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RESEARCH ARTICLE
www.lpr-journal.org
Soliton Burst and Bi-Directional Switching in the Platform
with Positive Thermal-Refractive Coefficient Using an
Auxiliary Laser
Yanjing Zhao, Liao Chen, Chi Zhang, Weiqiang Wang, Hao Hu, Ruolan Wang,
Xinyu Wang, Sai T. Chu, Brent Little, Wenfu Zhang,* and Xinliang Zhang*
Dissipative Kerr solitons in optical microresonators enable the generation
of stable ultrashort pulses and phase-locked frequency combs, leading to
their widespread applications. For traditional platforms with positive thermal-
refractive coefficient, strong thermal effect increases the difficulties of soliton
triggering and prohibits the deterministic control of soliton number. Here,
using an auxiliary laser to tune thermal effect, soliton burst and bi-directional
switching are demonstrated in high-index doped silica glass platform.
First, by varying the parameters of the auxiliary laser, the thermal effect tuning
of the microresonator is studied with different thermal compensation states
achieved, leading to distinct soliton switching features. Especially, the solitons
burst and bi-directional switch in over-compensated state. The corresponding
process is recorded in real time based on a temporal magnification
system, uncovering transient dynamics from continuum background
noise to soliton formation. Finally, the deterministic generation of solitons is
enabled with controllable soliton number spanning from 1 to 21. The present
work provides insight into soliton dynamics and enables soliton generation
on demand with a large range of soliton numbers inside a single device.
1. Introduction
Kerr frequency combs based on high-Q microresonators have
revolutionized the field of frequency metrology with their com-
pact footprint, large bandwidth, and low power consumption.[1,2 ]
Among all these remarkable progresses in this area over
recent years, dissipative Kerr solitons (DKSs)[3] have emerged
Y. Zhao, L. Chen, C. Zhang, H. Hu, R. Wang, X. Zhang
Wuhan National Laboratory for Optoelectronics and School of Optical
and Electronic Information
Huazhong University of Science and Technology
Wuhan 430074, China
E-mail: xlzhang@mail.hust.edu.cn
Y. Z h a o
DTU Fotonik
Department of Photonics Engineering
Technical University of Denmark
Ørsteds Plads 343, Lyngby DK-2800, Denmark
The ORCID identification number(s) for the author(s) of this article
can be found under https://doi.org/10.1002/lpor.202100264
DOI: 10.1002/lpor.202100264
as a milestone, which enable mutually
phase-locked frequency combs with
stable ultrashort pulse trains. DKSs rep-
resent stable and local patterns, resulting
from the double balances between para-
metric gain and cavity loss, as well as
Kerr nonlinearity and dispersion.[4] They
have attracted significant attentions to
a wide range of applications, such as
terabit coherent communications,[5,6 ]
optical clocks,[7] frequency synthesis,[8]
distance ranging,[9,10 ] and ultralow-noise
microwave generation.[11–13 ] The prereq-
uisite of all these practical applications is
the deterministic triggering of DKSs. The
DKS formation requires the pump laser
to be in the effectively red-detuned region
of the cavity resonance. For traditional
platforms including silica (SiO2),[14,15 ]
magnesium fluoride (MgF2),[3,11 ] sili-
con nitride (Si3N4),[16–19 ] silicon (Si),[20]
diamond,[21] Hydex,[22] and aluminum
gallium arsenide (AlGaAs),[23] the
positive thermal effect coefficient makes the pump laser unsta-
ble in red-detuned region while thermal locked in blue-detuned
region.[24] To trigger the DKSs, complicated techniques[3,25–33 ]
have been developed. First reported in materials with slower
thermal effect occurring on milliseconds, the DKSs can be
generated by optimizing frequency tuning speed and final
detuning of pump laser.[3] To mitigate faster thermal effect with
W. Wang, X. Wang, B. Little, W. Zhang
State Key Laboratory of Transient Optics and Photonics
Xi’an Institute of Optics and Precision Mechanics (XIOPM)
Chinese Academy of Sciences (CAS)
Xi’an 710119, China
E-mail: wfuzhang@opt.ac.cn
W. Wa n g, X. Wa ng, W. Zh a n g
University of Chinese Academy of Sciences
Beijing 100049, China
S. T. Chu
Department of Physicsand Materials Science
City University of Hong Kong
Hong Kong 999077, China
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sub-microsecond response time, power and frequency kicking
methods are proposed with abrupt change of pump power[25,26 ]
or frequency.[27,28] Once the multi-soliton is formed, the soliton
number can be reduced by further backward tuning of pump
frequency.[29] Moreover, it is reported that an adjacent mode on
the red-side of the pump resonance can passively stabilize the
thermal dynamics.[18] All the above methods need to experience
the high-power chaotic state, leading to the stochasticity of soli-
ton number. A passive mechanism for single soliton generation
is demonstrated based on spatial mode-interaction.[30] Recently,
the deterministic DKS formation without chaotic stages and
soliton bursts have been demonstrated in auxiliary-assisted mi-
crocavities, while the soliton switching is still unidirectional.[31]
Besides, lithium niobite (LN) platform has presented soliton
burst and bi-directional switching based on its unique photore-
fractive effect, which induces an intensity-dependent decrease
in refractive index (opposite to the thermal refractive effect[32]).
