# Octave-spanning Kerr soliton microcombs on thin-film lithium niobate

Yunxiang Song1,∗, Yaowen Hu1, Xinrui Zhu1, Kiyoul Yang1,∗, Marko Lončar1,∗
1John A. Paulson School of Engineering and Applied Sciences, Harvard
University, Cambridge, MA, USA.
∗Corresponding authors<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>

###### Abstract

Dissipative Kerr solitons from optical microresonators, commonly referred to
as soliton microcombs, have been developed for a broad range of applications,
including precision measurement, optical frequency synthesis, and ultra-stable
microwave and millimeter wave generation, all on a chip. An important goal for
microcombs is self-referencing, which requires octave-spanning bandwidths to
detect and stabilize the comb carrier envelope offset frequency. Further,
detection and locking of the comb spacings are often achieved using frequency
division by electro-optic modulation. The thin-film lithium niobate photonic
platform, with its low loss, strong second-order nonlinearity, and large
Pockels effect, is ideally suited for these tasks. However, octave-spanning
soliton microcombs are challenging to demonstrate on this platform, largely
complicated by strong Raman effects hindering reliable fabrication of soliton
devices. Here, we demonstrate entirely connected and octave-spanning soliton
microcombs on thin-film lithium niobate. With appropriate control over
microresonator free spectral range and dissipation spectrum, we show that
soliton-inhibiting Raman effects are suppressed, and soliton devices are
fabricated with near-unity yield. Our work offers an unambiguous method for
soliton generation on strongly Raman-active materials. Further, it anticipates
monolithically integrated, self-referenced frequency standards in conjunction
with established technologies, such as periodically poled waveguides and
electro-optic modulators, on thin-film lithium niobate.

Figure 1: DKS device and operation. a Scanning electron microscope images of
microring array (left), microring waveguide cross section (right, top), and
zoom-in of a pulley coupler used for dissipation engineering (right, bottom).
The white outlines around the waveguide cross section are a guide to the eye.
b Simulated (solid red line) and measured (blue dots) integrated dispersion
$D_{\text{int}}$ of a 50 $\mu$m-radius microring, assuming bus waveguide width
0.85 $\mu$m, microring waveguide width 1.62 $\mu$m, coupling gap 1.06 $\mu$m,
pulley interaction angle $45\degree$, and waveguide height 0.33 $\mu$m (for
definition of these parameters and detailed comparison between designed and
fabricated devices, please refer to the Supplementary information). c
Simulated coupling quality factor $Q_{c}$ for the same parameters used in b.
Measured data (blue dots) is obtained by extracting $Q_{c}$ from resonances in
the microring transmission spectrum. Black line labels $Q_{i}\sim$ 1 million.
d Comb power as a photodetector voltage when the pump is swept across a
microring resonance, from red to blue side of resonance and back (background
color). Two discrete steps marked by black dashed lines correspond to single-
and multi-DKS states, indicating bidirectional access under a pump frequency
sweep speed of 10 Hz. e Single-DKS and f multi-DKS spectra corresponding to
steps in d. The comb spacing is about 410.15 GHz and the comb span is about
110 (112.4) THz for the single-DKS (multi-DKS) state. The dips in both DKS
spectra around 203 THz is in good agreement with the $Q_{c}$ peak around
$201.5$ THz, as predicted in Fig. 1c.

##  I Introduction

Integrated optical frequency combspasquazi2018micro ; gaeta2019photonic ;
fortier201920 ; diddams2020optical ; chang2022integrated , based on
microresonator dissipative Kerr solitons (DKS)herr2014temporal ;
kippenberg2018dissipative , have shown promise in providing portable and
efficient solutions to a variety of applications, including stable
opticalspencer2018optical , millimeter wavetetsumoto2021optically , and
microwaveli2014electro ; liu2020photonic ; yao2022soliton ;
kudelin2023photonic ; sun2023integrated frequency generation, precision
spectroscopysuh2016microresonator ; picque2019frequency , astrophysical
spectrometer calibrationobrzud2019microphotonic ; suh2019searching , and
massively parallel communicationsmarin2017microresonator ;
jorgensen2022petabit ; yang2022multi ; rizzo2023massively ,
computingfeldmann2021parallel ; xu202111 ; bai2023microcomb , and
rangingriemensberger2020massively . These technological developments motivate
the exploration of fully stabilized microcombs, which can provide low-noise
and phase coherent frequencies over broad bandwidths, on a chip. Achieving
such microcombs critically relies on the detection and stabilization of both
the comb carrier envelope offset frequency and the comb spacingudem2002optical
. Octave-spanning bandwidths coupled with second harmonic generation is
required for self-referencing of the carrier envelope offset frequency, and
electro-optic modulation is used to convert terahertz comb spacings, typical
to octave-spanning DKS, down to the gigahertz (GHz) regime. While the Si3N4
and AlN photonic platforms have realized octave-spanning DKSli2017stably ;
pfeiffer2017octave ; liu2021aluminum ; weng2021directly , full stabilization
of them remains challenging. Current stabilization efforts require off-chip
lasersbrasch2016photonic ; spencer2018optical ; liu2021aluminum , frequency
doublersbrasch2017self ; spencer2018optical ; newman2019architecture ,
cascaded chains of bulk electro-optic modulatorsbrasch2016photonic ;
drake2019terahertz ; moille2023kerr , and dual comb sourcesspencer2018optical
; newman2019architecture , due to the small Pockels effect in AlN and the
absence of second-order nonlinearity altogether on Si3N4.

