# Broadband polarization insensitivity and high detection efficiency in high-
fill-factor superconducting microwire single-photon detectors

Dileep V. Reddy<EMAIL_ADDRESS>Department of Physics, University of
Colorado, Boulder, Colorado 80309, USA  National Institute of Standards and
Technology, Boulder, Colorado 80305, USA  Negar Otrooshi  Department of
Physics, University of Colorado, Boulder, Colorado 80309, USA  National
Institute of Standards and Technology, Boulder, Colorado 80305, USA  Sae Woo
Nam  National Institute of Standards and Technology, Boulder, Colorado 80305,
USA  Richard P. Mirin  National Institute of Standards and Technology,
Boulder, Colorado 80305, USA  Varun B. Verma  National Institute of Standards
and Technology, Boulder, Colorado 80305, USA

###### Abstract

Single-photon detection via absorption in current-biased nanoscale
superconducting structures has become a preferred technology in quantum optics
and related fields. Single-mode fiber packaged devices have seen new records
set in detection efficiency, timing jitter, recovery times, and largest
sustainable count rates. The popular approaches to decreasing polarization
sensitivity have thus far been limited to introduction of geometrically
symmetric nanowire meanders, such as spirals and fractals, in the active area.
The constraints on bending radii, and by extension, fill factors, in such
designs limits their maximum efficiency. The discovery of single-photon
sensitivity in micrometer-scale superconducting wires enables novel meander
patterns with no effective upper limit on fill factor. This work demonstrates
simultaneous low-polarization sensitivity ($1.02\pm 0.008$) and high detection
efficiency ($>91.8\%$ with $67\%$ confidence at $2\times 10^{5}$ counts per
second) across a $40$ nm bandwidth centered at 1550 nm in 0.51 $\mu\text{m}$
wide microwire devices made of silicon-rich tungsten silicide, with a $0.91$
fill factor in the active area. These devices boasted efficiencies of
96.5-96.9% $\pm$ 0.5% at $1\times 10^{5}$ counts per second for 1550 nm light.

##  I Introduction

Superconducting nanowire single-photon detectors (SNSPDs) are a premier
technology for applications that require fast, high-efficient detection and
high-timing resolution. Their utility spans such diverse areas as fundamental
research Hochberg  _et al._ (2019), communications Mao  _et al._ (2018); Chen
_et al._ (2020), metrology Slussarenko  _et al._ (2017), remote sensing Zhu
_et al._ (2017), materials research Chen  _et al._ (2018), and astronomy
Zhuang, Zhang, and Shapiro (2018); Khabiboulline  _et al._ (2019). Such
detectors in single-mode fiber-packaged form have been fruitfully employed in
several ground-breaking quantum-optics experiments Shibata, Honjo, and Shimizu
(2014); Dixon  _et al._ (2014); Shalm  _et al._ (2015); Takesue  _et al._
(2015); Najafi  _et al._ (2015); Jin  _et al._ (2015); Weston  _et al._
(2016); Saglamyurek  _et al._ (2016). Within the past five years, fiber-
packaged SNSPDs have seen new records set in such diverse figures-of-merit as
system-detection efficiency (SDE) Reddy  _et al._ (2020); Hu  _et al._ (2020);
Chang  _et al._ (2021), timing jitter Korzh  _et al._ (2020), and low dark
counts Shibata  _et al._ (2017). The field is making advances towards joint
high performance in multiple metrics simultaneously. One such goal is high SDE
coupled with low polarization sensitivity.