Soliton burst efficiently eliminates the well-known triggering
problem in DKSs, and the bi-directional switching enables
deterministic soliton number tuning. However, a key challenge
is how to achieve such process in traditional comb generation
platforms without similar photorefractive effect.
In this work, soliton burst and bi-directional switching is
demonstrated in a high-index doped silica glass microring res-
onator (MRR) using an auxiliary laser. First, the thermal effect
tuning of the MRR is studied in details to manipulate soliton
switching features. By tuning the polarization, power, and fre-
quency of auxiliary laser, different thermal compensation state
can be achieved. In the under-compensated state, the effective
thermal effect behaves similarly to the initial characteristics
of the platform. Differently, in the over-compensated state,
the effective thermal effect performs inversely to the original
platform, similar to the LN platform with photorefractive effect.
Consequently, soliton self-starts and bi-directionally switches in
the MRR, which are observed in real time based on the temporal
magnification system. The transient dynamics are uncovered,
including soliton formation from continuum background noise
and the unique soliton number increasing process. Furthermore,
it is verified that this phenomenon is almost independent of the
pump tuning speed. On a much longer time scale, soliton burst
and bi-directional switching still stably exist, allowing a much
easier realization of deterministic control of soliton number.
This principle works for all other traditional existing material
platforms (including Si3N4, Si, etc.) to realize soliton burst and
bi-directional switching, which is particularly important for
deterministic soliton generation and number control according
to the specific application needs.
2. Principle of Thermal Effect Tuning
When the pump laser is effectively red-detuned with a con-
stant pump power, Kerr solitons can be supported within a
certain range of the effective detuning,[3,33 ] which is defined
as the soliton existence range (SER).[29] SER is validated to
be degenerate with the number of solitons (N) based on the
Lugiato–Lefever equation.[29,34,35 ] In different material platforms,
the solitons exhibit distinct switching dynamics, which is related
to the effective laser-resonance frequency detuning of the pump
during the process.[29] For traditional platforms with positive
thermal-refractive coefficient (like Si3N4, Si, Hydex, etc.),[16–20,22]
the effective detuning is defined as 2𝜋𝛿eff =́𝜔0p−𝜔p,where
𝜔pindicates pump laser frequency, and ́𝜔0pis pump resonant
frequency shifted by thermal-refractive effects. In single pump
case (Figure 1a), for stable soliton states with thermal equilib-
rium, the thermally induced resonance shift is approximately
proportional to the Q-power product (i.e., the product of Q factor
and power coupled into the resonator) of the pump field:
ΔT∝QpPcp (1)
where ΔT=𝜔0p−́𝜔0pis the thermally induced resonance shift
with the cold cavity resonance frequency 𝜔0p,Qpis the quality
factor of the pump mode, Pcp is the power coupled into the res-
onator from the pump lasers. Thus, the effective detuning of the
pump can be rewritten as 2𝜋𝛿eff =𝜔0p−𝜔p−Δ
T=2𝜋𝛿 −Δ
T
with the absolute detuning 2𝜋𝛿 =𝜔0p−𝜔p.Figure1bpresentsa
typical example of pump Q-power product evolution in a forward
tuning process. During soliton region, the resonant wavelength
is blue-shifted with the pump Q-power product decreasing, as
shown in Figure 1c. Each time solitons are annihilated, the
pump laser reentered the SER during backward tuning process,
while the forward tuning would further push the pump laser
away from SER. Thus, there is soliton number decreasing in
backward tuning and no soliton switching in forward tuning.[29]
Recently, the LN platform presents negative photo-refractive
coefficient, which red-shifts all resonance wavelengths with
intracavity power increasing.[32] Therefore, soliton burst and
bi-directional switching is enabled in LN platform, while these
soliton switching features are challenging to be achieved in
traditional platforms with positive thermal-refractive coefficient.
By introducing an extra auxiliary laser, another degree of
freedom is added to tune total Q-power product and thus the
thermally induced resonance shift. For dual pump based on an
auxiliary laser (Figure 1d), the thermally induced resonance shift
is approximately proportional to the Q-power product of total
intracavity field:
ΔT∝(QpPcp +QauPcau )(2)
Here, Qau is the quality factors of the auxiliary mode, Pcau is the
power coupled into the resonator from the auxiliary laser.
Initially, the auxiliary laser is frequency tuned into a resonance
center and kept blue-detuned. Meanwhile, the pump laser is off
resonance, as shown in state I of Figure 1e. Subsequently, the
pump laser is tuned into the resonance from the blue side, grad-
ually increasing intracavity pump power and heating the cavity.