The ultra-low loss thin-film lithium niobate (TFLN) photonic
platformzhu2021integrated ; boes2023lithium offers a promising solution for
realizing fully stabilized microcombs, featuring strong electro-optic
effectwang2018integrated ; hu2021chip ; xu2022dual for dividing large comb
spacings, efficient $\chi^{(2)}$ interactionwang2018ultrahigh ;
jankowski2020ultrabroadband ; mckenna2022ultra for frequency doubling, and
large $\chi^{(3)}$ Kerr effectwang2019monolithic for broadband DKS generation.
However, while high-speed electro-optic modulation and efficient second
harmonic generation are established on TFLN, an entirely connected and octave-
spanning DKS is hard to realize. The primary challenge lies in the low
threshold Raman lasing driven by high Raman gain over significant
bandwidthsyu2020raman ; zhao2023widely , which inhibits DKS formation and
drastically complicates systematic fabrication and testing of DKS
devicesgong2019soliton . Previously, TFLN has been used to demonstrate
uniquely self-starting and bidirectionally accessible DKShe2019self ;
gao2023compact , dispersion-engineered DKS spanning up to four-fifths of an
octavegong2020near , photorefraction-enabled free-running
DKSwan2023photorefraction , electro-optically tunable microwave-rate
DKShe2023high , and electro-optically modulated DKSsong2024hybrid . Raman
suppression methods based on pulleyHe:21 ; he2023high and self-
interferencegong2020photonic couplers have been explored. Despite these
milestones, a conclusive understanding towards the design of reliably
repeatable, octave-spanning DKS devices, as well as their realization in a
scalable and high yield fashion, is outstanding.

Here, we demonstrate octave-spanning soliton microcombs on TFLN and provide
detailed guidelines for achieving a high yield of DKS supporting devices, over
various design parameters. We show that octave-spanning DKS can be realized by
systematic dispersion engineering and effective suppression of stimulated
Raman scattering (SRS) using two different methods: (i) the free spectral
range (FSR) control method that relies on precise management of the
microresonator FSR and (ii) the dissipation engineering method that creates
strongly frequency-dependent microresonator to bus waveguide coupling. While
the FSR control method can result in an entirely connected DKS spanning
131-263 THz with a comb spacing of 658.89 GHz, it places stringent constraints
on microresonator FSRs due to the large Raman gain bandwidth $\Gamma\sim 558$
GHzbasiev1999raman ; ridah1997composition . Furthermore, we find that in the
FSR$\gtrsim\Gamma$ regime, DKS generation is not deterministic and device
yield worsens as the FSR decreases. Conversely, the dissipation engineering
method is robust against FSR variations and consistently provides high yield:
more than 88 % of resonance modes across 20 devices support DKS states. Using
this method, we also generate entirely connected DKS spanning 126-252 THz with
a comb spacing of 491.85 GHz.

##  II Results

DKS on TFLN
In our work, a DKS is initiated by a red-detuned, continuous wave (CW) pump
coupled to a microresonator, where self-phase modulation of the pump is
counter-acted by anomalous dispersion, and the microresonator loss is
compensated by third-order parametric gain. These double-balancing conditions
give rise to a DKS that features mode-locked frequency comb spectrum with
characteristic sech2 spectral envelopekippenberg2018dissipative . The
microresonators employed here are dispersion-engineered ring resonators
(microrings) with radii in the 30-60 $\mu$m range (Fig. 1a), fabricated on
Z-cut TFLN (Z-TFLN) on insulator wafers (Methods). The microrings support
fundamental transverse electric (TE) modes with intrinsic quality factors
($Q_{i}$) in the 1-2 million range, in the telecommunications C-band. The
simulated and measured integrated dispersion ($D_{\text{int}}$) for a typical
50 $\mu$m-radius microring is shown in Fig. 1b. This microring is evanescently
coupled to a bus waveguide using a pulley coupler, which leads to a modal
dissipation profile $Q_{c}$ with strong frequency dependence, as shown in Fig.
1c (for detailed study of the $Q_{c}$ dependence on pulley coupler parameters,
please refer to the Supplementary information).

A CW laser source, providing 100 mW of on-chip power, is used to pump one
microring resonance resulting in single and multi-DKS steps in the generated
comb power trace (Fig. 1d). Notably, DKS states can be accessed by sweeping
the laser in both directions. This is a unique property of TFLN DKSshe2019self
; wan2023photorefraction and is due to the interplay between photorefraction
on one hand, and thermo-optic and Kerr effects on the other. Optical spectrum
corresponding to the single-DKS (multi-DKS) step in Fig. 1d is shown in Fig.
1e (f), with comb spacing of about 410.15 GHz and total span of about 110
(112.4) THz. Power dips in both spectra (around 203 THz) are due to the anti-
phase-matched condition of the pulley coupler and correspond to the $Q_{c}$
peak in Fig. 1c. This coupling condition allows critical coupling of the pump
mode and strongly overcouples the Raman mode, thereby suppressing resonance-
enhanced stimulated Raman scattering (SRS) in favor of four-wave-mixing (FWM)
and DKS generation, which we discuss next.