We define polarization sensitivity (PS) for a device as the ratio of the
maximum to minimum SDE across all input polarization states of photons.
Traditional fiber-coupled SNSPDs have consisted of nanowire meanders covering
the active area (where photons are expected to be absorbed) in a zig-zag
pattern. The geometry forms a grating-like structure of parallel strips of
superconductor spaced by a dielectric. Consequently, SNSPDs have inherently
possessed a non-unity PS Anant  _et al._ (2008); Redaelli  _et al._ (2016);
Zheng  _et al._ (2016); Redaelli  _et al._ (2017). While such meanders allow
for unity PS at a specific wavelength via cleverly engineered anti-reflection
coatings Reddy  _et al._ (2019), reliable unity-PS across significant
bandwidths has remained unrealized in high-efficiency devices. Applications
that require high efficiency and throughput Shalm  _et al._ (2015); Ghafari
_et al._ (2019); Shalm  _et al._ (2021) often use polarization controllers
before directing light to the detectors, which is a significant source of
loss. High-SDE devices with either unity, or infinite PS (meaning no
sensitivity to one polarization) would mitigate such issues. Such detectors
would also close a security loophole in standard phase-encoding quantum-key
distribution implementations Wei  _et al._ (2019).

Historical approaches to achieving unity PS have sought to spatially
symmetrize the nanowire-meander geometries. PS values of 1.02-1.04 have been
measured in spiral SNSPDs since 2008 Dorenbos  _et al._ (2008); Henrich  _et
al._ (2013); Huang  _et al._ (2017) with limited SDE. In 2012, Verma et al.
fabricated a two-layer 3D-SNSPD with perpendicularly oriented meanders, and
showed a PS of 1.02 with an SDE of 87.7% Verma  _et al._ (2012). Space-filling
fractals such as Sierpinski or Hilbert curves have also been studied as a
means of introducing discrete rotational symmetries into nanowire meanders Gu
_et al._ (2015). The fractal approach has seen steady improvement Chi  _et
al._ (2018); Meng  _et al._ (2020a), and has recently realized a PS of $1.00$
at 91% efficiency Meng  _et al._ (2020b). The introduction of turns and
hairpin bends in the active area renders the outer-radii regions of such
fractal-meander nanowires relatively insensitive to photons Clem and Berggren
(2011); Meng  _et al._ (2020b), thus limiting their efficiency. Other
innovations that do not symmetrize the meander geometry have focused on high-
refractive index dielectric media surrounding the nanowires to reduce the
effective grating-index contrast Redaelli  _et al._ (2016); Zheng  _et al._
(2016); Redaelli  _et al._ (2017); Xu  _et al._ (2017); Mukhtarova  _et al._
(2018). Alternatively, instead of minimizing PS, deliberate introduction of
grating-like asymmetries in the optical stack using dielectric or metal slots
to maximize PS have also been considered Xu  _et al._ (2018); Li and Jiao
(2019).

Figure 1:  (a) Simulated current density in a candelabra-style hair-pin bend
McCaughan  _et al._ (2021) (see supplementary). (b) SEM image of section of
cadelabra meander nanowire showcasing high fill-factor. (c) Optical microgram
of device chip showing speed-up PdAu resistor.

The year 2020 witnessed several observations of micrometer-wide
superconducting structures being sensitive to single photons when current
biased. While such scales were trivial for higher-energy photons such as
X-rays Yang  _et al._ (2021), Korneeva et al. showed the first such instance
for near-infrared (IR) photons Korneeva  _et al._ (2020). Specifically, they
observed that 3.3 nm thick, 2 $\mu\text{m}$ wide molybdenum silicide (MoSi)
microstrips could detect photons of wavelength 1 $\mu\text{m}$. Chiles et al.
modified their tungsten silicide (WSi) recipe to increase the stoichiometric
proportion of silicon, and demonstrated near-IR photon sensitivity in wires as
wide as 4 $\mu\text{m}$ Chiles  _et al._ (2020). Similar results have been
observed in niobium nitride (NbN) Vodolazov  _et al._ (2020). This new result
has spurred interest in gaining a better understanding of the photon-detection
mechanism in such devices. It has also enabled a new class of superconducting
microwire single-photon detectors (SMSPDs), resulting in new active-area
records being set in free-space coupled devices Charaev  _et al._ (2020); Lita
_et al._ (2021); Steinhauer, Gyger, and Zwiller (2021).

