Photonic chip based optical frequency comb using soliton induced Cherenkov radiation

V. Brasch,1 T. Herr,1, 2 M. Geiselmann,1 G. Lihachev,3, 4

M.H.P. Pfeiffer,1 M.L. Gorodetsky,3, 4 and T.J. Kippenberg1, ∗

1École Polytechnique Fédérale de Lausanne (EPFL), CH–1015, Switzerland2Current address: Centre Suisse d’Electronique et Microtechnique SA (CSEM), CH–2002, Switzerland

3Faculty of Physics, M.V. Lomonosov Moscow State University, Moscow 119991, Russia4Russian Quantum Center, Skolkovo 143025, Russia

Optical frequency combs[1, 2] provide a series of equidistant laser lines and have revolutionized thefield of frequency metrology within the last decade. Originally developed to achieve absolute opticalfrequency measurements, optical frequency combs have enabled advances in other areas[3] such asmolecular fingerprinting[4, 5], astronomy[6], range finding[7] or the synthesis of low noise microwavesignals[8]. Discovered in 2007[9, 10], microresonator (Kerr) frequency combs have emerged as analternative and widely investigated method to synthesize optical frequency combs offering compactform factor, chipscale integration, multi-gigahertz repetition rates, broad spectral bandwidth andhigh power per frequency comb line. Since their discovery there has been substantial progress infundamental understanding[11–13], theoretical modeling[14–16], on-chip planar integration[17, 18]and resulting applications[19–21]. Yet, in no demonstration could two key properties of opticalfrequency combs, broad spectral bandwidth and coherence, be achieved simultaneously. Here weovercome this challenge by accessing, for the first time, soliton induced Cherenkov radiation[22, 23] inan optical microresonator. By continuous wave pumping of a dispersion engineered, planar siliconnitride microresonator[17, 18], continuously circulating, sub-30 fs short temporal dissipative Kerrsolitons[24–26] are generated, that correspond to pulses of 6 optical cycles and constitute a coherentoptical frequency comb in the spectral domain. Emission of soliton induced Cherenkov radiationcaused by higher order dispersion broadens the spectral bandwidth to 2/3 of an octave, sufficient forself referencing[1, 2], in excellent agreement with recent theoretical predictions[16] and the broadestcoherent microresonator frequency comb generated to date. Once generated it is shown that thesoliton induced Cherenkov radiation based frequency comb can be fully phase stabilized. The overallrelative accuracy of the generated comb with respect to a reference fiber laser frequency comb ismeasured to be 3 · 10 −15.

The ability to preserve coherence over a broad spectral bandwidth using soliton induced Cherenkovradiation marks a critical milestone in the development of planar optical frequency combs, enablingon one hand application in e.g. coherent communications[19], broadband dual comb spectroscopy[27]and Raman spectral imaging[28], while on the other hand significantly relaxing dispersion require-ments for broadband microresonator frequency combs[29] and providing a path for their generationin the visible and UV. Our results underscore the utility and effectiveness of planar microresonatorfrequency comb technology, that offers the potential to make frequency metrology accessible beyondspecialized laboratories.

Optical solitons are propagating pulses of light thatretain their shape due to a balance of nonlinearity anddispersion[24–26, 30]. In the presence of higher orderdispersion optical solitons can emit soliton Cherenkovradiation[22, 23]. This process, also known as disper-sive wave generation, is one of the key nonlinear fre-quency conversion mechanisms of coherent supercontin-uum generation[31, 32], which allows substantially in-creasing the spectral bandwidth of pulsed laser sources.The generation of a coherent supercontinuum from apulsed laser propagating through an optical photoniccrystal fiber, has been a defining experimental advance,which has enabled the first self-referenced optical fre-quency comb[1, 2] and has given access to coherent broad-band spectra in the visible. This breakthrough has es-tablished the frequency comb technology with repetitionrates up to around 1 GHz now at the heart of a variety of

∗ Corresponding author: tobias.kippenberg@epfl.ch

applications[2, 3]. However, a growing number of applica-tions require pulse repetition rates in excess of 10 GHz[3].Beside the difficulty to generate multi-gigahertz repeti-tion rates with conventional lasers, spectral broadeningof such pulses is impeded by the inherent reduction ofpulse energy with increasing repetition rate, which makessoliton spectral broadening inefficient.