Figure 2: FSR control and dissipation engineering methods for SRS suppression.
a Schematic of FSR control and dissipation engineering methods. In the FSR
control method (top), empty microring modes are far detuned from the peak
Raman gain (red shaded region), effectively lowering the Raman gain
coefficient. This method prefers large microring mode spacings (dark blue
line) compared to the Raman gain bandwidth. Otherwise, small microring mode
spacings (dashed red line) provide low loss conditions for the Raman gain
which lowers the Raman lasing threshold. The dissipation engineering method
(bottom), on the other hand, strongly overcouples modes near peak Raman gain
and introduces significant loss. This leads to suppression of SRS irrespective
of microring FSR. b Transmission spectrum of an FSR-controlled, 40
$\mu$m-radius microring with FSR$\sim$491.7 GHz close to $\Gamma$ and
satisfying $\Delta$/FSR$\sim$38.5. Gray shaded region indicates the bandwidth
of the optical amplifier (191.5-194.7 THz range) used in the experiment. c
Transmission spectrum of a dissipation-engineered, 50 $\mu$m-radius microring
with FSR$\sim$410.6 GHz. High frequency modes are undercoupled due to the
$Q_{c}$ peak placed around 200 THz, and consequently, modes within the
amplifier bandwidth are critically coupled while Raman modes are strongly
overcoupled. d, e Spectra generated by pumping modes marked by red crosses in
b, c, respectively. In d, four modes generating distinct nonlinear states are
selected (unmarked modes generate SRS), while in e, four consecutive modes
supporting nearly identical DKS are shown (unmarked modes support DKS). Figure
3: DKS yield. Percentage of microring modes that yield DKS states (solid) or
SRS (dashed), utilizing the FSR control method (red) and dissipation
engineering method (blue). Microrings with radii 30, 40, 50, and 60 $\mu$m
(FSRs of about 660, 492, 400, and 335 GHz, on average) were measured.
Dissipation-engineered microrings with radius 30 were not attempted (star). If
the comb power trace of a pump mode indicates clear evidence of DKS steps (as
in Fig. 1b and Supplementary information), it contributes to a DKS count.
Otherwise, it contributes to an SRS count. The number of modes resulting in
DKS and SRS, for each microring radius and each SRS suppression method, is
labeled. A total of 396 modes across 94 microrings have been tested, where all
microrings selected satisfied design guidelines.

Resonantly enhanced SRS vs. Kerr effect
Z-TFLN is known to feature strong SRS associated with the
$\chi^{(3)}$-coupling between the fundamental TE mode and the crystalline
E(LO8) vibrational modegong2019soliton . As a CW pump enters a microring
resonance mode from the red-detuned side, it prompts an immediate energy
transfer from the pump mode to unoccupied resonance modes around the Raman
gain band, if the SRS threshold is lower than those of other nonlinear
processesyu2020raman ; zhao2023widely . Such Raman lasing behavior clamps the
pump power at the SRS threshold provided Raman gain is not saturated, and it
inhibits DKS generation within the appropriate pump-resonance detuning
conditions. To enter DKS states, the Kerr-mediated FWM process which seeds
sideband modes must occur instead of SRSchembo2013spatiotemporal .

To qualitatively describe the competition between SRS and DKS formation, we
consider the ratio between the resonance-enhanced power thresholds of these
processes, given by

$\zeta=\frac{P_{\text{th}}^{\text{Kerr}}}{P_{\text{th}}^{\text{SRS}}}\sim\frac{Q_{L}^{R}}{Q_{L}^{P}}\cdot\frac{g_{\text{eff}}^{\text{SRS}}(\delta)}{g^{\text{Kerr}}},$
(1)