Therefore, all resonances are thermally shifted to longer wave-
lengths, which in turn pushes the resonance away from the aux-
iliary laser and cools the cavity in counter-balance, illustrated
as state II in Figure 1e. When the pump laser is tuned across
the resonance into the red-detuned region, the frequency comb
abruptly transitions from the high-power chaotic state into the
low-power soliton state. The sudden decrease of intracavity pump
power blue-shifts the resonances, causing the auxiliary laser re-
entering the resonance and mitigating the intracavity power de-
crease. As a result, the thermal resonance shift is greatly reduced
and the generated soliton can be stabilized, shown as state III
in Figure 1e. The double-resonance feature originates from the
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Figure 1. a–c) Single pump case. a) Scheme of single pump. b) The Q-power product evolution of pump field when the pump laser sweeps across the
resonance from blue side. c) The evolution of thermal shifted resonant wavelength and soliton switching features during the forward and backward
tuning processes. The dashed lines indicate the hypothetical resonant wavelength, because it is not predicable in non-soliton states. d–g) Dual pump
case using an auxiliary laser. d) Scheme of dual pump. e) Principle of thermal effect tuning method using an auxiliary laser. f) The Q-power product
evolution of pump, auxiliary and total field when the pump laser sweeps across the resonance from blue side in under-compensated, critical-compensated
and over-compensated states. g) The evolution of thermal shifted resonant wavelength and soliton switching features during the forward and backward
tuning processes in under-compensated, critical-compensated, and over-compensated states.
soliton-induced “S-resonance” and “C-resonance” related to the
continuous wave pump.[29] Compensated by the auxiliary field,
the total intracavity energy is no longer solely determined by the
intracavity pump energy.
By tuning the polarization, power, and frequency of the aux-
iliary laser, the Q-power product evolution can be varied. Here,
according to the Q-power product variations of the pump and
auxiliary fields, we define three states to describe the degree of
thermal compensation effect. Figure 1f illustrates the simulation
results of the three states, and the specific numerical process can
be found in the Supporting Information. When the pump Q-
power product variation is greater than auxiliary Q-power prod-
uct variation, the MRR is in the under-compensated state. In
thermal equilibrium, all resonances are red-shifted with the in-
crease of pump Q-power product. The soliton switching feature
behaves similarly to the initial characteristics of the platform, as
depicted in Figure 1g. Besides, when the pump Q-power prod-
uct variation is ideally compensated by the auxiliary Q-power
product variation, the MRR is in the critical-compensated state
where all resonances are kept almost unchanged. The degener-
acy of SER prohibits any soliton switching in bi-directional tun-
ing process. This delicate state can theoretically exist but is chal-
lenging to be achieved in experiments, as it requires extremely
precise control of the auxiliary effective detuning. Lastly, when
the pump Q-power product variation is weaker than the auxiliary
Q-power product variation, the MRR is in the over-compensated
state. The soliton switching feature performs inversely to the
original platform. With the soliton number decreasing, the pump
Q-power product decreases while the total Q-power product in-
creases, leading to the red shift of all resonance wavelengths.
Such effect is similar to the photo-refractive effect in LN plat-
form, which enables soliton burst and bi-directional switching.
Thus, there is soliton number decreasing in the forward tuning
process and soliton number increasing in the backward tuning
course. Here, the slopes of the soliton existence range are differ-
ent in Figure 1c,g, which are influenced by the pump power.[31]
At a relatively high pump power for single pump, soliton evolu-
tion has a typical positive slope; in contrast, at lower pump power
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Figure 2. a) Experimental setup. AWG, arbitrary waveform generator; EDFA, erbium-doped fiber amplifier; CIR, high power circulator; FPC, fiber polar-
ization controller; FBG, fiber Bragg grating; PD, photodiode; OSA, optical spectrum analyzer; OSC, oscilloscope; TMS, temporal magnification system.
The inset is the image of the packaged MRR used in the experiment. b) Experimentally measured power evolution of the pump and auxiliary laser when
tuning the pump laser into resonance with a fixed frequency auxiliary laser.
assisted by an auxiliary laser, it shows an inverse-slope. Notably,
the horizontal axis ranges in the three figures of Figure 1f are dif-
ferent, indicating an enhanced suppression of thermal broaden-
ing phenomenon from the under-, critical- to over-compensated
state. Therefore, simply by introducing an auxiliary laser, the ther-
mal effect can be effectively tuned in traditional platforms, which
eventually changes soliton switching features.
3. Experimental Results
3.1. Thermal Effect Tuning Using an Auxiliary Laser
Figure 2a shows our experimental setup. A high-index doped sil-
ica glass MRR is utilized for frequency comb generation. This
high-Q add-drop MRR is butterfly packaged, as illustrated in the
inset. The free spectral range (FSR) is 49 GHz, and cross-section
of the waveguide is 2 ×3μm2.[36] The TM00 and TE00 mode both
exhibit anomalous dispersion in communication band with the Q
factor of 2.05 ×106and 1.69 ×106, respectively.[37] The pump and
auxiliary lasers are amplified to similar power and counter prop-
agate in the MRR to mitigate the thermal effect and to be better
separated in the output. Then the two lasers are coupled out from
specific drop-ports of the MRR. At the pump output, the light is
divided into four parts: one is sent to an optical spectrum analyzer
(OSA) to monitor spectral evolution, one is sent to the temporal
magnification system (TMS) to observe real-time temporal evolu-
tion, and the other two are sent to the fiber Bragg grating (FBG)
filters to separate the generated comb light (1500–1550 nm and
1560–1610 nm) and pump light (1555 ±2.5 nm) for correspond-
ing power detections. Besides, the auxiliary output is sent to an
FBG filter (1550 ±1 nm) followed by a photodetector to monitor
its power. In our experiment, the pump and auxiliary wavelength
is set near 1557 nm and 1550 nm, respectively. The pump power
is boosted to 3.0 W while the auxiliary power is amplified to 3.5 W.