One new route to these high repetition rate and broad-band frequency combs was established with the discov-ery of microresonator frequency combs[9, 10]. Sincethe first experiments, the field of microresonator fre-quency combs, also known as Kerr frequency combs,has made substantial advances, such as the demonstra-tion of frequency comb generation in CMOS compatiblephotonic chips using silicon nitride resonators[17, 18] aswell as in other integrated microresonators[18, 33, 34],the achievement of electronically detectable microwaverepetition rates[35, 36], the generation of octave span-ning (yet high noise) spectra[37, 38], the extension tomid IR[39, 40] , generation of combs with pulsed out-

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put in normal dispersion resonators[41] and the abil-ity to detect the carrier envelope offset frequency[42].Proof of concept applications have been realized in co-herent telecommunication[19], miniature optical atomicclocks[21], optical waveform synthesis[12] and low noisemicrowave generation[43].

Moreover a detailed understanding of the Kerr combformation process has been obtained: The Kerr combformation process[11] can lead to multiple sub-comb for-mation in microresonators for which the variation ofthe free spectral range is small compared to the cav-ity linewidth; a parameter regime which in particu-lar photonic chip based microresonators fall into. Theformation of sub-combs can give rise to loss of coher-ence, multiple beat-notes and amplitude and phase noise.Low noise, coherent operation in this regime can stillbe achieved via sub-comb synchronization[11], which in-volves either probabilistic tuning techniques such as δ-∆matching[11], injection-locking[44] and mode-locking[45]or parametric seeding[46]. In the opposite regime (whichoccurs in micro-toroid resonators[9] or crystalline res-onators pumped in the mid IR[39]) low phase noise canbe achieved at reasonable pump power for narrow band-width frequency combs[11–13]. Most recently temporaldissipative cavity (or dissipative Kerr) soliton formationhas been observed in crystalline microresonators, leadingto narrow, coherent frequency combs[26].

Recent theoretical advances based on models usingthe Lugiato-Lefever equation[16, 47, 48] have predictedthat accessing solitons and soliton induced Cherenkovradiation[16, 29, 49] provides a path to the reliable gener-ation of broadband and coherent frequency combs, whichcan span a full octave, sufficient for self referencing. Thisregime therefore makes external broadening superfluous.

Our experimental platform are silicon nitride (Si3N4further called SiN) optical microresonators, which arehighly suitable for integrated nonlinear photonics dueto its large band gap and the resulting wide trans-parency window[18] and which are compatible with spaceapplications[50]. Pioneering work[17] demonstrated op-tical frequency comb generation in a SiN microresonator,providing a path to planar, CMOS compatible frequencycomb sources. Here we utilize 800 nm thick SiN ringresonators with 238µm diameter embedded in SiO2 (seeFig. 1a-d and cf. Methods section) resulting in anomalousgroup velocity dispersion (GVD) around 1.5µm. The mi-croresonator fabrication was optimized in order to mit-igate avoided crossings of different mode families thatcan locally alter dispersion[51]. The resonance frequen-cies of one mode family can be approximated around thepump resonance with eigenfrequency ω0 as a Taylor se-ries ωµ = ω0 +

∑j Djµ

j/j! with j ∈ N, where µ ∈ Zis the mode number counted from the designated pumpresonance. Here D1/2π is the free spectral range of theresonator and D2 is related to the GVD parameter β2 byD2 = − cnD

21β2. Figure 1e shows the integrated disper-

sion Dint(µ) of a given mode number µ relative to thepump mode at µ = 0; i.e. Dint(µ) ≡ ωµ − (ω0 +D1µ) =

DispersiveWave

Pump

ZeroDispersion

Anomalous DispersionNormal Dispersion

ZeroDInt

Opt

ical

Pow

er (d

B)

0D Int

(a.u

.)

Recoile

a

b

c

Optical Frequency (a.u.)

Soliton

DInt

20 μm

2 μm

500 nm

100 μm

a

d

c

b

FIG. 1. Temporal soliton generation and soliton in-duced Cherenkov radiation in a planar SiN microres-onator. a,b Colored scanning electron microscopy imagesof a SiN optical microresonator with the same geometry asthe one used but without the SiO2 encapsulation. Shown inblue is the silicon substrate. Colored in magenta is the SiO2pedestal with the SiN waveguide (orange) on top. b, An im-age of the chip at lower magnification. c, A close-up of thecoupling region between bus waveguide and resonator (similargeometry as used). d, A cross section of a fabricated devicethat also shows the top cladding (SiO2, colored purple). e,A schematic of the integrated dispersion Dint(µ) as a func-tion of optical frequency and the associated soliton dynam-ics. Regions with positive (negative) curvature have anoma-lous (normal) group velocity dispersion (GVD). Around thepump Dint(µ) can be approximated by a parabola (red dashedline), indicating that it is dominated by quadratic, anomalousGVD. Therefore the resonator supports the formation of tem-poral solitons around this wavelength. Due to the presence ofhigher order material and waveguide dispersion the region ofanomalous GVD is finite. In the absence of fourth and higherorder dispersion (D1, D2, D3 6= 0 and Dp = 0 for p > 3) thezero dispersion point (ZDP) occurs at µZDP = −D2D3 (givenby D′′int(µZDP) = 0). Additionally, the integrated dispersionhas at least one zero crossing, occurring at µ = −3D2