where $P_{\text{th}}^{\text{Kerr}},P_{\text{th}}^{\text{SRS}}$ are the FWM and
SRS power thresholds, $Q_{L}^{P},Q_{L}^{R}$ are the loaded quality factors of
the pump mode and Raman mode (Raman mode is defined as the microring resonance
mode closest to the Raman gain peak located at $f^{P}-\Delta$, where $f^{P}$
is the pump frequency and $\Delta\sim 18.94$ THz is the Raman
shiftbasiev1999raman ; ridah1997composition ), $g^{\text{Kerr}}$ is the FWM
gain coefficient, $g_{\text{eff}}^{\text{SRS}}(\delta)$ is the Raman gain
function, and $\delta=f^{R}-(f^{P}-\Delta)$ the detuning between the Raman
mode and the Raman gain peak $f^{P}-\Delta$. When $\zeta<1$, DKS formation is
favored over SRS. However, since
$g_{\text{eff}}^{\text{SRS}}(\delta=0)/g^{\text{Kerr}}\sim 31\gg 1$, the
$\zeta>1$ regime is typical and SRS is routinely observed. Importantly,
$\zeta$ may be lowered by explicitly engineering
$Q_{L}^{P},Q_{L}^{R},g_{\text{eff}}^{\text{SRS}}(\delta),$ and
$g^{\text{Kerr}}$. Among these parameters, $g^{\text{Kerr}}=4\pi
n_{2}f^{P}/c$, where $c$ is the speed of light and $n_{2}$ is the nonlinear
coefficient (proportional to $\chi^{(3)}$), is not easily tunable. On the
other hand, microring resonance frequencies can circumvent the Raman gain band
through careful mode placement and FSR control, such that $\delta$ is large
for the Raman modeokawachi2017competition ; gaeta2019photonic and
$g_{\text{eff}}^{\text{SRS}}(\delta)$ is reduced from its peak value.
Alternatively, introducing a highly dissipative channel for the Raman mode
while maintaining efficient coupling for the pump modehe2023high ;
gong2020photonic reduces $Q_{L}^{R}/Q_{L}^{P}$ greatly. The former method we
refer to as “FSR control method” and the latter “dissipation engineering
method”. Both methods effectively lower $\zeta$ and are conceptually described
in Fig. 2, along with representative nonlinear states obtained by pumping four
different modes in each case. Further, Fig. 3 statistically analyzes the
efficacy of both methods for DKS generation and SRS suppression in Z-TFLN, by
pumping 396 modes across 94 microrings with 4 distinct radii in the 30-60
$\mu$m range.

Figure 4: Dispersion engineering and octave-spanning DKS on TFLN. a Integrated
dispersion $D_{\text{int}}$ of four microring resonators. b Single-DKS state
from a 658.45 GHz FSR microring with large anomalous dispersion. No dispersive
waves are produced at moderate pump powers of about 50 mW on-chip. c Single-
DKS state from a 659.05 GHz microring with reduced anomalous dispersion,
compared to b. A single dispersive wave at high frequency is generated with a
similar pump power. d Octave-spanning single-DKS state (131 to 263 THz,
labeled by blue arrows) from a 658.89 GHz FSR microring broadened by dual
dispersive waves. This microring utilizes the FSR control method for DKS
generation. e Octave-spanning single-DKS state (126 to 252 THz, labeled by
green arrows) from a 491.85 GHz FSR microring broadened by dual dispersive
waves. A weak coupling resonance induced distortion in the spectral envelope
is visible near 210 THz. This microring utilizes the dissipation engineering
method for DKS generation.

FSR control method
In the FSR control method, we minimize spectral overlap between the Raman gain
band and adjacent microring Raman modes, thereby tuning $\delta$ away from $0$
and reducing the effective Raman gain $g_{\text{eff}}^{\text{SRS}}(\delta)$.
Optimized modal positions in the vicinity of Raman gain are schematically
illustrated in the top panel of Fig. 2a. The peak Raman gain is centered
between two unoccupied modes, $\Delta$/FSR is a half-integer, and
$\delta=$FSR$/2$. When $\delta$ is not large enough (red dashed line in Fig.
2a, top), Raman lasing conditions are fulfilled before FWM can occur. Since
$\delta$ is proportional to FSR, the larger the FSR (blue solid line in Fig.
2a, top), the smaller the $g_{\text{eff}}^{\text{SRS}}(\delta)$
okawachi2011octave . To date, this approach has been effective for Kerr comb
generation in crystalline materials with small $\Gamma$, such as diamond
$(\Gamma\sim 60$ GHz) and silicon $(\Gamma\sim 105$
GHz)okawachi2017competition ; gaeta2019photonic . In Z-TFLN, $\Gamma$
associated with the E(LO8) vibrational mode is 558 GHz, thus a large FSR is
required. This restricts the utility of the FSR control method since frequency
combs with large FSR have limited usability. Furthermore, large FSR requires
rings with small radii ($<40$ $\mu$m), which can suffer from increased bending
losses resulting in larger thresholds $P_{\text{th}}^{\text{Kerr}}\sim
1/(Q_{L}^{P})^{2}$, as well as from scattering-induced mode couplings that
lead to $Q_{L}^{P}$ and $Q_{L}^{R}$ variations across different modes. This
may be detrimental to the consistency of SRS suppression and renders this
approach less deterministic, especially when FSR$\gg\Gamma$ cannot be achieved
due to fabrication limitations.

To test this method, we fabricated a microring with 39.84 $\mu$m-radius and
measured FSR about 491.7 GHz, satisfying $\Delta$/FSR$\sim$38.5 and
FSR$\sim\Gamma$. The transmission spectrum of this device is shown in Fig. 2b.
Four resonance modes (red crosses) were separately pumped with about 100 mW
on-chip power, and two out of four resonances yielded exclusively single or
multi-DKS states, as shown in Fig. 2d. The other two resonances produced
strong Raman lasing (single and cascaded Raman shifts of the pump light) and
Raman-assisted modulation instability (Raman light coupled with chaotic
sideband generation) which are not mode-locked frequency combs. Results
collected across many microrings and their modes indicate that, while the FSR
control method can produce DKS states, the outcome is hard to predict, and it
is not robust in suppressing SRS on TFLN, down to the smallest microring
dimensions that may still achieve low loss.