With both lasers aligned to TM polarization, Figure 2b presents
the experimentally measured power evolution of the pump and
auxiliary laser when tuning the pump light into resonance and
keeping the auxiliary fixed. It is a typical example of the over-
compensated state. As the output of the pump and auxiliary field
experience different splitting and attenuation, it is challenging to
characterize the total power evolution, which is not given here.
Similar to the theoretical prediction, the intracavity pump power
variation is indeed compensated by the auxiliary laser, therefore
passively mitigating thermal effect of the resonator.
For the device used here, as the TM00 mode possesses higher
Q factor than TE00 mode, it leads to stronger intracavity field
enhancement and narrower resonance. With the auxiliary laser
aligned to different polarization, distinct thermal compensation
effects are obtained. Thus, another degree of freedom is intro-
duced to tune the thermal effect. Notably, it is demonstrated that
all three thermal compensation states can be achieved with TM-
polarized auxiliary laser (see Supporting Information). Mean-
while, there is only under-compensated state when the auxiliary
laser is aligned to TE polarization. Hereinafter, the pump param-
eters and auxiliary power are kept unchanged. We only use the
polarization and frequency of auxiliary laser to alter different ther-
mal compensation states.
Then, we conduct a detailed study of thermal effect tuning
process. According to the theoretical prediction, we achieve dif-
ferent thermal compensation states as well as soliton switching
features, which is verified by the recorded comb power evolution.
By varying the polarization and frequency of the auxiliary laser
and fixing the power, the thermal effect can be tuned. With the
TE-polarized auxiliary laser, we obtain the under-compensated
state, where the total Q-power product is dominated by the pump
Q-power product. When the pump Q-power product is reduced,
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Figure 3. Thermal effect tuning using an auxiliary laser. a) In the under-compensated case, 10 overlaid experimental traces of the output comb light
in the pump forward tuning over the resonance with the same pump power and tuning speed; the inset is the magnified soliton region of the traces.
b) In the under-compensated case, an experimental trace in the forward tuning (tangerine curve) followed by one trace in the backward tuning (yellow
curve) with soliton number decreasing process. c) In the over-compensated case, 10 overlaid experimental traces of the output comb light in the pump
forward tuning over the resonance with the same pump power and tuning speed; the inset is the magnified soliton region of the traces. d) In the over-
compensated case, an experimental trace in the forward tuning (tangerine curve) followed by one trace in the backward tuning (yellow curve) with soliton
number increasing process.
the total Q-power product decreases, leading to the blue-shift
of the SER. Thus, there is no soliton switching via forward
tuning. Figure 3a shows 10 overlaid experimental traces of the
output comb light when the pump laser is tuned forward with
the same power and tuning speed. The soliton area is enlarged
in the inset, indicating the stable soliton generation with no
soliton switching. Besides, the backward tuning process reopens
the possibility of soliton number decreasing, as illustrated in
Figure 3b. Once a soliton is lost, the blue-shifted SER pushes
the pump laser reentering the SER and stabilizing the lower
number soliton state. Such soliton switching features are similar
to the case when the MRR is single pumped.[29]
On the contrary, when the effective detuning of TM polarized
auxiliary laser is close to the TM resonance linewidth, the res-
onator transfers in to the over-compensated state, where the total
Q-power product is dominated by the auxiliary Q-power product.
When the pump Q-power product is reduced, the total Q-power
product increases, leading to the red-shift of the SER. Each time a
soliton is lost, the pump laser reenters the SER in forward tuning
as the SER is red-shifted. Figure 3c shows 10 overlaid experimen-
tal traces of the output comb light in the pump forward tuning.
As illustrated in the inset, there is obvious soliton number de-
creasing in all sweeps, including nearly 20 consecutive soliton
annihilation processes, which is rarely reported before. On the
other hand, Figure 3d depicts the backward tuning process. The
soliton number increasing induces the blue-shift of the SER, sta-
bilizing the higher number soliton state. Thus, soliton number
increasing is enabled in the backward tuning, accompanied by
obvious power dips during each switching. Such power dips are
analyzed in the next section.
Therefore, by varying the polarization, power, and fre-
quency of the auxiliary laser, the thermal effect can be tuned
for different soliton switching features. The soliton number
decreasing can only be achieved with a further backward tun-
ing process in under-compensated state, while it is directly
obtained via forward tuning in over-compensated state. Be-
sides, the soliton number increasing is demonstrated in the
experiment, which has never been reported in such material
platform.
3.2. Soliton Burst and Bi-Directional Switching
Traditionally, the high-speed frequency scanning from blue-
detuned region[3] is the necessary prerequisite to acquire self-
thermal locking[24] and trigger soliton states. As the auxiliary
laser compensation scheme stabilizes the pump in red-detuned
region, the soliton generation is enabled by direct red-side pump
entrance without experiencing the high-power chaotic state.
However, the bi-directional switching between different soliton
states has so far not been reported in conventional platforms[31,38 ]
except the LN system.[32] This phenomenon can be achieved in
the over-compensated state where the thermally induced reso-
nance shift behaves inversely with the intracavity pump power
variation during soliton states.
