# Multi-Octave Frequency Comb from an Ultra-Low-Threshold Nanophotonic
Parametric Oscillator

Ryoto Sekine1,∗, Robert M. Gray1,∗, Luis Ledezma1, Selina Zhou1, Qiushi
Guo1,2, Alireza Marandi1,†
1Department of Electrical Engineering, California Institute of Technology,
Pasadena, California 91125, USA.
2Department of Physics, CUNY, New York, New York 10017, USA.
∗These authors contributed equally to this work.
†Email<EMAIL_ADDRESS>
###### Abstract

Ultrabroadband frequency combs coherently unite distant portions of the
electromagnetic spectrum. They underpin discoveries in ultrafast science and
serve as the building blocks of modern photonic technologies. Despite
tremendous progress in integrated sources of frequency combs, achieving multi-
octave operation on chip has remained elusive mainly because of the energy
demand of typical spectral broadening processes. Here we break this barrier
and demonstrate multi-octave frequency comb generation using an optical
parametric oscillator (OPO) in nanophotonic lithium niobate with only
femtojoules of pump energy. The energy-efficient and robust coherent spectral
broadening occurs far above the oscillation threshold of the OPO and detuned
from its linear synchrony with the pump. We show that the OPO can undergo a
temporal self-cleaning mechanism by transitioning from an incoherent operation
regime, which is typical for operation far above threshold, to an ultrabroad
coherent regime, corresponding to the nonlinear phase compensating the OPO
cavity detuning. Such a temporal self-cleaning mechanism and the subsequent
multi-octave coherent spectrum has not been explored in previous OPO designs
and features a relaxed requirement for the quality factor and relatively
narrow spectral coverage of the cavity. We achieve orders of magnitude
reduction in the energy requirement compared to the other techniques, confirm
the coherence of the comb, and present a path towards more efficient and wider
spectral broadening. Our results pave the way for ultrashort-pulse and
ultrabroadband on-chip nonlinear photonic systems for numerous applications.

Figure 1: Principle and design of the multi-octave nanophotonic OPO. a,
Illustration of the sync-pumped OPO on thin-film lithium niobate with key
features highlighted. b, Microscope image of several devices when the one in
the center is pumped at 1 $\mu$m. The chip glows green due to second harmonic
generation (SHG). The top inset is a scanning electron microscope image of the
spiral region and the bottom is a picture of the entire chip containing 16
OPOs. c, Illustration showcasing how short pump pulses can take advantage of
near-zero-dispersion-engineered OPAs. The simulated gain profiles are shown in
the top for a waveguide with 60 fs2/mm half-harmonic GVD and 26 fs/mm GVM and
in the bottom for a near-zero-dispersion waveguide. The solid orange line
marks the center wavelength of the pump and the orange shaded regions mark the
3-dB bandwidth (BW) of the 100-fs source. d, Depiction of the different
regimes of operation of the OPO as a function of pump pulse energy, along with
the roundtrip-to-roundtrip temporal output of the OPO in each regime.

Broadband optical frequency combs are among the great achievements of modern
optics 1, 2. Recently, increasing efforts are focused on the realization of
broadband frequency combs in nanophtonic platforms 3, 4, 5 with applications
including dual-comb spectroscopy 6, optical communications 7, optical
frequency synthesis 8, 9, and laser ranging 10. However, the spectral coverage
of integrated frequency comb sources remains far behind their table-top
counterparts using high-pulse-energy lasers and discrete components, which
have recently surpassed six-octave spectra 11, 12. Such multi-octave frequency
combs are valuable for applications such as ultrashort pulse synthesis13,
attosecond science14, and bio-chemical sensing and imaging 15, 16, 17.

Integrated sources of short-pulse frequency combs typically generate
picojoules or femtojoules of pulse energies 2, 4, 18, 19, 20 and their
spectral coverage barely reaches an octave 21, 22. This has necessitated
further spectral broadening stages for many applications, which so far have
been realized strictly using table-top systems with discrete amplifiers and
components 1, 23, 8. A femtojoule-level multi-octave coherent spectral
broadening mechanism has so far been beyond the reach of current photonic
technologies, and hence, a path towards a fully integrated multi-octave
frequency comb has remained elusive.

