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To achieve photon-pair generation scaling, we optimize the quality factor of microring resonators for efficient continuous-wave-pumped spontaneous four-wave mixing. Numerical studies indicate that a high intrinsic quality factor makes high pair rate and pair brightness possible, in which the maximums take place under overcoupling and critical-coupling conditions, respectively. We fabricate six all-pass-type microring resonator samples on a silicon-on-insulator chip involving gap width as the onl
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Generation rate scaling: the quality factor
optimization of microring resonators
for photon-pair sources
KAI GUO,
1,
*XIAODONG SHI,
2
XIAOLIN WANG,
1
JUNBO YANG,
3
YUNHONG DING,
2
HAIYAN OU,
2
AND YIJUN ZHAO
1
1
College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410073, China
2
Department of Photonics Engineering, Technical University of Denmark, Kgs. Lyngby 2800, Denmark
3
Center of Material Science, College of Liberal Arts and Sciences, National University of Defense Technology, Changsha 410073, China
*Corresponding author: guokai07203@hotmail.com
Received 17 January 2018; revised 27 March 2018; accepted 29 March 2018; posted 4 April 2018 (Doc. ID 320070); published 23 May 2018
To achieve photon-pair generation scaling, we optimize the quality factor of microring resonators for efficient
continuous-wave-pumped spontaneous four-wave mixing. Numerical studies indicate that a high intrinsic quality
factor makes high pair rate and pair brightness possible, in which the maxim ums take place under overcoupling
and critical-coupling conditions, respectively. We fabricate six all-pass-type microring resonator samples on a
silicon-on-insulator chip involving gap width as the only degree of freedom. The signal count rate, pair brightness,
and coincidence rate of all the samples are characterized, which are then compared with the modified simulations
by taking the detector saturation and nonlinear loss into account. Being experimentally validated for the first time
to the best of our knowledge, this work explicitly demonstrates that reducing the round-trip loss in a ring cavity
and designing the corresponding optimized gap width are more effective to generate high-rate or high-brightness
photon pairs than the conventional strategy of simply increasing the quality factor.
© 2018 Chinese Laser Press
OCIS codes: (190.4380) Nonlinear optics, four-wave mixing; (270.0270) Quantum optics; (190.4360) Nonlinear optics, devices.
https://doi.org/10.1364/PRJ.6.000587
1. INTRODUCTION
A quantum-correlated photon-pair source is a key resource in
research of quantum optics such as quantum information
processing [1] and quantum communication [2]. Thereinto,
the most mature technology is quantum key distribution
(QKD), where the nature of correlated photon pairs is applied
to suffice high-security communication [3–7]. Sources capable
of QKD are required to emit single photons in a probabilistic
manner with low noise, preferably in the telecom wavelength
range, to benefit from the compatibility of optical fiber net-
works [8]. Moreover, the single photon generated from sponta-
neous nonlinear processes has a naturally correlated twin
photon, which makes it possible to apply the detection of
one photon (signal) to herald the existence of the other (idler).
While the initially heralded photon-pair sources have been
demonstrated via spontaneous downconversion in optical crys-
tals [9] or quasi-matched waveguides [10], and via spontaneous
four-wave mixing (SpFWM) in optical fibers [8,11], a number
of experiments were carried out in the past decade via SpFWM
in integrated waveguide platforms, of which the material can be
crystalline silicon [12–14], amorphous silicon [15], silica [16],
silicon nitride [17], and AlGaAs [18]. Integrated waveguides
often have large refractive index contrast leading to strong light
confinement and high nonlinear interaction, which enables
efficient photon-pair generation within a few millimeters.
Moreover, by employing either butt-coupled [19] or vertical-
coupled approaches [20], integrated waveguides are compatible
with fiber-based systems; thus, it can be applied as the nonlin-
ear medium of photon-pair sources instead of optical fibers, to
avoid broadband spontaneous Raman scattering noise [11]. In
addition, thanks to the mature fabrication methods of semicon-
ductors and integrated circuits, which enable a variety of func-
tionalities [21], efficient quantum communication systems are
in the progress of on-chip integration [22,23].
Although photon-pair sources using SpFWM in integrated
waveguides are often driven by a pulsed pump, the continuous-
wave (CW) pump, with advantages of cheaper, more stable, and
especially easier on-chip integration, is also widely employed.
