optics] 11 Apr 2016
2
also been proposed [22], but, to the best our knowledge,
have not been experimentally demonstrated. Further-
more, compared with 1D subwavelength gratings, the di-
electric metasurfaces provide more control over the phase
shifts and are polarization insensitive [16, 18, 23].
II. DESIGN
To design the FP filters, we first simulate and design
transmissive dielectric metasurfaces using the rigorous
coupled wave analysis (RCWA) technique [24]. We use
transmissive dielectric metasurfaces that consist of amor-
phous silicon (
α
-Si,
n
= 3
.
40) nano-posts on a square
lattice (period: 600 nm, height: 400 nm) embedded in
low-index SU-8 (
n
= 1
.
57). The metasurface param-
eters are determined for achieving a large variation in
the transmission phase by changing the width of the
nano-posts, while the transmission is high enough within
the wavelength range from 1450 nm to 1700 nm, as plot-
ted in Fig. 2(a,b). We use DBRs as the high reflectivity
mirrors forming the FP resonator. Each of the DBRs
consists of 4 pairs of
α
-Si and SiO
2
(
n
= 1
.
47) quarter-
wavelength stacks. The simulated reflection spectrum of
such a DBR is plotted in Fig. 2(c), and shows a stop-band
in the range of ∆
λ
300 nm around
λ
= 1550 nm with
reflectivities
R >
0
.
99. When the cavity thickness is a
half integer multiple of wavelength divided by the cavity
refractive index, the FP resonance is formed inside the
cavity and allows a single Lorentzian shaped peak in the
transmission spectrum. For this work, we chose the longi-
tudinal mode number of 3 and found a single resonance
within the DBR’s stopband when the spacing between
the DBR mirrors was filled with
1
.
2-
μ
m-thick SU-8
polymer. Then, we incorporated the metasurface layers
inside the SU-8 cavity layer to introduce the phase shift,
and thus shift the resonance wavelengths of the FP res-
onators without changing the physical distances between
the mirrors (Figure 2(d)). We used the transfer ma-
trix formalism to calculate the transmission spectra for
a set of filters, using the complex transmission/reflection
coefficients for the metasurface layers obtained via the
RCWA simulations.
In Figure 2(e), the simulated transmission spectra for a
set of designed filters are plotted. For this set, the widths
of the
α
-Si nano-posts range from 120 nm to 430 nm. By
changing the widths of nano-posts array, the resonance
wavelengths of the bandpass filters vary from 1450 nm to
1700 nm, spanning a 250 nm bandwidth (∆
λ/λ
c
= 16%),
while the physical distance between the two mirrors in
each filter is fixed. The planar form of these filters allows
their fabrication using a single binary lithography step.
Each of the filters has a high transmission around the
passband due to the low loss materials used in the de-
signed nano-post metasurfaces. The square cross section
of the nano-posts and the square form of the lattice lead
to the polarization insensitivity of the metasurface layer
and the filters.
III. METHOD AND MEASUREMENT RESULTS
A. Fabrication
As a proof of concept, the designed set of filters
was fabricated on a single fused silica substrate. First,
the bottom DBR layers, a 258-nm-thick SiO
2
spacer
layer and a 400-nm-thick
α
-Si layer were deposited by
plasma-enhanced chemical vapor deposition (PECVD).
The nano-post patterns were defined by electron beam
lithography, first transferred into an aluminum oxide
hard mask using a lift-off technique, and then to the
α
-Si layer by dry etching [18]. Then, SU-8 polymer was
spun and hard-baked, planarizing the entire area on the
substrate [25]. Finally, the top DBR layers were de-
posited by PECVD over the planar SU-8 layer. The
cross-sectional scanning electron microscope image of the
fabricated structure is shown in Fig. 3(a). Two bird’s-
eye views of the
α
-Si nano-posts with two different widths
before spinning the SU-8 are also shown in Fig. 3(a) as
insets. Each of the DBRs were composed of 4 alternating
pairs of
α
-Si and SiO
2
layers (
α
-Si layers: 112 nm, SiO
2
layers: 258 nm).
B. Characterization
The fabricated bandpass filter array was characterized
by measuring the transmission spectra of the filters. A
supercontinuum source was focused onto the fabricated
filters using an objective lens, the transmitted light was
collected using another objective lens, and its spectrum
was measured using an optical spectrum analyzer. The
normalized transmission spectra were calculated by mea-
suring the spectrum without the sample. Fig. 2(e) shows
the simulated transmission spectra computed for the fab-
ricated designs, and Fig. 3(b) shows the measured trans-
mission spectra for the corresponding set of the filters
with normalization. The resonance wavelengths show
good agreement between their simulated and measured
values. The measured quality factor was
700, and
the measured absolute transmission power was 16% in
average. The transmission measured from the area hav-
ing no
α
-Si nano-posts shows similar peak transmission
values and quality factors, indicating that the relatively
low transmission and the measured linewidths of the fil-
ters are due to the loss from the fabricated DBRs. The
deposited DBR layers have significant surface roughness
leading to scattering loss. Optimization of the PECVD
deposition conditions is expected to reduce the surface
roughness of the deposited layers and improve the qual-
ity factors as well as the transmission power of the filters.