Substantial spectral broadening is typically achieved by passing femtosecond
or picosecond pulses with 0.1-10 nJ of energy through waveguides, crystals or
fibers with quadratic ($\chi^{(2)}$) or Kerr ($\chi^{(3)}$) nonlinearity with
various designs 24, 1, 25, 26, 27, 28. Among these schemes, waveguides with
quadratic nonlinearity are becoming increasingly more efficient, especially
because of the recent progress on quasi-phase matching and dispersion
engineering 29, 24, 26 and show superior performances over their cubic
counterparts. However, to reach an octave of coherent spectrum and beyond they
still need 10’s of picojoules of energy29, which is far beyond the current
capability of integrated frequency comb sources.

Resonant enhancement of spectral broadening is expected to improve the energy
requirements. However, such experiments have so far remained below an octave
30, 31, 23. This is mainly because of the overly constrained dispersion
requirements of cubic coherent spectral broadening schemes especially when
combined with high-Q requirements. In fact, even linear components in
nanophotonics with multi-octave spectral response are still challenging to
design and realize 32. In contrast, quadratic nonlinearity not only leads to
lower energy requirements in single-pass configurations, but it also offers a
wider range of nonlinear processes for ultrawide coherent spectral broadening
resulting from nonlinear interactions of distant portions of the spectrum11,
12. However, a proper resonator design is necessary to enable an operation
regime where a sequence of quadratic nonlinear processes can yield coherent
spectral broadening towards multi-octave operation.

A promising path towards such a multi-octave nonlinear resonator is based on
synchronously (sync-) pumped degenerate OPOs, which so far have been
successfully used in bulk optics for efficient phase-locked down-conversion
via half-harmonic generation of broadband frequency combs 15, 33, 34, 35.
Recent studies indicate the potential of sync-pumped OPOs for extreme pulse
shortening and spectral broadening while preserving the coherence properties
of the pump 36. However, lack of dispersion engineering in bulk nonlinear
crystals, low parametric gain bandwidths, and multi-picojoule thresholds have
put limitations on their applicability for compact and ultrabroadband
frequency comb applications. Recent developments of dispersion-engineered
optical parametric amplifiers (OPAs) 37 and narrowband sync-pumped OPOs 38 in
lithium niobate nanophotonics promise a path towards overcoming these
limitations and accessing a new regime of ultrabroadband ultra-low-energy
nonlinear optics that has not been accessible before.

Figure 2: OPO characterization. a, Oscillation peaks of the OPO as the pump
repetition rate is modulated by a piezoelectric transducer (PZT) in the pump
laser cavity at 600 Hz. b, Signal spectrum at 35 fJ of pump energy for three
different roundtrip detunings and c, the corresponding OPO signal growth as a
function of pump energy for different oscillation peaks and their slope
efficiencies, $\eta_{\mathrm{SL}}$. d, Output spectra from the OPO cavity at
54 fJ, 109 fJ, and 380 fJ of pump. e, Spectral overlap between the broadened
pump using a PCF and the SHG output of the integrated device with a cavity. f,
The resulting radio-frequency (RF) beatnote at three different pump
$f_{\mathrm{CEO}}$ frequencies when the chip is pumped at 380 fJ. g, Example
beatnote between a free space and on-chip OPO pumped at 109 fJ and $\sim$8 fs
of cavity detuning. h, Interference of these two coherent OPOs filtered around
2.1 $\mu$m as their relative delay is scanned. The interference is observed
only when their $f_{\mathrm{CEO}}$ frequencies are the same, while the
beatnote is observed only when they are different by $f_{\mathrm{rep}}$/2.

In this work, in sharp contrast to previous realizations of nonlinear photonic
resonators, we judiciously design and realize an on-chip sync-pumped OPO
featuring a low-finesse resonator which couples only frequencies near the
half-harmonic of the pump while leaving the pump and its high-harmonics non-
resonant. It is near-zero dispersion engineered for the pump and its half-
harmonic. The nanophotonic sync-pumped OPO operates with a record-low
threshold of $\sim$18 fJ. Due to its low-energy, intense, phase-sensitive
amplification, we discovered an operation regime of the OPO where the
nonlinear phase compensates the cavity detuning, yielding temporal self
cleaning and a multi-octave coherent spectrum. We measured a two-octave
frequency comb at $\sim$109 fJ of pump energy and experimentally confirmed its
coherence. We numerically replicate the broadband nonlinear dynamics
associated with such a multi-octave broadening and provide design guidelines
for even broader outputs.