Dissipation engineering method
In the dissipation engineering method, we utilized a pulley-shaped microring
to bus waveguide coupler, which tailors the dissipation rates of microring
modes within the Raman gain band relative to those within the C-band (optical
amplifier operating band). This significantly increases the SRS threshold
while maintaining a low FWM threshold for the pump. The amount of dissipation
per mode, in addition to intrinsic material absorption and scattering losses
(reflected by the intrinsic quality factors $Q_{i}^{P}$ and $Q_{i}^{R}$), is
determined by the coupling to external channels (reflected by the coupling
quality factors $Q_{c}^{P}$ and $Q_{c}^{R}$) which extracts energy from that
mode. The overall loaded quality factor is then
$(Q_{L})^{-1}=(Q_{i})^{-1}+(Q_{c})^{-1}$, which enters the expression for
$\zeta$. Assuming $Q_{i}^{P}\sim Q_{i}^{R}$ (a good approximation since
$f^{P}$ and $f^{R}$ are sufficiently close and far from the material band
gap), we have $Q_{L}^{R}/Q_{L}^{P}\ll 1$ provided $Q_{c}^{R}/Q_{c}^{P}\ll 1$.
If this ratio is small enough, it may offset
$g_{\text{eff}}^{\text{SRS}}(\delta)/g^{\text{Kerr}}$ completely for arbitrary
$\delta$, and enforce the DKS generation condition $\zeta<1$. This method thus
requires engineering $Q_{c}^{R}$ relative to $Q_{c}^{P}$ such that
$Q_{c}^{R}/Q_{c}^{P}\ll 1$. Importantly, standard point couplers provide
$Q_{c}^{R}/Q_{c}^{P}\sim 1/5$ for a critically coupled pump, while pulley
couplers enable $Q_{c}^{R}/Q_{c}^{P}\lesssim 1/40$ (Supplementary
information). The latter is attributed to strongly frequency-dependent $Q_{c}$
near anti-phase matched coupling resonances (realized as in Fig.
1c)moille2019broadband . When such coupling resonances are just higher
frequency than the pump band (C-band), pump modes may be critically coupled
while Raman modes are strongly overcoupled. Therefore, $\zeta<1$ is possible
even considering the worst case
$g_{\text{eff}}^{\text{SRS}}(\delta=0)/g^{\text{Kerr}}\sim 31$, thereby
lifting all restrictions on the microring dimensions in principle. This is
schematically illustrated in the bottom panel of Fig. 2a, where Raman mode
loss cannot be balanced by Raman gain regardless of the FSR, and Raman lasing
is always suppressed.

The transmission spectrum of a dissipation-engineered microring with 50
$\mu$m-radius is shown in Fig. 2c. It has a measured FSR about 410.6 GHz,
resulting in $\Delta$/FSR$\sim$49.2 and $\delta\sim 0.2\cdot$FSR=82.2 GHz. We
note that without dissipation engineering, such $\delta$ would likely result
in SRS with high probability based on FSR control arguments. The undercoupled
modes around 198 THz indicate presence of a $Q_{c}$ resonance just higher
frequency than the C-band, which ensures critically coupled modes in the
C-band and strongly overcoupled Raman modes, consistent with our dissipation
engineering design strategy. Four consecutive resonances (red crosses) were
separately pumped with about 100 mW on-chip power. All resonances yielded a
single-DKS state, as shown in Fig 2e. In fact, these resonances also support
many multi-DKS steps, indicating suppressed SRS over a wide range of pump-
resonance detuning. Applying this method, a much more complex DKS phase space
can be revealed, and multi-DKS states with higher pump-to-comb conversion
efficiencies are readily accessible on TFLN.

Comparison of methods and DKS yield
To carefully verify our proposed methods and evaluate DKS yield statistics, we
tested 94 dispersion-engineered microrings (applying either method for SRS
suppression) and a total of 396 modes across these rings, as shown in Fig. 3.
We confirm that engineering the microring dissipation spectrum can
significantly increase DKS yield up to 96 % (50 $\mu$m-radii) and greater than
88 % for all other microring dimensions tested. The deviation from 100 % yield
can be attributed to (i) pumping near mode crossings or (ii) $Q_{c}$
sensitivity to frequency, where in some microrings a few modes in the
amplifier bandwidth were undercoupled (and did not yield DKS) while the rest
of the modes were critically coupled (and yielded DKS). In the FSR control
method, we note that occasional DKS generation is possible even when the FSR
is a fraction of $\Gamma$, or when the half-integer condition is imperfect
resulting in $\delta<$FSR/2. This may be explained by dissipation rates of the
fundamental TE modes further altered by scattering-induced mode coupling and
possibly crossings between mode families, which in turn decreases
$Q_{L}^{R}/Q_{L}^{P}$ and lowers $\zeta$, though in an inconsistent way.