3
IV. CONCLUSION
We proposed and experimentally demonstrated a pla-
nar bandpass filter array based on vertical FP resonators.
The filters have Lorentzian shape passband, and the cen-
ter wavelength of each filter can be independently con-
trolled by changing the in-plane dimensions of a low-loss
dielectric metasurface layer inserted between two reflec-
tors. The planar geometry and the compatibility with
binary lithography process, as well as the polarization
insensitivity and large bandwidth of the proposed filter
array make it ideal for implementation of low cost on-chip
spectrometers with high resolving powers.
ACKNOWLEDGMENT
This work was supported by Samsung Electronics and
DARPA. Y. H. was supported by a Japan Student Ser-
vices Organization (JASSO) fellowship. S. M. K. was
supported by the DOE Light-Material Interactions in En-
ergy Conversion Energy Frontier Research Center funded
by the US Department of Energy, Office of Science, Of-
fice of Basic Energy Sciences under Award no. DE-
SC0001293. The device nanofabrication was performed
in the Kavli Nanoscience Institute at the California In-
stitute of Technology.
Corresponding author: A.F: faraon@caltech.edu
[1] G Minas, R F Wolffenbuttel, and J H Correia, “A lab-on-
a-chip for spectrophotometric analysis of biological flu-
ids.” Lab Chip
5
, 1303–1309 (2005).
[2] Babak Momeni, Siva Yegnanarayanan, Mohammad
Soltani, Ali A. Eftekhar, Ehsan Shah Hosseini, and Ali
Adibi, “Silicon nanophotonic devices for integrated sens-
ing,” J. Nanophotonics
3
, 031001 (2009).
[3] Christina P Bacon, Yvette Mattley, and Ronald De-
Frece, “Miniature spectroscopic instrumentation: Appli-
cations to biology and chemistry,” Rev. Sci. Instrum.
75
,
1–17 (2004).
[4] R F Wolffenbuttel, “MEMS-based optical mini- and mi-
crospectrometers for the visible and infrared spectral
range,” J. Micromech. Microeng.
15
, S145 (2005).
[5] Zhixuan Xia, Ali Asghar Eftekhar, Mohammad Soltani,
Babak Momeni, Qing Li, Maysamreza Chamanzar, Siva
Yegnanarayanan, and Ali Adibi, “High resolution on-
chip spectroscopy based on miniaturized microdonut res-
onators.” Opt. Express
19
, 12356–12364 (2011).
[6] Bernardo B. C. Kyotoku, Long Chen, and Michal Lipson,
“Sub-nm resolution cavity enhanced microspectrometer,”
Opt. Express
18
, 102–107 (2010).
[7] P. Cheben, J. H. Schmid, A. Delˆage, A. Densmore,
S. Janz, B. Lamontagne, J. Lapointe, E. Post, P. Wal-
dron,
and D.-X. Xu, “A high-resolution silicon-on-
insulator arrayed waveguide grating microspectrometer
with sub-micrometer aperture waveguides.” Opt. Express
15
, 2299–2306 (2007).
[8] Shao-Wei Wang, Changsheng Xia, Xiaoshuang Chen,
Wei Lu, Ming Li, Haiqian Wang, Weibo Zheng, and
Tao Zhang, “Concept of a high-resolution miniature spec-
trometer using an integrated filter array,” Opt. Lett.
32
,
632–634 (2007).
[9] J H Correia, M Bartek, and R F Wolffenbuttel, “High-
selectivity single-chip spectrometer in silicon for opera-
tion in visible part of the spectrum,” IEEE Trans. Elec-
tron Dev.
47
, 553–559 (2000).
[10] Arvin Emadi, Huaiwen Wu, Ger de Graaf, and Reinoud
Wolffenbuttel, “Design and implementation of a sub-nm
resolution microspectrometer based on a linear-variable
optical filter,” Opt. Express
20
, 489–507 (2012).
[11] Nada A. O’Brien, Charles A. Hulse, Donald M. Friedrich,
Fred J. Van Milligen, Marc K. von Gunten, Frank Pfeifer,
and Heinz W. Siesler, “Miniature near-infrared (NIR)
spectrometer engine for handheld applications,” in
Proc.
SPIE
, Vol. 8374 (2012) p. 837404.
[12] Jing Xiao, Fuchuan Song, Kijeong Han, and Sang-Woo
Seo, “Fabrication of CMOS-compatible optical filter ar-
rays using gray-scale lithography,” J. Micromech. Micro-
eng.