By tuning the initially red-detuned pump laser backward and
forward, the comb power is recorded in Figure 4a, indicating the
soliton bi-directional switching feature. Meanwhile, the ultrafast
soliton dynamics are observed in real time based on the temporal
magnification system. With the third order dispersion elimi-
nated to avoid temporal aberrations, 1.4-ns recording length
and 580-fs resolution are achieved without synchronization
control and splicing algorithm (see Supporting Information).
When the pump laser gradually enters the resonance from
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Figure 4. Soliton burst and bi-directional switching. a) The experimental trace of the output comb light when the pump laser is tuned backward and
forward across a few soliton steps. The dashed grey lines give the number of solitons. The dashed black circle I, II and III indicate the soliton burst,
power dip and soliton number decreasing process. b) Temporally resolved trace of the soliton burst indicated as I in b). A and B represent two points in
time. c) Temporal evolutions of soliton burst at point A and B measured by the temporal magnification system. The white circles indicate single soliton
state. d) Temporally resolved trace of the power dip indicated as II in b). e) Temporal evolution of power dip measured by the temporal magnification
system. f) Magnification of the power dip indicated as the red box in e). g) Temporally resolved trace of the soliton number decreasing indicated as III
in b). h) Temporal evolution of soliton number decreasing from N =6toN=1 measured by the temporal magnification system.
red-side, the comb power climbs up with progressively increased
amplitude noise, presented in Figure 4b. As seen from the
measured temporal evolution in Figure 4c, there is stochastic
switching between different soliton states and modulation
instability state, where the single solitons are indicated by the
white circles. This unstable switching occurs in approximately
100 ns, much faster than the thermal response time 1.35 μsand
pump laser tuning speed, implying its origin from the self-phase
modulation (SPM) and cross-phase modulation (XPM) induced
resonance shift.[31] Since the intracavity power of the pump
and auxiliary field change in different directions, the XPM
induced resonance shift counter-balances the SPM induced res-
onance shift. On the other hand, with the increased intracavity
pump power, the slower thermal effect gradually blue-shifts
the resonance away from the pump as the resonator is in over-
compensated state, further promoting the soliton switching.
Once the resonance shift reaches an equilibrium under the inter-
action of thermal effects and SPM induced by a certain number
of solitons, the stable soliton state is achieved. In our case, such
soliton burst process leads to the stable generation of six solitons.
With the pump wavelength further decreased, the comb power
increases with obvious staircase pattern, revealing that the Kerr
comb transits from a lower number to higher number soliton
state. Intriguingly, the soliton number increasing process is
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usually accompanied by a power dip, which does not exist during
the soliton number decreasing course. Figure 4d illustrates the
magnified soliton increasing passage from six to seven solitons,
while its temporal evolution is shown in Figure 4e. It is notable
that the amplitude noise in power dip is much stronger than
that in stable soliton states. Previous research has demonstrated
that the low-detuning boundary of the SER corresponds to the
breathing region.[39–41 ] When the pump effective detuning is
reduced within the six-soliton step, the transition from station-
ary to oscillating solitons causes interactions among different
solitons, resulting in their random conversion. The ultrafast
soliton dynamics is depicted in Figure 4f with the white circles
implying the transient single soliton states. Besides, it is noted
that the power dip duration is less than 2 μs, comparable to the
thermal response time. Thus, with the thermal effect kicking
in, the triggering of higher number solitons blue-shifts all
resonances and pushes the resonance away from the pump
laser. The pump effective detuning reenters the stable SER and
the seven-soliton state is stabilized. The further pump backward
tuning induces further soliton number increasing process with
similar principle, leading to the ten-soliton state in the end.
Throughout the backward tuning process, the SERs are near the
low-detuning boundary, therefore the measured signal is rather
noisy, which is similar to the results in LN.[32] Notably, this helps
to reveal the underlying physics that the soliton burst and soliton
number increasing dynamics are observed in real time.
Then the pump laser is tuned forward. As the pump laser is
away from the resonance, the SER increases and the ten-soliton
state is gradually stabilized, which is verified by the reduced am-
plitude noise in the measured signal. With further forward tun-
ing, the intracavity solitons are successively extinct down to the
single soliton state and finally all annihilated (10 →9→…→
1→0). As reported in previous works,[29,42 ] the comb power
presents a regular staircase pattern with similar stair length and
height. The exact soliton number can be accurately inferred from
the step height, which is marked out by the grey lines in Fig-
ure 4a. Strikingly, there is no power dips during the soliton num-
ber decreasing process. As the soliton switching occurs at the
high-detuning boundary of the SER, the system never enters the
unstable breathing region. Figure 4g shows the comb power dur-
ing the soliton number decreasing passage from six to one. Con-
sistent with the comb power evolution, the solitons disappear
one-by-one, of which the extinction points are illustrated by the
white lines in Figure 4h. All solitons possess downward trajecto-
ries, resulting from the influence of Raman self-frequency shift
and high-order dispersion terms.[33,43,44 ] Therefore, bi-directional
switching of solitons can be obtained by bi-directional tuning of
pump laser in over-compensated state.
It would be better if related numerical demonstrations were
further introduced based on the Lugiato–Lefever equation (LLE).