Dispersion engineering and octave-spanning DKS
Finally, in conjunction with the SRS suppression methods developed, we
engineer the microring waveguide cross section by controlling the waveguide
height, width, sidewall angle, bending radius, and cladding properties to
achieve $D_{\text{int}}$ suitable for octave-spanning DKS (Fig. 4a). DKS
states and their spectra are determined by the microring integrated dispersion
$D_{\text{int}}(\mu)$, where $\mu$ denotes the comb line number relative to
the pump mode ($\mu=0$), given by
$D_{\text{int}}(\mu)=\sum_{n=2}^{\infty}\frac{D_{n}}{n!}\mu^{n}$. When the
pump experiences small anomalous dispersion ($D_{2}\gtrsim 0$), higher order
dispersions ($D_{n}$ for $n\geq 3$) are non-negligible and responsible for
broadening single- and multi-DKS states into frequencies of normal
dispersionbrasch2016photonic , significantly extending the comb bandwidth
through dispersive wave emissions at $\mu_{\text{DW}}$ where
$D_{\text{int}}(\mu_{\text{DW}})\sim 0$. Using the FSR control method, we
fabricated three microrings with 30.3 $\mu$m-radius resulting in measured FSRs
in the 658-659 GHz range (Fig. 4b-d). While $\Delta$/FSR$\sim$28.7 is not
perfect half integer, we found the reduction in
$g_{\text{eff}}^{\text{SRS}}(\delta)$ to be sufficient in practice, owing to
the large FSR. For these devices, we showcase a DKS with sech2 spectrum, a DKS
broadened by one dispersive wave, and an octave-spanning DKS (131-263 THz,
pumped with about 363 mW on-chip power) broadened by dual dispersive waves.
Using the dissipation engineering method, we fabricated a pulley-coupled
microring with measured 491.7 GHz FSR, which also supports an octave-spanning
DKS (126-252 THz, pumped with about 375 mW on-chip power).

##  III Discussion

In summary, we demonstrated dispersion-engineered DKS states spanning up to an
octave on Z-TFLN, using two distinct methods: microring FSR control and
dissipation engineering. Our work is complemented by a statistically-validated
understanding of DKS generation from TFLN microrings, as opposed to production
of Raman scattered light. The DKS spectral bandwidth may be further improved
by pushing dispersive waves to be an octave apart, simplifying carrier
envelope offset frequency detection and stabilization by offering powerful
comb lines with high signal-to-noise ratio. Their powers may be further
enhanced when utilizing self-balanced solitonsmoille2023kerr and may generate
even stronger second harmonic signals under $f$-2$f$ self-referencing, in turn
producing higher-quality locking beat notes. Such an improvement in comb span
would require microring waveguides with larger anomalous dispersion. This is
necessarily accompanied by a higher DKS threshold, which must be offset by
improving $Q_{L}^{P}$ and thus $Q_{i}^{P}$. The $Q_{i}^{P}$ typical to
microring dimensions in this work is between 1 and 2 million for modes in the
C-band, mainly limited by initial 600 nm Z-TFLN requiring shallow etched
waveguides for optimal $D_{\text{int}}$. Simulations suggest that film
thicknesses between 480 to 500 nm allow fully etched waveguides to yield
octave-spanning $D_{\text{int}}$ (Supplementary information), while a recent
report has shown the tight confinement provided by ridge waveguides on Z-TFLN
may increase $Q_{i}^{P}$ up to 4.9 million for microring dimensions considered
in our workgao2023compact . Further, the on- and off-chip facet losses may be
reduced from 6 dB per facet in our proof of concept demonstrations (single
mode waveguides exposed through manual cleaving) to 1.7 dB per facet using
inverse taper couplershe2019low , greatly improving DKS extraction from the
chip as well as reducing off-chip pump power requirements to be compatible
with butt-coupled distributed feedback laser sources enabling further
integration. In addition to FSR control and dissipation engineering methods,
mode crossings and other spectral defects that may locally lower $Q_{L}^{R}$
was not explored here, but may have contributed to DKS generation by chance.
Importantly, such features can be explicitly engineered through matching
effective indices between the fundamental TE pump and other mode families at
the Raman-shifted frequency, though any detrimental effect on
$D_{\text{int}}(\mu)$ must be evaluated. Defect mode engineering utilizing
photonic crystal microrings may achieve similar ends, where sidewall
corrugations strongly couple oppositely propagating modes at specific
frequencieslu2020universal ; yu2021spontaneous ; zhang2024spectral and may
induce high loss at a mode near $f^{P}-\Delta$, in which case $f^{P}$ is
expected to generate DKS by the arguments of our work.