Figure 3: Simulation results showing different operation regimes of the
nanophotonic OPO. a, Transition from (i) near-threshold coherent operation to
(ii) incoherent operation and (iii) back to coherent operation when the pump
energy is increased. The roundtrip temporal evolution (i-iii) and output
spectra (iv-vi) are shown for three different pump intensities using
experimental parameters and at a cavity detuning of -10.5 fs. b, A three-
octave coherent OPO. The same experimental parameters are used except that the
last one mm of the PPLN was replaced with a chirped poling period. The pump
pulse energy was at 250 fJ.

Operating principle and design

Figure 1a illustrates the design of the on-chip sync-pumped OPO, with the
fabricated device shown in Fig. 1b. The input/output couplers are designed to
allow resonance only around the half-harmonic of the pump (see supplementary
section I), and the cavity is designed to be minimally dispersive for these
wavelengths. To phase and frequency lock the OPO, the OPO is nearly sync-
pumped at degeneracy, requiring a cavity round-trip time of 4 ns for a pump
comb with a 250 MHz repetition rate. With the effective index of our
nanophotonic lithium niobate waveguides (wgs), this amounts to a 53-cm-long-
cavity.

To achieve the ultra-high, ultra-broad, phase-sensitive gain at fJ pump pulse
energies that enables coherent broadband comb generation, the OPO includes a
10.8 mm OPA with proper dispersion engineering and quasi phase matching (QPM).
Specifically, we target minimizing the group velocity dispersion (GVD) of the
pump and signal, as well as the group velocity mismatch (GVM) between the pump
and signal 37. Figure 1d illustrates the large gain bandwidth that can be
accessed when coupling a 100-fs pump to a near-zero dispersion engineered
waveguide, as opposed to one with large dispersion that is favored for broadly
tunable OPOs39, 38. The designs for the poling period, cavity length, and
couplers for sync-pumped operation can be found in the Supplementary, Section
I.

Figure 1d illustrates the different regimes of operation of this nanophotonic
OPO. At low pump pulse energies, the OPO goes above threshold when the gain
overcomes the loss inside the cavity. This is conventionally the regime where
OPOs are operated to yield coherent outputs phase-locked to the pump34. At
higher pump pulse energies a degenerate OPO is known to transition to an
unstable operation regime where the phase-locked operation deminishes40, 41.
Here however, we find that far above threshold, the OPO can undergo a
transition to the phase-locked regime as a result of the nonlinear phase being
compensated by the cavity. This emergence of coherence is akin to the spatial
self-cleaning in multimode fibers42, which is emphasized in the accompanying
time domain plots as a temporal self-cleaning mechanism, where after a finite
number of roundtrips the output pulse intensity is seen to stabilize with
ultrashort features in the multi-octave case.

Experimental results

In Fig. 2a-c, we show the near-threshold performance of the nanophotonic OPO.
Scanning the repetition rate of the pump by 600 Hz, we observe the oscillation
peaks of the OPO as depicted in Fig. 2a. These peaks are characteristic of
doubly-resonant operation34. We can actively lock the pump repetition rate to
the center of each of these peaks, and the near-threshold signal spectra of
three such peaks at distinct detunigs between the pump repetition period and
cavity round-trip time, $\Delta T_{RT}$, are shown in Fig. 2b. In Fig. 2c we
show the measured input-output pulse energy growth of these same peaks. We can
extrapolate the threshold and slope efficiencies, $\eta_{SL}$, and define the
peak with the lowest threshold as the zero cavity detuned state. For this peak
we estimate an OPO threshold of $\sim$18 fJ.