We have modified the LLE to incorporated the influence of
thermal effect and auxiliary laser. In the existing thermal effect
model, the thermal coefficient a is generally set as a constant,
which contains both thermo-expansion effect and thermo-
refractive effect.[24] However, the thermo-refractive coefficient
dn/dT can change significantly with the temperature, even
increasing by 2 magnitudes.[45] On the other hand, the thermal
response time needs to be delicately chosen to accelerate the
simulation, which simultaneously requires proper modifica-
tion of thermal effect parameters.[19,29 ] With the interaction of
thermal effect and auxiliary laser, there are many parameters
in our simulation, significantly increasing the complexity and
difficulty. The two reasons might cause the failure of reproduc-
ing related experimental phenomena in simulation. With more
detailed characterization of thermal parameters for the micro-
resonator and careful modification of numerical parameters,
the convincible simulations could be investigated in the near
future.
3.3. Deterministic Control of Kerr Soliton Number
As the intracavity power variation of pump light is well compen-
sated by that of the auxiliary laser, the thermal shifts of all reso-
nances are greatly mitigated. Thus, the fast frequency tuning is
no longer indispensable to balance thermal effect on microsec-
ond timescale and trigger solitons. In other words, the frequency
tuning speed is independent of the thermal response time, which
enables stable soliton generation at arbitrary frequency sweeping
speed. With a much slower laser scanning speed, Figure 5ashows
the experimental output comb power evolution during the soli-
ton bi-directional switching process. The duration of the entire
process is approximately 40 s, which is 20 000 times longer than
that of the process in Figure 5a. As the thermal effect can stably
settle under this condition, the soliton switching is more regular
and ordered. Besides, limited by the sampling interval, the power
dips are not recorded in the soliton number increasing course,
which might still exist. In such a long-time scale, the spectrum
of each soliton step can be recorded by the OSA, illustrated in
Figure 5b–h. Corresponding schematic depictions of the soliton
distribution in the resonator are depicted to the upper right of
each spectrum. Without experiencing a high-power chaos, the 2-
soliton state is directly achieved. With further backward tuning,
the soliton number is consecutively increased from two to five.
Subsequently, for the forward tuning process, the comb jumps
from the 5-soliton state to the 3-soliton state. Then the solitons
are annihilated one by one to the single soliton state, and fi-
nally the comb collapses. By simply tuning the pump wavelength,
the soliton number can be continuously dialed from one to five,
which are verified by the measured comb power intensity (step
height) and spectra. This bi-directional switching feature allows
the soliton number to increase and decrease repetitively. Besides,
each soliton step lasts for several seconds, meaning that we have
enough time to stop laser tuning at arbitrary soliton state, so as to
achieve deterministic control of soliton number in practical appli-
cations. According to the results in Figure 5, the solitons are bun-
dled up. Actually, such soliton burst and bi-directional switching
process leads to the discretization of temporal soliton separation
defined by 11.2881◦and 12.6990◦(see Supporting Information).
Notably, other higher number of soliton states up to 21-soliton
can be also obtained if the pump wavelength is further reduced
during the backward tuning. In addition, the single soliton is self-
started and achieved in bi-directional sweeping (see Supporting
Information).
Simply based on slow pump wavelength tuning, even manual
tuning, the freely accessing and versatile switching of solitons
can be achieved, leading to the soliton generation on demand
with a large range of soliton numbers inside a single device.
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Figure 5. Deterministic Kerr soliton generation. a) The experimental trace of the output comb light when the pump laser is tuned backward and forward
across several soliton steps at slow tuning speed. b–h) Optical spectra of different soliton states recorded at steps I to VII indicated in a). Schematic
depictions of the soliton distribution in the resonator are shown to the upper right of each spectrum.
4. Conclusion
In summary, based on thermal effect tuning using an auxiliary
laser, the control of soliton switching features is demon-
strated in a high-index doped silica glass MRR. By varying
the polarization, frequency and power of the auxiliary laser,
different thermal compensation states can be achieved, where
soliton switching features behave quite diversely. In the under-
compensated state, there is no soliton switching during the
forward tuning and only soliton number decreasing in the
backward tuning. On the contrary, in the over-compensated
state, the soliton number decreases in the forward tuning and
increases in the backward tuning. Besides, the soliton burst
and bi-directional switching is reported in the platform with
positive thermal-refractive coefficient, and the corresponding
temporal evolution is recorded in real time. It indicates that the
soliton self-stating experiences a stochastic switching between
different soliton states and modulation instability state, which is
induced by the SPM. In addition, the soliton number increasing
is frequently accompanied by obvious power dips, introduced
by the thermal effect and soliton breathing. By significantly
slowing down the pump sweeping speed, the soliton switch-
ing is more regular and ordered without power dips as the
thermal effect can stably settle. The deterministic accessing
and versatile switching of solitons enable soliton generation
on demand with a large range of soliton numbers inside a
single device even by manual pump tuning. In principle, the
method can apply to all other existing material platforms to
manipulate soliton switching features. This demonstration
enriches the physical understanding of soliton dynamics and
provides an architecture to deterministically control the soliton
number.
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Supporting Information
Supporting Information is available from the Wiley Online Library or from
the author.