The DKSs demonstrated and methods introduced enable direct integration of
octave-spanning optical frequency combs with existing advancements on the TFLN
platform. Combined with high-speed electro-optic modulation and efficient
second harmonic generation on-chip, fully stabilized integrated frequency
standards are realizable through the detection of near-THz comb spacings using
electro-optic down-conversion and detection of carrier envelope offset
frequency using octave-separated comb lines coupled with $f$-2$f$
interferometry. Towards this goal, reproducible fabrication of the octave-
spanning DKS source is critical to benchmarking such a large-scale system
combining various photonic integrated components, also a core proponent to our
work which may accelerate future system development. Such systems would
provide a complete microwave to optical link with significant potential for
application. For example, making use of integrated laser technologyde2021iii ;
han2021electrically ; shams2022electrically ; snigirev2023ultrafast , small
form factor optical frequency synthesizers and frequency-precise spectroscopic
light probes are possible. Considering the mutual synergies of second- and
third-order nonlinearities on TFLN for comb generation and stabilization, we
envision chip-scale TFLN frequency comb systems to meet technology’s growing
needs for compact generators of an equidistant grid of ultra-stable and
mutually coherent optical frequencies.

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##  IV Methods

Device fabrication
Dissipative Kerr soliton (DKS) microrings are fabricated on commercial Z-cut
thin-film lithium niobate (Z-TFLN) on insulator wafers (NanoLN). The wafer
stack consists of 600 nm Z-TFLN and 2 $\mu$m thermal oxide atop a 0.525 mm
silicon handle. Bus and microring waveguides are patterned on hydrogen
silsesquioxane (HSQ) resist using electron-beam lithography (EBL). An etching
process involving numerous iterations of Ar+-based reactive ion etching and
wet etching is optimized to steepen waveguide sidewalls (72 degrees) by
periodically removing material redeposition acting as an effective etch mask.
The HSQ resist is stripped with dilute hydrogen-fluoride (HF) solution and the
devices are annealed in a high-temperature, oxygen-rich environment. Finally,
bus waveguides are exposed through manual cleaving, resulting in 6 dB loss per
facet, on average. We note that our fabrication process reduces device
dimensions compared to their initial design, due to extensive wet etching. For
integrated dispersion $D_{\text{int}}$ comparisons, the measured
$D_{\text{int}}$ for an as-designed microring waveguide top width is compared
with a simulation assuming a 0.1 $\mu$m-reduced top width. For $Q_{c}$
comparisons, we rely on experimentally fine-tuning the bus waveguide width and
coupling gap around a simulated optimal point.

Dispersion simulation and measurement
Integrated dispersion
$D_{\text{int}}(\mu)=\sum_{n=2}^{\infty}\frac{D_{n}}{n!}\mu^{n}$ of a
microring waveguide is simulated by computing the eigenmodes of its cross
section, using a commercial eigenmode solver (Lumerical MODE). Broadband
effective index information is obtained which is used to calculate
$D_{\text{int}}(\mu)$. The $D_{\text{int}}(\mu)$ of a microring is measured
experimentally by scanning a tunable, C/L-band external cavity diode laser
(ECDL) and obtaining the microring resonance mode positions. Such transmission
spectra are normalized, and their frequency axes are calibrated using a fiber-
based Mach-Zehnder interferometer (MZI) reference (191.3 MHz fringe spacing
near 1.55 $\mu$m). This fringe spacing is calibrated against a frequency
difference generated by a near 1.55 $\mu$m carrier frequency and its electro-
optic sidebands. The resonance positions in the C/L-band are located, and the
fitted FSR ($D_{1}$) at the pump frequency is removed. Such a measurement
gives access to the experimental $D_{\text{int}}(\mu)$ expanded about $\mu=0$
and enables direct comparison against simulation.

DKS generation experiment
DKS states are generated by a single-tone, continuous-wave pump (C-band ECDL)
amplified by an erbium-doped fiber amplifier (EDFA). The amplified pump passes
a polarization controller and is coupled onto the Z-TFLN chip by a lensed
fiber. A 10 Hz electrical ramp is fed into the ECDL’s piezo-actuated frequency
control to locate microring resonances and map comb power vs. pump-resonance
detuning (Fig. 1b and Supplementary information). Once DKS steps are
identified, the electrical ramp signal is turned off and the pump frequency is
manually tuned into the DKS existence range starting from red side of
resonance. Note that a self-starting DKS may identically be triggered with an
initially blue-detuned pump frequency. Once the DKS state is entered, no
additional locking mechanism is required. The generated comb spectra are
collected by a lensed fiber and detected using two optical spectrum analyzers
(Yokogawa AQ6370D, AQ6375), which cover their full bandwidth. A tunable fiber
Bragg grating (FBG) filter is used to remove the pump frequency, when
monitoring comb power or taking select spectra.