Superconducting microwires have already been used to make spiral-meander
SMSPDs by Xu et al. Xu  _et al._ (2021), acheiving a PS of 1.03 with 92.2%
efficiency at the wavelength 1550 nm. The maximum fill factor they reported
was 0.8. The presence of curvature in the current’s path in the active area is
still suboptimal for SDE due to current crowding Yang  _et al._ (2009); Clem
and Berggren (2011). The traditional meander design (parallel strips of
superconductor separated by dielectric medium) when conjoined with micrometer-
scale wire widths offers a trivial means of reaching near-unity fill factors.
This would compensate for the refractive-index grating effect that
differentially scatters orthogonal polarizations Anant  _et al._ (2008);
Redaelli  _et al._ (2016); Zheng  _et al._ (2016); Redaelli  _et al._ (2017).
The minimum gap between parallel, straight segments of superconductor in a
traditional meander is limited by the resolution of the electron-beam writing
and etch process, and is typically on the order of 40-100 nm. At such gap
widths, the current crowding at the inner radii of the hairpin bends Clem and
Berggren (2011); Baghdadi  _et al._ (2021); Xiong  _et al._ (2021) of a
traditional meander would be exacerbated for microwires, causing such a device
to latch at a very low bias current Yang  _et al._ (2009). The current-
crowding effect is nullified if the fill-factor at a hairpin bend is at or
below 0.33 Clem and Berggren (2011); Jönsson  _et al._ (2021).

In this work, we introduce the candelabra meander (see supplementary), which
utilizes optimized 90-degree and 180-degree bending primitives (defined in the
python CAD-layout library phidl McCaughan  _et al._ (2021)) to slowly turn the
microwire outside of the active area, enabling us to maintain a high active-
area fill factor whilst minimizing current crowding (see fig. 1(a)). The
design is inspired by similar structures used in optical waveguides, where a
specific length is to be maintained within an area/footprint constraint while
minimizing optical loss at the bends. This solution has recently been
independently proposed by Jönsson et al. Jönsson  _et al._ (2021). The
candelabra meander requires a longer length of microwire to cover the same
active area as a traditional meander (see fig. 1(b)), resulting in increased
kinetic inductance. Using the silicon-rich tungsten silicide (WSi) recipe
developed by Chiles et al. Chiles  _et al._ (2020), we fabricated fiber-
coupled, candelabra-meander SMSPDs with 0.51 $\mu\text{m}$ wide wires and a
0.91 fill factor in the active area. These meanders were embedded in the
Bragg-grating and three-layer anti-reflection-coating based optical stack
which was previously employed to break the SDE record Reddy  _et al._ (2020).
We show that these devices have a near-unity PS of better than 1.02 and a high
SDE of better than 91.8% (67% confidence at $2\times 10^{5}$ counts per
second) over a wide bandwidth of 40 nm centered at a wavelength of 1550 nm,
and SDEs in the range of 96.5-96.9% $\pm$ 0.5% (at $1\times 10^{5}$ counts per
second) at 1550 nm. This paves the way for utilization of superconducting
microwires for lowering polarization sensitivity in highly-efficient single-
photon detectors.

##  II Fabrication and experimental setup

The SMSPDs presented here were fabricated on a 76.2 mm diameter silicon wafer.
Thirteen alternating layers of silicon dioxide (SiO2, thickness $266.75\pm
0.84$ nm) and amorphous silicon ($\alpha$Si, thickness $141.7\pm 0.27$
nm)–starting with SiO2–were deposited onto the substrate using plasma-enhanced
chemical vapor deposition (PECVD), forming a 6.5-period Bragg reflector at
1550 nm. We then deposited gold terminals and 100 $\Omega$ palladium-gold
(PdAu) speed-up resistors Reddy  _et al._ (2020) (see fig. 1(c)) using a
photolithographic lift-off process. We then deposited a 2.2 nm layer of
silicon-rich WSi Chiles  _et al._ (2020) with a 2-nm thick $\alpha$Si capping
layer using a magnetron sputtering tool. A candelabra meander for $0.51$
$\mu\text{m}$ wide wires and $50$ nm gap width was then patterned onto an
electron-beam resist layer.