22
, 025006 (2012).
[13] Nanfang Yu and Federico Capasso, “Flat optics with de-
signer metasurfaces,” Nature Mater.
13
, 139–150 (2014).
[14] Saman Jahani and Zubin Jacob, “All-dielectric metama-
terials,” Nat. Nanotechnol.
11
, 23–36 (2016).
[15] Alexander V. Kildishev, Alexandra Boltasseva,
and
Vladimir M. Shalaev, “Planar photonics with metasur-
faces,” Science
339
, 1232009 (2013).
[16] S Vo, David Fattal, W V Sorin, Zhen Peng, Tho Tran,
M Fiorentino, and R G Beausoleil, “Sub-Wavelength
Grating Lenses With a Twist,” IEEE Photonics Technol.
Lett.
26
, 1375–1378 (2014).
[17] Dianmin Lin, Pengyu Fan, Erez Hasman, and Mark L
Brongersma, “Dielectric gradient metasurface optical el-
ements.” Science
345
, 298–302 (2014).
[18] Amir Arbabi, Yu Horie, Alexander J Ball, Mahmood
Bagheri,
and Andrei Faraon, “Subwavelength-thick
lenses with high numerical apertures and large efficiency
based on high-contrast transmitarrays,” Nat. Commun.
6
, 1–6 (2015).
[19] Amir Arbabi, Yu Horie, Mahmood Bagheri, and Andrei
Faraon, “Dielectric metasurfaces for complete control of
phase and polarization with subwavelength spatial res-
olution and high transmission.” Nat. Nanotechnol.
10
,
937–943 (2015).
[20] Jacob B Khurgin, “How to deal with the loss in plas-
monics and metamaterials.” Nat. Nanotechnol.
10
, 2–6
(2015).
[21] K Walls, Q Chen, J Grant, S Collins, D R S Cumming,
and T D Drysdale, “Narrowband multispectral filter set
for visible band,” Opt. Express
20
, 21917–21923 (2012).
[22] Sumanth Kaushik and Brian R. Stallard, “Two-
dimensional array of optical interference filters produced
by lithographic alterations of the index of refraction,” in
Proc. SPIE
, Vol. 2532 (1995) pp. 276–281.
[23] Amir Arbabi, Mahmood Bagheri, Alexander J. Ball,
Yu Horie, David Fattal, and Andrei Faraon, “Controlling
the phase front of optical fiber beams using high contrast
metastructures,” in
Lasers and Electro-Optics (CLEO),
2014 Conference on
(Optical Society of America, 2014)
p. STu3M.4.
4
[24] Victor Liu and Shanhui Fan, “S4: A free electromagnetic
solver for layered periodic structures,” Comput. Phys.
Commun.
183
, 2233–2244 (2012).
[25] Yu Horie, Amir Arbabi, Seunghoon Han,
and An-
drei Faraon, “High resolution on-chip optical filter array
based on double subwavelength grating reflectors,” Opt.
Express
23
, 29848–29854 (2015).
5
mirror
mirror
metasurface
λ
1
λ
2
λ
3
FIG. 1. Schematic of the proposed bandpass filter array composed of vertical DBR-based micro-cavities, in which transmissive
dielectric metasurface layers are inserted as phase shifting layers to tune their resonance wavelengths over a broad bandwidth.
150
200
250
300
350
400
Si pos
t width (nm
)
0.0
0.2
0.4
0.6
0.8
1.0
Phase (2π)
SU-8
α-Si nano-posts
SiO
2
150
200
250
300
350
400
Si pos
t width (nm
)
0.0
0.2
0.4
0.6
0.8
1.0
Transm
issi
on
1.45
μm
1.5 μm
1.55
μm
1.6 μm
1.65
μm
1.7 μm
1450
1500
1550
1600
1650
1700
W
ave
lengt
h (nm
)
0.990
0.992
0.994
0.996
0.998
1.000
Re
ectivity
top DBR
botto
m
α-Si nano-posts
(dielectric metasurface)
SU-8 cavity
top DBR
Transmission
Reection
Input
bottom DBR
fused silica substrate
1450
1500
1550
1600
1650
1700
W
ave
lengt
h (nm
)
0.0
0.2
0.4
0.6
0.8
1.0
Transm
issi
on
(a)
(b)
(c)
(e)
(d)
FIG. 2. (a) Transmission round-trip phase, and (b) transmission intensity induced by
α
-Si nano-posts as a function of post
width for different wavelengths. The inset figure in (a) represents the refractive index profile of the dielectric metasurface
considered. (c) The simulated reflection spectrum of DBRs. (d) Schematic illustration of the proposed filters. The filters are
composed of two DBR mirrors and a phase shifting dielectric metasurface layer. The metasurface is made of a uniform array of
square cross section nano-posts. (e) Simulated transmission spectra of a set of filters as shown in (d) with different nano-post
widths.