of 17
Nature Photonics
| Volume 17 | November
2023 | 977–983
977
nature photonics
https://doi.org/10.1038/s41566-023-01257-2
Article
Soliton pulse pairs at multiple colours in
normal dispersion microresonators
Zhiquan Yuan
1,4
, Maodong Gao
1,4
, Yan Yu
1,4
, Heming Wang
1,2
,4
,
Warren Jin
2,3
,4
, Qing-Xin Ji
1
, Avi Feshali
3
, Mario Paniccia
3
, John Bowers
2
& Kerry Vahala
1
Soliton microcombs are helping to advance the miniaturization of a
range of comb systems. These combs mode lock through the formation
of short temporal pulses in anomalous dispersion resonators. Here, a new
microcomb is demonstrated that mode locks through the formation of
pulse pairs in coupled normal dispersion resonators. Unlike conventional
microcombs, pulses in this system cannot exist alone, and instead phase
lock in pairs wherein pulses in each pair feature different optical spectra. The
pairwise mode-locking modality extends to multiple pulse pairs and beyond
two rings, and it greatly constrains mode-locking states. Two- (bipartite) and
three-ring (tripartite) states containing many pulse pairs are demonstrated,
including crystal states. Pulse pairs can also form at recurring spectral
windows. We obtained the results using an ultra-low-loss Si
3
N
4
platform
that has not previously produced bright solitons on account of its inherent
normal dispersion. The ability to generate multicolour pulse pairs over
multiple rings is an important new feature for microcombs. It can extend
the concept of all-optical soliton buffers and memories to multiple storage
rings that multiplex pulses with respect to soliton colour and that are
spatially addressable. The results also suggest a new platform for the study
of topological photonics and quantum combs.
Microresonator solitons exist through a balance of optical nonlin
-
earity and dispersion, which must be anomalous for bright soliton
generation
1
3
. Moreover, microresonators must feature high optical
Q factors for low pump power operation of the resulting microcomb.
Although these challenges have been addressed at telecommunication
wavelengths using a range of material systems
1
, ultra-low-loss Si
3
N
4
resonators
4
,
5
do not yet support bright solitons as their waveguides
feature normal dispersion
4
. Furthermore, all resonator materials are
dominated by normal dispersion at shorter wavelengths. Although it
is possible to form normal dispersion combs
6
, the temporally short
pulse nature and highly reproducible spectral envelopes of anomalous
dispersion soliton combs
1
have generated keen interest in methods to
induce anomalous dispersion for bright soliton generation in normal
dispersion systems. Such methods have in common the engineering
of dispersion through coupling of resonator mode families, including
those associated with concentric resonator modes
7
,
8
, polarization
9
,
10
or
transverse modes
11
,
12
. As an aside, such coupled resonators have also
been used to improve normal dispersion comb formation
13
,
14
and to
boost the power efficiency of bright combs
15
.
Here we engineer anomalous dispersion in ultra-low-loss Si
3
N
4
resonators by partially coupling resonators (Fig.
1a
). Such geometry
introduces unusual new features to bright soliton generation; for
example, spectra resembling single soliton pulse microcombs form
instead from coherent pulse pairs (Fig.
1a
). The pulse pairs circulate
in a mirror-image-like fashion in the coupled rings to form coherent
comb spectra (Fig.
1b
) with highly stable microwave beat notes (Fig.
1c
).
Received: 30 January 2023
Accepted: 23 June 2023
Published online: 3 August 2023
Check for updates
1
T. J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, CA, USA.
2
ECE Department, University of California Santa
Barbara, Santa Barbara, CA, USA.
3
Anello Photonics, Santa Clara, CA, USA.
4
These authors contributed equally: Zhiquan Yuan, Maodong Gao, Yan Yu,
Heming Wang, Warren Jin.
e-mail:
jbowers@ucsb.edu
;
vahala@caltech.edu
Nature Photonics
| Volume 17 | November
2023 | 977–983
978
Article
https://doi.org/10.1038/s41566-023-01257-2
Recurring spectral windows
Before addressing pulse-pair propagation in the two- and three-ring
systems, the conventional mode-family coupling approach is consid-
ered
7
,
8
,
10
. A concentric resonator system is chosen as a representative
example (upper-left panel, Fig.
2a
). The characteristics of this system
are identical to other methods. First, a phase-matching condition must
be satisfied such that the absolute mode number of each ring (or each
coupled mode) must be equal at the same optical frequency. This mode
number determines the wavelength at which soliton formation is pos
-
sible. Second, the free-spectral-range values (FSR
A
and FSR
B
) of the
uncoupled mode families of rings A and B must be close in value com-
pared with their average FSR = (FSR
A
+ FSR
B
)/2 so that phase matching
occurs over a large number of modes. With these conditions satisfied,
the resulting dispersion will be as illustrated schematically in Fig.