Due to the ultra-thin nature of the WSi layer (which limits amount of light
absorption per transmissive pass), we needed to cover a larger active area
than in comparable optical stacks that utilize other materials and thicknesses
Reddy  _et al._ (2020) to account for the extra beam divergence. Therefore,
the candelabra meander covered a rhomboidal active area with a minor diagonal
of length $80$ $\mu\text{m}$ and a major diagonal of length $174$
$\mu\text{m}$ (the shortest possible major diagonal for a given minor diagonal
length, fill factor and bend radius). The meander pattern was then transferred
onto the WSi layer using SF6-based reactive-ion etching. We then deposited a
three-layer anti-reflection (AR) coating of $\alpha\text{Si}$ ($28\pm 0.27$
nm), SiO2 ($123.1\pm 0.84$ nm), and $\alpha\text{Si}$ ($183.5\pm 0.27$ nm) in
that order onto the microwire layer. These thicknesses were determined to
minimize reflection of vertically incident 1550 nm light using rigorous
coupled-wave analysis (RCWA) simulations Moharam and Gaylord (1981); Li  _et
al._ (2016). Vias were then selectively etched into the AR-coating to enable
wirebonding access to the gold pads. Deep-reactive-ion etching was then used
to etch through the wafer substrate in a keyhole pattern (see fig. 1(c)),
which enabled easy liberation of the device dies and their mounting into the
fiber-ferrule self-aligning package developed by Miller et al. in 2011 Miller
_et al._ (2011). SMF28e+ fiber pigtails terminating at AR-coated, 2.5-mm-
diameter ceramic ferrules were then inserted into the self-aligning packages.

Figure 2:  (a) The raw amplified RF-pulse from device D1, as well as twenty
comparator-conditioned pulses vertically scaled-down by a factor of 10. (b)
The counts versus bias-current curve at 1550 nm for device D1 at about
$2.3\times 10^{5}$ detections per second. (c) The system-detection
efficiencies (SDE) for various incident photon rates for all three devices
biased at 5 $\mu$A, for 1550 nm photons.

Four devices from a single wafer were mounted inside a sorption-based cryostat
and cooled to 720-730 mK. The devices were electrically accessible through SMA
ports, and optically accessible through splicing into the bare ends of the
fiber pigtails outside of the cryostat. The system-detection efficiency (SDE)
reported here is defined as the probability for the device to register a
detection given that a photon is launched into the fiber pigtail Reddy  _et
al._ (2020). All measurements were performed using a highly attenuated,
tunable, continuous-wave laser passed through a 1x2 optical switch and two
different types of polarization controllers. An all-fiber polarization
controller was used for algorithmic polarization optimizations at various
wavelengths. A free-space polarization controller was later used to fully scan
the Bloch sphere at 1550 nm. A NIST-calibrated power meter, and a rack-
mounted, “monitoring” power meter were used for all equipment calibrations
Reddy  _et al._ (2020). The devices were quasi-current-biased using a bias
tee, a 100 k$\Omega$ series resistor, and a programmable voltage source. The
detection pulses were amplified using two room-temperature RF amplifiers,
conditioned into square pulses using comparators, and plugged into an
electronic pulse counter. The design, fabrication, calibration procedures, and
error analysis are described in greater detail in the supplementary material.

##  III Measurement results and discussion

Figure 3:  SDE versus wavelength for all three detectors (D1, D2, D3) at
count-rates of $2\times 10^{5}$ per second. The rates were maximized and
minimized (see legend) at constant incident photon rate using an all-fiber
polarization controller and the python nlopt library. Figure 4:  Normalized
count rates at a constant photon rate (of about $2.3\times 10^{5}$ per second)
with polarization state varied over the entire Bloch sphere using a free-space
polarization controller. See subplot titles for detector numbers.