SRS suppression calculation
SRS is a parasitic nonlinear process in TFLN microrings inhibiting DKS
generation. We proposed two strategies to bias microrings in favor of DKS
generation, based on Raman mode placement coupled with large FSR and
dissipation engineering of Raman modes. Such strategies are conceived by
comparing the threshold powers of SRS against four-wave-mixing (FWM):

$P_{\text{th}}^{\text{SRS}}=\frac{\pi^{2}n_{0}^{2}f^{P}f^{R}}{c^{2}g_{\text{eff}}^{\text{SRS}}(\delta)}\cdot\frac{V_{\text{eff}}}{Q_{L}^{R}Q_{L}^{P}}$
(2)

and

$P_{\text{th}}^{\text{Kerr}}=\frac{\pi^{2}n_{0}^{2}(f^{P})^{2}}{c^{2}g^{\text{Kerr}}}\cdot\frac{V_{\text{eff}}}{(Q_{L}^{P})^{2}},$
(3)

where $n_{0}$ is the pump mode effective index, $V_{\text{eff}}=2\pi
RA_{\text{eff}}$ is the pump mode effective mode volume, $A_{\text{eff}}$ is
the pump mode effective mode area, $R$ is the microring radius, $f^{R},f^{P}$
are the Raman and pump mode frequencies, $g^{\text{Kerr}}=4\pi
n_{2}f^{P}/c\sim 0.146$ cm/GW is the FWM gain coefficient, $n_{2}=1.8\cdot
10^{-19}$ m2/W is the nonlinear index, $g_{\text{eff}}^{\text{SRS}}(\delta)$
is the effective SRS gain function for the E(LO8) vibrational mode (peak gain
$g_{\text{eff}}^{\text{SRS}}(\delta=0)\sim 4.51$ cm/GW, scaled to 1.55 $\mu$m
using measured values at 1 $\mu$mjohnston1968stimulated ), and $\delta$ is the
detuning between peak SRS gain and the nearest microring resonance mode. The
$g_{\text{eff}}^{\text{SRS}}(\delta)$ has a center $\Delta\sim$18.94 THz away
from the pump and a bandwidth $\Gamma\sim$558 GHzbasiev1999raman ;
ridah1997composition . A ratio of

$\zeta=\frac{P_{\text{th}}^{\text{Kerr}}}{P_{\text{th}}^{\text{SRS}}}\sim\frac{Q_{L}^{R}}{Q_{L}^{P}}\cdot\frac{g_{\text{eff}}^{\text{SRS}}(\delta)}{g^{\text{Kerr}}}<1$
(4)

supports DKS generation over SRS. Without special considerations, $\zeta>1$
for the fundamental transverse-electric (TE) mode at C-band frequencies in
Z-TFLN. The FSR control and dissipation engineering methods tune the terms in
$\zeta$ so that $\zeta$ is maximally decreased.

Coupler simulation for dissipation engineering
The microresonator coupling is defined by the coupling rate $\kappa_{c}$
between the microresonator and the bus waveguide. The structure which
facilitates evanescent coupling is called the coupler. The $\kappa_{c}$ of the
coupler is represented by $\kappa_{c}=|t|^{2}\cdot c/(n_{g}R)$, where $t$ is
the cross-coupling transmission of the coupler, $c$ is the speed of light,
$n_{g}$ is the group index, and $R$ is the microresonator radius. Coupler
design is important for DKS generation on TFLN as parasitic SRS, also based on
the third-order nonlinear optical response, has a stronger gain coefficient
(in most cases) than the Kerr nonlinear gain. The dissipation engineering
method employs pulley couplers to increase the SRS threshold and suppresses
Raman lasing in favor of DKS generation at all optical pump powers. These
couplers are designed such that the pump frequency is critically coupled (in
terms of coupling rates, $\kappa_{i}(f^{P})\sim\kappa_{c}(f^{P})$) while the
Raman mode $f^{R}$ is strongly overcoupled compared to the pump
$\kappa_{c}(f^{P})\ll\kappa_{c}(f^{R})$ and
$\kappa_{i}(f^{P})\sim\kappa_{i}(f^{R})\ll\kappa_{c}(f^{R})$. This set of
conditions provides efficient resonance enhancement of the pump field while
increasing the lasing threshold for microresonator modes near $f^{R}$,
favoring DKS generation. The design of these couplers thus focuses on the
$\kappa_{c}(f^{P})$ and $\kappa_{c}(f^{R})$ contrast arising from strongly
frequency-dependent $t(f^{P})$ and $t(f^{R})$, where $t$s are directly
accessed using 3-D electromagnetics simulations of the coupling structure
using a commercial finite-difference time-domain solver (Flexcompute Tidy3D).
Coupling quality factors $Q_{c}(f)=2\pi f/\kappa_{c}(f)$ are inversely
proportional to the coupling rates.

Data availability The data that support the plots within this paper and other
findings of this study are available from the corresponding author upon
reasonable request.

Code availability The code used to produce the plots within this paper is
available from the corresponding author upon reasonable request.

Competing interests M.L. is involved in developing lithium niobate
technologies at HyperLight Corporation.

## Acknowledgments

This work is supported by the Defense Advanced Research Projects Agency
(HR001120C0137, D23AP00251-00), Office of Naval Research (N00014-22-C-1041),
National Science Foundation (OMA-2137723, OMA-2138068), U.S. Navy
(N68335-22-C-0413), and National Research Foundation of Korea. The authors
thank Rebecca Cheng and Neil Sinclair for discussions. Y.S. acknowledges
support from the AWS Generation Q Fund at the Harvard Quantum Initiative. All
devices in this work were fabricated at the Harvard Center for Nanoscale
Systems.