Acknowledgements
Y.Z. and L.C. contributed equally to this work. The authors gratefully ac-
knowledged Prof. Kerry Vahala for helpful discussions and valuable sug-
gestions for our work. The authors thank Xi’an Institute of Optics and Pre-
cision Mechanics (XIOPM), Chinese Academy of Sciences (CAS) for de-
vice fabrication. The authors thank Prof. Heng Zhou for heplful discussion
of the thermal effect simulations. The work was supported by National
Key Research and Development Project (Grant No. 2019YFB2203102),
the National Science Foundation of China (NSFC) (Grant Nos. 61927817,
61735006, 61631166003, 61675081, 61505060, and 62005090), China
Postdoctoral Science Foundation (Grant No. 2018M640692).
Conflict of Interest
The authors declare no conflict of interest.
Data Availability Statement
The data that support the findings of this study are available from the cor-
responding author upon reasonable request.
Keywords
frequency comb, soliton, thermal effect
Received: May 18, 2021
Revised: July 24, 2021
Published online:
[1] A. L. Gaeta, M. Lipson, T. J. Kippenberg, Nat. Photonics 2019,13, 158.
[2] T. Rosenband, D. Hume, P. Schmidt, C.-W. Chou, A. Brusch, L. Lorini,
W. Oskay, R. E. Drullinger, T. M. Fortier, J. E. Stalnaker, S. A. Did-
dams, N. R. Newbury, W. C. Swann, W. M. Itano, D. J. Winelandn, J.
C. Bergquist, Science 2008,319, 1808.
[3] T. Herr, V. Brasch, J. D. Jost, C. Y. Wang, N. M. Kondratiev, M. L.
Gorodetsky, T. J. Kippenberg, Nat. Photonics 2014,8, 145.
[4] P. Grelu, N. Akhmediev, Nat. Photonics 2012,6, 84.
[5] P. Marin-Palomo, J. N. Kemal, M. Karpov, A. Kordts, J. Pfeifle, M. H.
Pfeiffer, P. Trocha, S. Wolf, V. Brasch, M. H. Anderson, R. Rosenberger,
K. Vijayan, W. Freude, T. J. Kippenberg, C. Koos, Nature 2017,546,
274.
[6] H. Hu, F. Da Ros, M. Pu, F. Ye, K. Ingerslev, E. P. da Silva, M. Nooruz-
zaman, Y. Amma, Y. Sasaki, T. Mizuno, Y. Miyamoto, L. Ottaviano, E.
Semenova, P. Guan, D. Zibar, M. Galili, K. Yvind, T. Morioka, L. K.
Oxenløwe, Nat. Photonics 2018,12, 469.
[7] Z.L.Newman,V.Maurice,T.Drake,J.R.Stone,T.C.Briles,D.T.
Spencer, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, B. Shen, M.-G. Suh,
K. Y. Yang, C. Johnson, D. M. S. Johnson, L. Hollberg, K. J. Vahala, K.
Srinivasan, S. A. Diddams, J. Kitching, S. B. Papp, M. T. Hummon,
Optica 2019,6, 680.
[8] D. T. Spencer, T. Drake, T. C. Briles, J. Stone, L. C. Sinclair, C. Fredrick,
Q. Li, D. Westly, B. R. Ilic, A. Bluestone, N. Volet, T. Komljenovic, L.
Chang, S. H. Lee, D. Y. Oh, M.-G. Suh, K. Y. Yang, M. H. P. Pfeiffer, T.
J. Kippenberg, E. Norberg, L. Theogarajan, K. Vahala, N. R. Newbury,
K. Srinivasan, J. E. Bowers, S. A. Diddams, S. B. Papp, Nature 2018,
557, 81.
[9] M.-G. Suh, K. J. Vahala, Science 2018,359, 884.
[10] P. Trocha, M. Karpov, D. Ganin, M. H. Pfeiffer, A. Kordts, S. Wolf, J.
Krockenberger, P. Marin-Palomo, C. Weimann, S. Randel, W. Freude,
T. J. Kippenberg, C. Koos, Science 2018,359, 887.
[11] W. Liang, D. Eliyahu, V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko,
D. Seidel, L. Maleki, Nat. Commun. 2015,6,1.
[12] X. Xie, R. Bouchand, D. Nicolodi, M. Giunta, W. Hänsel, M. Lezius, A.
Joshi, S. Datta, C. Alexandre, M. Lours, P.-A. Tremblin, G. Santarelli,
R. Holzwarth, Y. L. Coq, Nat. Photonics 2017,11, 44.
[13] X. Xue, A. M. Weiner, Front. Optoelectron. 2016,9, 238.
[14] P. Del’Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, T. J.
Kippenberg, Nature 2007,450, 1214.
[15] K. Y. Yang, D. Y. Oh, S. H. Lee, Q.-F. Yang, X. Yi, B. Shen, H. Wang, K.
Vahala, Nat. Photonics 2018,12, 297.
[16] B. Stern, X. Ji, Y. Okawachi, A. L. Gaeta, M. Lipson, Nature 2018,562,
401.
[17] V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. Pfeiffer, M. L.
Gorodetsky, T. J. Kippenberg, Science 2016,351, 357.
[18] Q. Li, T. C. Briles, D. A. Westly, T. E. Drake, J. R. Stone, B. R. Ilic, S. A.
Diddams, S. B. Papp, K. Srinivasan, Optica 2017,4, 193.
[19] C. Bao, Y. Xuan, J. A. Jaramillo-Villegas, D. E. Leaird, M. Qi, A. M.
Weiner, Opt. Lett. 2017,42, 2519.
