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
faraon@caltech.edu
Abstract:
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.
© 2016 Optical Society of America
OCIS codes:
(050.6624) Subwavelength structures; (050.2230) Fabry-Perot; (130.7408)
Wavelength filtering devices.
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| DOI:10.1364/OE.24.011677
| OPTICS
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1. Introduction
Spectroscopy is an essential tool in bio-chemical sensing applications, material characteriza-
tion, and multiple areas of scientific research. Modern spectrometers based on diffraction grat-
ings 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 inevitably bulky as the resolution of the spectrometer scales inversely with optical path
length, and thus are not suitable for miniaturization. For this purpose, several integrated op-
tics approaches have been explored [2–4], such as on-chip frequency filtering based on micro-
resonators [5], integrated diffraction gratings [6], and arrayed waveguide gratings [7]. However,
in many applications the optical 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 spectrom-
eters. 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 in-
formation by measuring intensities of the filtered 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 varying
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
#262916
Received 12 Apr 2016; revised 10 May 2016; accepted 17 May 2016; published 19 May 2016
(C)
2016
OSA
30
May
2016
| Vol.
24,
No.
11
| DOI:10.1364/OE.24.011677
| OPTICS
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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 demonstrate a new method to effectively vary
the central wavelengths of a FP filter set by inserting a transmissive dielectric 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 polarization of light [13–15]. One
particularly interesting class of metasurfaces are based on high index nano-posts surrounded
by a low index medium, which allow both high transmission as well as phase control capa-
bility by designing the geometry of the nano-posts. So far, various 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 resonant applications. As schemat-
ically shown in Fig. 1, the dielectric metasurface layers are incorporated in vertical FP res-
onators with relatively high quality factors. By incorporating transmissive metasurfaces with
different 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 between the two mirrors. Similar concepts for imple-
mentation 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 also been proposed [22], but, to the best our knowledge, have not been experimentally
demonstrated. Furthermore, compared with 1D subwavelength gratings, the dielectric metasur-
faces provide more control over the phase shifts and are polarization insensitive [16, 18, 23].
2. 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 amorphous 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
parameters 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 plotted in Figs. 2(a) and 2(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
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.
#262916
Received 12 Apr 2016; revised 10 May 2016; accepted 17 May 2016; published 19 May 2016
(C)
2016
OSA
30
May
2016
| Vol.
24,
No.
11
| DOI:10.1364/OE.24.011677
| OPTICS
EXPRESS
11679
150
200
250
300
350
400
Si post 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 post width (nm)
0.0
0.2
0.4
0.6
0.8
1.0
Transmi
ssion
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
avele
ngth (nm)
0. 990
0. 992
0. 994
0. 996
0. 998
1. 000
Reectivity
top DBR
bottom
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
avele
ngth (nm)
0.0
0.2
0.4
0.6
0.8
1.0
Transmi
ssion
(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 sim-
ulated 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) Simu-
lated transmission spectra of a set of filters as shown in (d) with different nano-post widths.
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
longitudinal 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 resonators without changing the physical
distances between the mirrors as shown in Fig. 2(d). We used the transfer matrix 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 Fig. 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 fabrica-
tion 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 designed nano-post metasurfaces. The
square cross section of the nano-posts and the square form of the lattice lead to the polarization
#262916
Received 12 Apr 2016; revised 10 May 2016; accepted 17 May 2016; published 19 May 2016
(C)
2016
OSA
30
May
2016
| Vol.
24,
No.
11
| DOI:10.1364/OE.24.011677
| OPTICS
EXPRESS
11680