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Generation rate scaling: the quality factor

optimization of microring resonators

for photon-pair sources

KAI GUO,

*XIAODONG SHI,

XIAOLIN WANG,

JUNBO YANG,

YUNHONG DING,

HAIYAN OU,

AND YIJUN ZHAO

College of Advanced Interdisciplinary Studies, National University of Defense Technology, Changsha 410073, China

Department of Photonics Engineering, Technical University of Denmark, Kgs. Lyngby 2800, Denmark

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.

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

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

Hz; however,

the correspo nding pair brightness of 4.0 × 10

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 

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



αv

(2)

and the coupling efficiency between two components, which is

quantified by the external quality factor



2ωπR

jκj

, (3)

where α denotes the round-trip loss coefficient, v

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





: (4)

From previous studies [41,44,45], the pair rate N

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

and present an approach of pair rate scaling by simply

increasing the gap width g. Although Ref. [40] shows that N

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

and Q

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

is quadratic

in the circling pump power P

[47], which is defined as

 P

jFω

j

, (5)

where P

denotes the incident pump power in the bus wave-

guide. The enhancement factor Fω

 follows

jFω

j



πRω

1  4Q

ω

− ω

res



∕ω

res



, (6)

which reaches the maximum

jFω

j

max



πRω

, (7)

when ω

 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

c,s∕i

γP

2πR

s∕i

jFω

res

− Δωj

jFω

res

 Δωj

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

c,s∕i



s∕i

res

e, p

e, s∕i

, (9)

where Q

and Q

s∕i

denote the total quality factor, Q

e,p

and

e,s∕i

denote the external quality factor, corresponding to the

pump and signal/idler, respectively. Furthermore, by using the

definition of B  N

∕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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