In Fig. 2d, we show three characteristic output spectra of the OPO. At 54 fJ
of pump we observe conventional OPO behavior. The pump, half-harmonic and
second-harmonic are all spectrally broadened, and there is noticeable sum
frequency generation (SFG) between the pump and half harmonic. At 109 fJ of
pump, we observe continuous spectra from 600 nm to 2710 nm, and at 380 fJ, we
observe three-octave-spanning spectra from 362 nm to 3261 nm. Notably for the
spectra above 2.5 $\mu$m, we observe molecular absorption features, here
predominately due to ambient H2O. The dip at 2.8 $\mu$m is associated with the
OH absorption peak in the LN and/or the buffer layer39, 43, and kinks near 680
nm and 1135 nm are due to mode crossings (see Supplementary Section II).

Figure 4: Performance comparison of (a), integrated spectral broadening, and
(b), frequency comb sync-pumped OPOs. a, Wavelength coverage and pump pulse
energies of integrated frequency comb spectral broadening schemes. The arrows
indicate the pump wavelength. b, Comb repetition rates and pump threshold
energies of sync-pumped OPOs. The marker shapes denote the different cavity
and nonlinear (NL) element compositions for each OPO, the categories being
free space, fiber, integrated and bulk, fiber, nanophotonic respectively. In
both figures, the top legend denotes the material of the nonlinear element.
Abbreviations, TFLN: thin-film lithium niobate, OP: orientation patterned, MF:
microstructured fiber, HNLF: highly nonlinear fiber.

First, we investigate the coherence of the second-harmonic portions of these
spectra using a spectrally broadened output of the pump by a photonic crystal
fiber. We interfere this broadened pump with the second-harmonic portion of
the on-chip OPO, the spectral overlap of which is shown in Fig. 2e. We show
sample beatnotes of the resultant carrier-envelope offset frequency,
$f_{\mathrm{CEO}}$, along with the pump repetition rate, $f_{\mathrm{rep}}$,
at 250 MHz when pumping at 380 fJ in Fig. 2f. By observing the shifting of
these beatnotes as the pump $f_{\mathrm{CEO}}$ is tuned, we verify that these
beatnotes correspond to $f_{\mathrm{CEO}}$. We observe similar
$f_{\mathrm{CEO}}$ beatnotes at 54 and 109 fJ of pump (see Supplementary
Section II). We also note that, as expected, these beatnotes were present
irrespective of the exact detuning of the cavity for all three pump pulse
energies.

To investigate the coherence of the longer-wavelength side of the on-chip OPO
output, we interfere it with that of a free-space OPO pumped by the same laser
using a filter centered around 2.1 $\mu$m. A degenerate OPO above threshold
can have two possible CEO frequencies which differ by $f_{\mathrm{rep}}/2$
depending on the oscillation peak34. When the on-chip OPO has a different CEO
from the free-space OPO, upon spatially and temporally overlapping their
outputs, beatnotes at $f_{\mathrm{rep}}/2$ are observed in the case that the
on-chip OPO is pumped at 54 fJ with zero detuning. At 109 fJ of pump energy,
while we did not observe the $f_{\mathrm{rep}}/2$ beatnote at zero detuning,
we did observe it at a cavity detuning of $\sim$8 fs, and this is shown in
Fig. 2g. At this same detuning, when both OPOs operate with equivalent CEO
frequencies, no $f_{\mathrm{rep}}/2$ beatnote is observed, and as the relative
delay between their outputs is scanned, the two OPOs
constructively/destructively interfere resulting in the fringes in Fig. 2h
(see Supplementary Section III). From these measurements, we confirm that the
down-converted combs at these two pump energies are coherent with respect to
the pump comb. In particular, at 109 fJ of pump, because both the half-hamonic
and second harmonic combs are coherent with respect to the pump and all
frequency portions of our spectrum are generated through parametric processes
of these three combs29, we conclude that at this detuning the continuous two-
octave wide spectrum as well as the second harmonic comb are coherent.
However, for the case of 380 fJ pumping, the beatnote and spectral fringes of
Fig. 2g and h were not observed for any roundtrip detuning, and hence we
consider this three-octave spectrum incoherent.