[20] A. G. Griffith, R. K. Lau, J. Cardenas, Y. Okawachi, A. Mohanty, R. Fain,
Y. H. D. Lee, M. Yu, C. T. Phare, C. B. Poitras, A. L. Gaeta, M. Lipson,
Nat. Commun. 2015,6, 6299.
[21] B. Hausmann, I. Bulu, V. Venkataraman, P. Deotare, M. Lonˇ
car, Nat.
Photonics 2014,8, 369.
[22] M. Peccianti, A. Pasquazi, Y. Park, B. E. Little, S. T. Chu, D. J. Moss,
R. Morandotti, Nat. Commun. 2012,3, 765.
[23] L. Chang, W. Xie, H. Shu, Q.-F. Yang, B. Shen, A. Boes, J. D. Peters,
W. Jin, C. Xiang, S. Liu, G. Moille, S.-P. Yu, X. Wang, K. Srinivasan, S.
B. Papp, K. Vahala, J. E. Bowers, Nat. Commun. 2020,11, 1331.
[24] T. Carmon, L. Yang, K. J. Vahala, Opt. Express 2004,12, 4742.
[25] V. Brasch, M. Geiselmann, M. H. Pfeiffer, T. J. Kippenberg, Opt. Ex-
press 2016,24, 29312.
[26] X. Yi, Q.-F. Yang, K. Y. Yang, K. Vahala, Opt. Lett. 2016,41, 2037.
[27] J. R. Stone, T. C. Briles, T. E. Drake, D. T. Spencer, D. R. Carlson, S. A.
Diddams,S.B.Papp,Phys.Rev.Lett.2018,121, 063902.
[28] N. Volet, X. Yi, Q.-F. Yang, E. J. Stanton, P. A. Morton, K. Y. Yang, K. J.
Vahala, J. E. Bowers, Laser Photonics Rev. 2018,12, 1700307.
[29] H. Guo, M. Karpov, E. Lucas, A. Kordts, M. H. Pfeiffer, V. Brasch,
G. Lihachev, V. E. Lobanov, M. L. Gorodetsky, T. J. Kippenberg, Nat.
Phys. 2017,13, 94.
[30] C. Bao, Y. Xuan, D. E. Leaird, S. Wabnitz, M. Qi, A. M. Weiner, Optica
2017,4, 1011.
[31] H. Zhou, Y. Geng, W. Cui, S.-W. Huang, Q. Zhou, K. Qiu, C. W. Wong,
Light: Sci. Appl. 2019,8, 50.
[32] Y. He, Q.-F. Yang, J. Ling, R. Luo, H. Liang, M. Li, B. Shen, H. Wang,
K. Vahala, Q. Lin, Optica 2019,6, 1138.
[33] M. Karpov, H. Guo, A. Kordts, V. Brasch, M. H. Pfeiffer, M. Zer-
vas, M. Geiselmann, T. J. Kippenberg, Phys. Rev. Lett. 2016,116,
103902.
[34] I. Barashenkov, Y. S. Smirnov, Phys.Rev.E1996,54, 5707.
[35] S. Coen, H. G. Randle, T. Sylvestre, M. Erkintalo, Opt. Lett. 2013,38,
37.
[36] W. Wang, W. Zhang, S. T. Chu, B. E. Little, Q. Yang, L. Wang, X.
Hu, L. Wang, G. Wang, Y. Wang, W. Zhao, ACS Photonics 2017,4,
1677.
[37] W. Wang, W. Zhang, Z. Lu, S. T. Chu, B. E. Little, Q. Yang, L. Wang, W.
Zhao, Photonics Res. 2018,6, 363.
[38] S. Zhang, J. M. Silver, L. Del Bino, F. Copie, M. T. Woodley, G. N.
Ghalanos, A. Ø. Svela, N. Moroney, P. Del’Haye, Optica 2019,6,
206.
[39] E. Lucas, M. Karpov, H. Guo, M. Gorodetsky, T. J. Kippenberg, Nat.
Commun. 2017,8,1.
Laser Photonics Rev. 2021, 2100264 © 2021 Wiley-VCH GmbH
2100264 (9 of 10)
www.advancedsciencenews.com www.lpr-journal.org
[40] M. Yu, J. K. Jang, Y. Okawachi, A. G. Griffith, K. Luke, S. A. Miller, X.
Ji, M. Lipson, A. L. Gaeta, Nat. Commun. 2017,8,1.
[41] C. Bao, J. A. Jaramillo-Villegas, Y. Xuan, D. E. Leaird, M. Qi, A. M.
Weiner, Phys.Rev.Lett.2016,117, 163901.
[42] X. Yi, Q.-F. Yang, K. Y. Yang, K. Vahala, Nat. Commun. 2018,9,1.
[43] X. Yi, Q.-F. Yang, K. Y. Yang, K. Vahala, Opt. Lett. 2016,41,
3419.
[44] S.Wang,H.Guo,X.Bai,X.Zeng,Opt. Lett. 2014,39, 2880.
[45] G. Moille, L. Chang, W. Xie, A. Rao, X. Lu, M. Davanco, J. E. Bowers,
K. Srinivasan, Laser Photonics Rev. 2020,14, 2000022.
Laser Photonics Rev. 2021, 2100264 © 2021 Wiley-VCH GmbH
2100264 (10 of 10)