D3, (given

by Dint(µ) = 0). In this case the soliton can emit solitonCherenkov radiation (also known as dispersive wave emis-sion) into the normal dispersion regime at around the fre-quency where Dint(µ) = 0 where phase matching occurs andthe transfer of energy from the soliton to the dispersive waveis most efficient. To obey energy conservation in the presenceof one strong dispersive wave the maximum of the generatedspectrum close to the pump is shifted away from the pump(recoil).

D2µ2

2! + D3µ3

3! + ... . Therefore Dint(µ) is equivalent tothe deviation of ωµ from an equidistant frequency griddefined by ω0 and D1.

When CW pumping an optical microresonator withanomalous GVD, bright temporal dissipative Kerr soli-tons can be formed[24–26]. The dynamics of this systemcan be described by a master equation[14, 16, 52] with

3

higher order dispersion and self-steepening effects addi- tionally taken into account:

∂A

∂t+ i∑j=2

Djj!

(∂

i ∂φ

)jA− ig

(1 +

iD1ω0

∂

∂φ

)|A|2A = = −

(κ2

+ i(ω0 − ωp))A+

√κηPin~ω0

. (1)

Here A(φ, t) =∑µAµe

iµφ−i(ωµ−ωp)t is the slowly vary-ing field amplitude, φ is the azimuthal angular coor-dinate inside the resonator, co-rotating with a soliton,

g =~ω20cn2n2Veff

the nonlinear coupling coefficient with n andn2 the linear and nonlinear refractive indices of the ma-terial, Veff = AeffL the effective nonlinear mode volumewith Aeff the effective nonlinear mode area and L thecavity length, κ the cavity decay rate, η the coupling ef-ficiency and Pin and ωp the pump power inside the buswaveguide and the frequency of the pump light[26]. For-mally, equation 1 is identical to the Lugiato-Lefever equa-tion (LLE)[24] extended with higher order terms relevantfor very short pulses[29]. In the frequency domain thisequation is equivalent to a set of coupled mode equations,which directly describes the amplitudes of the modesin the resonator[51] (cf. Methods). In the absence ofthird and higher order dispersion the LLE exhibits solu-tions that correspond to bright temporal solitons super-imposed on a CW background[53]:

A(φ) ≈ Acw +A1N∑j=1

sech

√2(ω0 − ωp)D2

(φ− φj)

eiψ0 ,(2)with amplitude A1, phase ψ0 and background Acw de-termined by dispersion, nonlinearity, pump power anddetuning, φi is the position of each soliton[26]. The min-imal pulse duration at half maximum for a given pump

power Pin is then given by ∆t3dB ≈ 2√−β2γFPin

, with F the

finesse and γ = ωn2cAeff the effective nonlinearity. Thesetemporal dissipative Kerr solitons have been observed infiber cavities[25] and in crystalline microresonators[26]and they occur only in the bistable regime, where simul-taneous existence of the upper branch (soliton) and lowerbranch (CW pump) solution is warranted[26].

When small higher order dispersion terms are present,the shape and velocity of the stationary solitonschange[22]. The spectrum of such perturbed soliton be-comes asymmetric with its maximum shifted from thepump frequency (cf. Fig. 1e). At the same time thetemporal soliton develops a radiation tail[22, 54] whichis the soliton Cherenkov radiation. This is in contrastto dispersive wave formation in the regime of unstablemodulation instability that can be explained by phasematching of cascaded four wave mixing[55]. Due to thesynchronization of the soliton and the Cherenkov radia-tion, this radiation can become comparable in strengthto the soliton itself and can not be treated as a smallperturbation[23, 56]. In this case another approach based

on the linearization of the LLE may be used[57] allow-ing to get complex valued µDW for the position of thesoliton Cherenkov radiation. Of the complex value theimaginary part is related to the width of the feature andthe real part gives its position. This position is approxi-mately given by the linear phase matching condition[55]that occurs for µDW = −3D2D3 for D4 = 0. In the presenceof D4 two peaks of Cherenkov radiation may occur near

µDW = − 2D3D4 ±√

( 2D3D4 )2 − 12D2D4 .