One out of the four mounted devices was found to be electrically open when
cooled down. We therefore only present the results for the remaining three
devices, labeled D1, D2, and D3. The kinetic inductance of 2.2-nm thick, Si-
rich WSi was measured to be $275$ $\text{pH}/\text{sq.}$, which is nearly
thrice the typical value for SNSPDs. This, along with the bigger active area
required, counteracts the gains made in decreasing total inductance through
micrometer-scale wire widths. We fabricated a 100 $\Omega$ speed-up resistor
in series with the microwire to gain a factor of two in recovery time Reddy
_et al._ (2020), yielding a value of $\approx 120$ ns. The width of the
comparator-conditioned square pulses averaged to around $175$ ns (see fig.
2(a)). The square pulses showed high variance in temporal width due to
electronic noise affecting the hysteresis-voltage threshold trigger set at the
comparators. Figure 2(b) shows the counts versus current bias for detector D1
at $2.3\times 10^{5}$ counts per second and 1550 nm photon wavelength. All
three detectors showed internal saturation at such count rates, with a dark-
count rate of $10^{4}$ per second when biased at 5 $\mu\text{A}$.

Figure 2(c) shows the measured SDE at optimal polarization (optimized using
the all-fiber polarization controller and the python nlopt library) versus
1550 nm photon rate for all three devices. The pile-up effect resulting from
the $\approx 175$ ns conditioned-square-pulse reset time Liu  _et al._ (2019);
Li  _et al._ (2019), along with any residual device nonlinearity, results in a
detection-rate dependent SDE. The standard error bars on the SDE estimate are
$\pm$(0.39-0.42) % at a photon rate of $2.3\times 10^{5}$ per second, and
$\pm$(0.49-0.52) % at photon rates of $1\times 10^{5}$ per second (see
supplementary material). The SDE at photon rates of $10^{5}$ per second are
around 96.5-96.9 % across the three devices, which is comparable to high-
efficiency SNSPDs with 100 ns recovery times Reddy  _et al._ (2020). The SDE
vs. photon rate trend line indicates that these devices are asymptotically
fully efficient at ultra-low photon rates, and that no light is being lost due
to beam divergence. We designate a rate of $2\times 10^{5}$ per second as a
conservative, dominant regime of application, and report efficiencies and
polarization sensitivities at these light levels in the abstract and
conclusion of this document. Furthermore, we report all efficiencies at a bias
current of $5$ $\mu\text{A}$, which is about 94-96% of the switching current
across all three devices.

In fig. 3 we plot the SDE for all three devices measured at a photon rate of
$2\times 10^{5}$ per second across the wavelength range of 1525-1575 nm. The
nlopt python library was used to find the settings for the all-fiber
polarization controller that maximized and minimized the SDE at a given
incident light level. All three detectors showed mean SDEs greater than 92% in
the 1530-1570 nm wavelength range. For reference, the maximum possible SDE
(limited due to pile-up effect Coates (1968); Walker (2002)) for devices with
a dead-time of 175 ns at a continuous input photon rate of $2\times 10^{5}$
per second is 96.5%. This procedure indicated that the all-fiber-controller-
derived PS did not exceed 1.006 across the entire bandwidth measured. The PS
in some instances was measured to be very close to unity, resulting in some
difficulty in optimization for the nlopt library. The optimization step for
device D3 at 1545 nm took nearly half-an-hour to halt for both maximization
and minimization, resulting in a “min. pol.” mean-SDE value exceeding the
“max. pol.” mean-SDE value.