To explain the dynamics of this OPO far above threshold and how coherence can
be established over such a broad spectrum, we turn to numerical simulations.
To capture the multi-octave nonlinear interactions occurring in the OPO, we
modeled the electric field in the nanophotonic cavity as a single envelope in
frequency domain which is evolved using the split-step Fourier method for
propagation in the PPLN region and a linear filter for the cavity feedback
(see Supplementary Section III for details). In Fig. 3a, we show how this
captures distinct regimes of operation when using parameters matching that of
the experiment. At 16 fJ the OPO goes above threshold and stabilizes after
$\sim$20 roundtrips. At this point, all the frequency translated components
(OPO, SHG, SFG of the pump and OPO) are coherent with respect to the pump and
they remain unchanged from roundtrip to roundtrip. As the pump pulse energy is
increased, fewer roundtrips are required for the OPO to form, and at 137 fJ of
pump ($\sim$9$\times$ above threshold) we see that the OPO output is
incoherent.

At roughly 204 fJ of pump ($\sim$13$\times$ above threshold), however, the the
half-harmonic is seen to acquire a $\pi$ phase shift through the nonlinear
interaction with the pump in each single-pass through the PPLN region. This
can be compensated by detuning the cavity by an odd number of OPO peaks, or by
adding a constant phase offset of $\pi$ between the pump and cavity,
corresponding to the carrier-envelope offset phase, $\phi_{\mathrm{CEO}}$, of
the pump (see Supplementary Section III). The former case is shown in Fig.
3a(iii) and shows a two octave coherent continuous comb that stabilizes after
roughly twenty roundtrips with temporal features as short as 4 fs (see
Supplementary Section III). The output spectrum is also very similar to the
detuned 109 fJ experimental result of Fig. 2d.

In simulation, we further investigate how to extend the coherent operation of
the OPO to even broader spectra. By replacing the last one mm of the PPLN
region with a chirped poling period for efficient second harmonic and sum-
frequency generation, we achieve a coherent three-octave continuous frequency
comb with $\sim$250 fJ of pump energy as shown in Fig. 3b.

Conclusion and discussion

In Fig. 4 we compare our results with other integrated spectral broadening
schemes and sync-pumped OPOs. The figure highlights how our nanophotonic OPO
design and its operation regime enable orders-of-magnitude improvement in the
energy efficiency of coherent spectral broadening. Our work represents the
lowest threshold sync-pumped OPO which is enabled by its near-zero-dispersion
design. This ultralow-threshold operation enabled accessing a previously
unexplored operation regime of the OPO far above threshold, where ultrabroad
coherent spectral broadening is established as a consequence of the balance
between cavity detuning and nonlinear phase shift.

In summary, we have experimentally demonstrated a nearly sync-pumped
nanophotonic OPO operating in the near zero-GVM, zero-GVD, fs-pumped, high-
gain low-finesse regime resulting in an ultra-broadband coherent output with
only $\sim$109 fJ of energy. The two-octave frequency comb enables
unprecedented opportunities for on-chip applications including wavelength
division multiplexing7, dual-comb spectroscopy44, and frequency synthesis5. We
show the OPO transitions from an incoherent to coherent operation regime and
demonstrate a path towards much broader frequency comb sources in the
femtojoule regime.

## Methods

Device fabrication. Our device was fabricated on 700-nm-thick X-cut MgO-doped
thin-film lithium nioabte on a SiO2/Si substrate (NANOLN). Following the
procedure in 37, we pattern Cr/Au poling electrodes with 16 fixed poling
periods ranging from 4.955-5.18 $\mu$m using lift-off and and apply a voltage
to periodically flip the ferroelectric domains. Upon poling we remove the
electrodes and subsequently etch the waveguides using Ar-milling and Hyrdogen
Silsesquioxane (HSQ) as the etch mask. Finally, the waveguide facets are
mechanically polished to allow for butt coupling. Each OPO has a footprint of
0.5 mm $\times$ 13 mm.