2a
(lower panel, green curves). Comparisons with the uncoupled disper-
sion curves (centre dashed blue and red lines) show that anomalous
dispersion is possible for the upper mode family branch.
Next consider the case in which two rings are placed side-by-side
and coupled together (Fig.
2a
, upper-right panel). The two ring cavi
-
ties differ only in length, with ring B being slightly longer than ring A
so that FSR
A
> FSR
B
. Considering the straight coupling section from a
coupled-mode perspective, the modes of the two rings will strongly
couple if they have matching wavevectors (or equivalently, resonance
frequencies), whereas there are no requirements on mode number
matching of the rings (that is, the mode number is not conserved). In
comparison with the concentric ring configuration, this dramatically
modifies the dispersion relation (Fig.
2a
, lower panel, orange curves).
Due to the loss of mode number conservation, inter-ring coupling
pushes the resonance frequencies away from that of the individual rings
The interaction of the pulses in the coupling section between the
rings is shown to induce anomalous dispersion, which compensates for
the overall normal dispersion of each ring. This pairwise compensation
spectrally recurs, thereby opening multiple anomalous dispersion
windows for the formation of multicolour soliton pairs. These windows
can be engineered during resonator design. Furthermore, the spectral
composition of each pulse in a pair is different. Figure
1b
, for example,
shows through- and drop-port spectra that reflect the distinct spectral
compositions of pulses in rings A and B (Fig.
1a
). This peculiar effect is
also associated with Dirac solitons
16
and it is shown that the two-ring
pulse pair represents a new embodiment of a Dirac soliton as the under
-
lying dynamical equation (see Methods) resembles the nonlinear
Dirac equation in 1 + 1 dimensions. Pulse pairing is also extendable to
higher-dimensional designs with additional normal dispersion rings.
For example, in Fig.
1d–f
, three pulses in three coupled rings alternately
pair to compensate for the normal dispersion of each ring.
In what follows, we first study the dispersion of this system and
compare it with past mode coupling methods. Experimental results,
including dispersion measurement and comb formation, are then pre
-
sented. Pairwise pulse formation is then studied in the time domain. In
presenting the results, it is convenient to resolve the ambiguity created
by pulse-pair spectra in two- and three-coupled rings that nonetheless
resemble single-pulse soliton spectra. To accomplish this, we denote
these cases as bipartite and tripartite soliton microcombs, respectively.
The need for such nomenclature is made clear by the demonstration
of multiple pulse-pair states, including a two-ring microcomb state
containing four pulses, which behaves as a two-pulse soliton crystal,
and a three-ring state with 12 pulses, which behaves as a four-pulse
soliton crystal
17
.
–100
0
100
Power (20 dB/div.)
c
Frequency (kHz
+ 19.9744 GHz)
–200
0
200
Power (20 dB/div.)
Frequency (kHz
+ 19.9735 GHz)
RBW
1 kHz
Wavelength (nm)
(
ω
μ
ω
0
D
1
μ
)/2π (GHz)
–3
–2
–1
0
1
2
Drop port
Through port
b
1,520
1,530
1,540
1,550
1,560
1,570
1,580
On-chip power (dBm)
–80
–70
–60
–50
–40
–30
–20
–10
0
a
Pump
Ring A
Ring B
Ring A
Ring B
Wavelength (nm)
1,520
1,530
1,540
1,550
1,560
1,570
1,580
(
ω
μ
ω
0
D
1
μ
)/2π (GHz)
–4
–3
–2
–1
0
1
f
On-chip power (dBm)
–80
–70
–60
–50
–40
–30
–20
–10
0
d
e
Ring A
Ring B
Ring C
Ring A
Ring B
Ring C
RBW
1 kHz
Fig. 1 | Soliton pulse pair generation in two- and three-coupled-ring
microresonators.
a
, Schematic showing coherent pulse pairs that form a
composite excitation. The inset is a photomicrograph of the two-coupled-ring
resonator used in the experiments. Rings A and B are indicated. Scale bar, 1 mm.
b
, Simultaneous measurements of optical spectra collected from the through
(pumping port) and drop ports in the coupled-ring resonator of
a
. The measured
mode dispersion is also plotted. Two dispersive waves are observed at spectral
locations corresponding to the phase matching condition, as indicated by
the dispersion curve.
c
, Radiofrequency spectrum of microcomb beatnote.
RBW, resolution bandwidth.
d
, Illustration of three-pulse generation in a
three-coupled-ring microresonator wherein pulses alternately pair. The inset
is a photomicrograph of the three-coupled-ring microresonator used in the
experiments. Scale bar, 1 mm.
e
, Measurement of optical spectrum of the
three pulse microcomb. The measured mode dispersion is also plotted.
f
, Radiofrequency spectrum of the microcomb beatnote.