The narrow linewidth of CW pumps gives rise to strong spec-
tral anticorrelation and projects the generated photon pairs into
a classi cal spectral mixture [24,25], which is desired for special
applications such as time–energy entanglement [26–28],
wavelength-multiplexed quantum communication [29,30],
and covert quantum communication [31,32]. Moreover, pho-
ton-pair sources capable of long-distance quantum communi-
cation are required to have a high pair rate, which corresponds
Research Article
Vol. 6, No. 6 / June 2018 / Photonics Research 587
2327-9125/18/060587-10 Journal © 2018 Chinese Laser Press
to vast photon pairs for cryptology coding, huge loss tolerance
for long-distance transmission, and enough photon pairs for
cryptology decoding. High pair brightness, corresponding to
high pair rate spectral density driven by specific pump power,
is also desired because a narrow photon-pair bandwidth does
not only make easier entanglement-based QKD but also makes
the promotion of quantum key rate possible by applying dense
wavelength division multiplexing. Noteworthily, the anticorre-
lation for CW-pumped sources can be avoided by using narrow
bandwidth filtering. However, it comes at the cost of reducing
photon pairs, where the pair brightness may become lower. As
shown in Ref. [14], by applying narrow-bandwidth (0.4 nm)
filtering to a CW-pumped source using a silicon strip wave-
guide, the highest pair rate can reach 1.6 × 10
6
Hz; however,
the correspo nding pair brightness of 4.0 × 10
5
s · mW · nm
−1
remains the same order of magnitude as that in other studies
[13,33]. A valid approach facilitating high pair brightness is
to use microring resonators (MRRs) instead of straight wave-
guides, which provides not only narrow-bandwidth filtering
but also strong cavity enhancement. Therefore, a number of
experiments were carried out using different MRR designs,
which achieved 1 to 2 orders of magnitude higher pair bright -
ness but with an ultrasmall footprint [34–41].
Although MRR has shown the capability of photon-pair
generation, it lacks a normative evaluation of the waveguide
design, for photon-pair generation in MRR of high pair rate
and high pair brightness. Moreover, a solid understanding of
the key parameters of different MRR structures, especially
the quality factor, is significant, based on which the optimiza-
tion may put forward an approach of generation rate scaling.
The quality factor is given by [42]
Q
λ
res
Δλ
, (1)
where λ
res
and Δλ denote the resonance wavelength and its full
width at half-maximum (FWHM), respectively. More specifi-
cally, for an all-pass-type MRR consisting of a bus waveguide
and a ring cavity, the total quality factor obtained from the
transmittance of the bus waveguide is jointly determined by
the round-trip loss in the ring cavity, which is quantified by
the intrinsic quality factor
Q
i
ω
αv
g
(2)
and the coupling efficiency between two components, which is
quantified by the external quality factor
Q
e
2ωπR
jκj
2
v
g
, (3)
where α denotes the round-trip loss coefficient, v
g
denotes the
light group velocity in the ring cavity, R denotes the radius of
the ring cavity, and κ denotes the coupling coefficient [43]. The
quality factor given by Eq. (1) follows
1
Q
1
Q
e
1
Q
i
: (4)
From previous studies [41,44,45], the pair rate N
c
has a
third-order polynomial dependence on Q, which indicates
the larger quality factor, the better performance. However, these
studies omit the impact of round-trip loss that results in
Q Q
e
and present an approach of pair rate scaling by simply
increasing the gap width g. Although Ref. [40] shows that N
c
has a seventh-order polynomial dependence on Q by taking all
types of loss into account and demonstrates good agreement
between simulations and measurements, their discussion based
on only one MRR does not present the potential quality factor
optimization that facilitates a higher pair rate. In addition, by
trading off pair rate and photon-pair bandwidth, it is valid to
achieve higher pair brightness B.
In this paper, we demonstrate the scaling approaches of
pair rate and pair brightness, respect ively, by involving Q
e
and Q
i
as degrees of freedom [46]. We fabricate six all-pass-
type MRRs on a silicon-on-insulator (SOI) chip with different
g and characterize the photon-pair sources using all samples
to verify the numerical predictions, taking the impact of non-
linear loss in SOI platforms and detector saturation into
consideration. In the end, the future direction for efficient
photon-pair generation in all types of microcavity platforms
is presented.
2. THEORETICAL APPROACHES
Based on SpFWM in a microcavity, the pair rate N
c
is quadratic
in the circling pump power P
c
[47], which is defined as
P
c
P
p
jFω
p
j
2
, (5)
where P
p
denotes the incident pump power in the bus wave-
guide. The enhancement factor Fω
p
follows
jFω
p
j
2
2v
g
Q
2
πRω
p
Q
e
1 4Q
2
ω
p
− ω
res
2
∕ω
2
res
, (6)
which reaches the maximum
jFω
p
j
2
max
2v
g
Q
2
πRω
p
Q
e
, (7)
when ω
p
ω
res
, that is, the pump is on-resonance. Assume
that only the signal/idler photons generated from one reso-
nance are counted, meanwhile the pump, signal, and idler
approximately have the same frequency of ω
res
; then, the pair
rate in signal/idler arms is calculated through
N
c,s∕i
γP
c
2πR
2
Z
s∕i
jFω
res
− Δωj
2
jFω
res
Δωj
2
dΔω,
(8)
where γ denotes the nonlinear coefficient. By substituting
Eq. (7) into Eq. (8), the pair rate in the on-resonance regime
is given by
N
c,s∕i
8v
4
g
γ
2
P
2
p
Q
4
p
Q
3
s∕i
ω
3
res
π
2
R
2
Q
2
e, p
Q
2
e, s∕i
, (9)
where Q
p
and Q
s∕i
denote the total quality factor, Q
e,p
and
Q
e,s∕i
denote the external quality factor, corresponding to the
pump and signal/idler, respectively. Furthermore, by using the
definition of B N
c
∕P
p
Δλ with a unit of s · mW · nm
−1
[27], the pair brightness becomes
588 Vol. 6, No. 6 / June 2018 / Photonics Research
Research Article
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