Optical measurements. The measurements were performed using a Menlo Orange
HP10 Yb mode-locked laser (MLL) centered at 1045 nm. It outputs 100-fs-long
pulses at 250 MHz with a $\pm 1$ MHz tuning range. Light was coupled to and
from the chip using Newport 50102-02 reflective objectives, chosen for their
minimal chromatic aberration. All of the results in this paper were performed
on a device with 5.075 $\mu$m poling period at 26°C, regulated by a
thermoelectric cooler (TEC). The lowest OPO threshold was obtained from a pump
repetition rate of 250.1775 MHz, which we define as the zero detuned state.
This device has a total throughput loss of 43.4 dB, and following the
methodology in 37, we measured the input and output coupling losses to be 35.7
dB and 7.7 dB respectively. For the results in Fig. 3a, the spectra were
collected by two different optical spectrum analyzers (OSA), specifically a
Yokogawa AQ6374 (350-1750nm) and AQ6376 (1500-3400 nm). For the three octave
spectra the wavelengths below 700 nm were taken with a high OH silica fiber
(Thorlabs M133) and the spectra above 1750 with an InF3 fiber (Thorlabs MF12).
All the other measurements were taken using a low OH silica fiber (Thorlabs
M72). The RF spectra was collected by an electronic spectrum analyzer (Rhode &
Schwarz FSW), combined with a high-speed silicon avalanche photodiode (Menlo
Systems APD210) in Fig. 2f and an InGaAs high speed photodiode (DSC2-40S) in
Fig. 2g.

Numerical simulations. We used commercial software (Lumerical Inc.) to solve
for the waveguide modes shown in Sections I and II of the Supplementary that
allowed us to dispersion engineer and quasi-phase-match our device. For the
nonlinear optical simulation, we solved an analytical nonlinear envelope
equation as described in Section III of the Supplementary. The simulations
were performed with no constant phase offset between the pump and cavity
unless specifically mentioned otherwise. This parameter effectively acts as a
carrier-envelope offset phase of the pump, $\phi_{\mathrm{CEO}}$. As the
simulations were performed with a time window of 1.7 ps, it should be
mentioned that a large portion of the short wavelength side of the spectrum
walked out of the time window of our simulation. For example, the simulated
GVM between our simulation reference frame at the half-harmonic signal
wavelength of 2090 nm and the second harmonic of the pump at 522 nm is 721
fs/mm. As a result, the up-converted portions of the spectrum in simulation
tend to be smaller than what was measured experimentally. In these simulations
we have only incorporated the effects of $\chi^{(2)}$ nonlinearity and have
not considered the effects of $\chi^{(3)}$. Especially given the low pulse
energies and low-finesse nature of our cavity, we believe this to be a good
approximation, yet it could be one additional reason for small discrepancies
between experiment and simulation.

## 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 computer code used to perform the nonlinear simulations in this paper is
available from the corresponding author upon reasonable request.

## Acknowledgements

The device nanofabrication was performed at the Kavli Nanoscience Institute
(KNI) at Caltech. The authors thank Dr. Mahmood Bagheri for loaning equipment.
The authors gratefully acknowledge support from ARO grant no.
W911NF-23-1-0048, NSF grant no. 1846273 and 1918549, AFOSR award
FA9550-20-1-0040, the center for sensing to intelligence at Caltech, and
NASA/JPL. The authors wish to thank NTT Research for their financial support.

## Authors Contributions

R.S. and A.M. conceived the project; R.S. fabricated the devices with
assistance from L.L., S.Z, and Q.G. R.G. and R.S. performed the measurements
and R.G. carried out the simulations with initial input from L.L. R.S. and
A.M. wrote the manuscript with inputs from all authors. A.M. supervised the
project.

## Competing Interests

L.L., and A.M. are inventors on granted U.S. patent 11,226,538 that covers
thin-film optical parametric oscillators. R.S., R.G., L.L., A.R., and A.M. are
inventors on a U.S. provisional patent application filed by the California
Institute of Technology (application number 63/466,188). R.G., L.L., and A.M.
are inventors on a U.S. provisional patent application filed by the California
Institute of Technology (application number 63/434,015) on 20 December 2022.
L.L. and A.M. are involved in developing photonic integrated nonlinear
circuits at PINC Technologies Inc. L.L. and A.M. have an equity interest in
PINC Technologies Inc. The other authors declare that they have no competing
interests.

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