The all-fiber polarization controller is not guaranteed to sample the entire
space of polarization states. Therefore we replaced it with a free-space
polarization controller, which transmits the light in free-space through a
linear polarizer, a quarter-wave plate, and a half-wave plate, all three of
which are mounted on controllable rotary mounts in that order. This controller
was used to scan the entire Bloch-sphere of polarization states. Figure 4
shows plots for transmission-corrected (see supplementary material) counts
normalized to the maximum counts across $21\times 21$ equally spaced
polarization settings on the Bloch sphere for all three detectors. The counts
were measured at an average count rate of $2.3\times 10^{5}$ per second while
the detectors were biased at 5 $\mu\text{A}$, and the measurement took 20
minutes for each device. Both dark counts and laser power had to be monitored
at each polarzation setting. A further 20 minutes was required after each
measurement session (per device) to measure the free-space polarization
controller transmission correction using two power meters at classical light
levels (see supplementary material). This measurement yielded PS of
$1.018-1.021\pm 0.008$ for the three devices without any smoothing function
applied to the plotted data. We report a conservative value of $1.02\pm 0.008$
for PS for our devices in the abstract and conclusion of this document.

The microwire recipe used in these devices Chiles  _et al._ (2020) required
the superconducting layer to be ultra-thin at around 2.2 nm. This is thinner
than typical for microwire devices explored thus far Korneeva  _et al._
(2020); Vodolazov  _et al._ (2020); Charaev  _et al._ (2020); Xu  _et al._
(2021). This resulted in a larger active-area requirement, causing a large
kinetic inductance. We employed a speed-up resistor to improve the recovery
time. This, along with the substantial length of the candelabra meander,
resulted in a large timing jitter of 1.5 ns. The candelabra meander, when used
in conjunction with superconducting microwires, can trivially hit near-unity
PS values Meng  _et al._ (2020b) due to their large fill-factors in the active
area. Additionally, the absence of bends within the active area can ensure
that the microwires are photon sensitive across their entire lateral width,
enabling simultaneous near-unity-PS and high-SDE single-photon detection
across a wide range of wavelengths. This capability will prove fruitful for
quantum optics experiments involving wavelength-division multiplexing, or
time-frequency entanglement spanning the low-loss C-band from fiber-optical
communications.

##  IV Conclusion

We introduced the candelabra meander as a new geometry for superconducting
nanowire and microwire single-photon detectors. This meander enables high-fill
factors in the active area without the deleterious effects of current crowding
at the hairpin bends that plagued the traditional meander geometry. We
utilized this in the fabrication of WSi-based SMSPDs with 0.51 $\mu\text{m}$
wide microwires and a fill factor of 0.91 in the active area. We embedded the
SMSPDs in the Bragg-reflector-based optical stack optimized for high
efficiency detection of 1550 nm photons. We then fiber-packaged these devices
and measured their polarization sensitivities and system-detection
efficiencies at various wavelengths and photon rates in the near-IR region. We
showed that this design achieves a PS of $1.02\pm 0.008$ and high efficiencies
of greater than 92% across a 40 nm bandwidth centered at 1550 nm. This
furthers the goal of development of fiber-coupled single-photon detectors with
joint high performance for multiple measures.

##  V Data availability statement

All of the experimental data gathered during the measurements made for these
results are available on a Zenodo repository:
https://doi.org/10.5281/zenodo.6036210. Copies of the same can be provided by
the authors upon request. The data and the python code for processing and
plotting will be provided as a zip-archive file (SHA-1
91599a67964d30b695b50b4719985533e98869a0) with a digital signature from the
primary author (gpg fingerprint: CC49 3CCF 1104 0DC7 36C4 5A7C E4E5 0022 5ED1
7577).

##  VI Acknowledgments

The authors would like to acknowledge Igor Veyshenker for providing us with
power-meter calibration. We thank Dr. Gautam A. Kavuri for help with timing-
jitter measurements. We thank Prof. Juliet Gopinath and her group for
accommodating our cryostat and experimental setup in their laboratory space in
the EECE department at University of Colorado, Boulder.

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