In Fig. 2b frequency comb assisted diode laserspectroscopy[58] measurements of the SiN resonator dis-persion are shown, revealing that around the pump wave-length the mode structure closely approaches a purelyanomalous GVD (albeit very weak avoided crossingsare still measurable, cf. inset and SI Fig. 6, that arehowever not expected to impact soliton formation[51]),fulfilling the requirements for bright soliton formationdiscussed above. The experimentally determined valueD2/2π = 2.4± 0.1 MHz is in close agreement with thevalue of D2/2π = 2.6 MHz obtained by finite elementmodeling (FEM) based on the resonator geometry. Whenpumping the resonator at 1560 nm via the bus waveguidewith Pin ∼ 500 mW, far above the parametric thresh-old as given by the cavity bifurcation criterion (i.e.γFPthresc/nπ ≈ κ/2), we observe features that arecanonical signatures of microresonator temporal solitonformation. While scanning the pump laser from higherfrequencies to lower frequencies over a resonance of theTM11 mode family a series of abrupt transmission stepsoccur. These discontinuities are also observed in the gen-erated frequency comb light, (cf. SI Fig. 9a and 5 for datafrom several other SiN microresonators). Such steps havebeen previously identified with temporal soliton forma-tion in crystalline microresonators[26], where each stepcorresponds to the successive reduction of the number ofsolitons circulating in the microresonator. The regimewhere steps are recorded coincides with a narrowing ofthe recorded repetition rate beat note (cf. SI Fig. 5c,d) inagreement with the low noise operation within the soli-ton formation regime. These observations thus indicatetemporal soliton formation in SiN microresonators.

To access the soliton states in a steady state, we devel-oped a laser tuning technique (cf. Methods) to overcomeinstabilities associated with the discontinuous transitionsof the soliton states. After tuning into the soliton stateit remains stable for hours without any further stabiliza-tion allowing to record the full optical spectrum and toinvestigate its coherence properties. The optical single

4

2000 1900 1800 1700 1600 1500 1400 1300

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150 160 170 180 200 210 220 230

225THz150THz 193.16THz / 1552nm157.2THz / 1907.1nm

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mode number−40 −20 0 20 40

012

DIn

t (G

Hz)

/2π

−100 0 1000

0.5

1

30fs

150 160 170 180 200 210 220 230190

−60

−40

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0

20

FIG. 2. Single optical soliton and soliton Cherenkov radiation in a SiN optical microresonator a, The opticalspectrum shows the characteristic shape of a single soliton state in the microresonator with soliton Cherenkov radiation. Theenvelope of the spectrum is smooth and follows for the higher frequency side a sech2-shape with a 3–dB width of 10.8 THz.The Cherenkov radiation manifests itself as a sharp, distinct peak at around 155 THz. The CW-pump is located at 192.2 THz,the line spacing is 189.2 GHz. The green dashed lines mark two frequencies between which the spectrum covers 2/3 of anoctave. The green solid line represents the spectral envelope derived from simulations. The two slightly different blues indicate

measurements done with two different optical spectrum analyzers. b, The integrated dispersion (Dint(µ) = D2µ2

2!+D3

µ3

3!+ ...)

from FEM simulations for the measured resonator geometry (grey solid line). The zero dispersion point (ZDP) is indicated by adashed line. To the left of the ZPD is the normal group velocity dispersion (GVD) and to its right the anomalous GVD regime.The blue dots around mode number 0 (inset shows a zoom-in) are measured positions of around 80 resonances and show goodagreement between the simulated dispersion and the measurements. c, The repetition rate beat note of the frequency combat the line spacing of 189.22 GHz shows a narrow linewidth of around 1 kHz (cf. Fig. 2b and Methods for details). d, Themeasured beat note of the generated frequency comb with a narrow linewidth reference laser positioned at 1552.0 nm (orangeline in a); offset is 1.92 GHz. e, The beat note of a fiber laser positioned at 1907.1 nm (red line in a) and the nearest combline; offset is 5.47 GHz. f, The intensity profile of the soliton pulse inside the resonator estimated from the measured spectrum(blue) and taken directly from the numerical simulation that yields the envelope in a (green) with FWHM of below 30 fs. Thepulse shape taken from the simulation shows a small asymmetry due to the effect of the Cherenkov radiation.

soliton spectrum for approximately 2 W of pump powerin the bus waveguide is shown in Fig. 2a and has sev-eral salient features. First, it covers a bandwidth of 2/3of an octave, from 150 THz to 225 THz. Second, it ex-hibits the characteristic hyperbolic secant spectral enve-lope near the pump that is associated with a temporalsoliton. The 3-dB bandwidth of the generated spectrumis 10.8 THz which corresponds to 29 fs optical pulses (i.e.a pulse with 6 optical cycles). This agrees well with

the expected bandwidth from the calculated minimumsoliton duration of ∆t3dB ≈ 25 fs. The soliton pulseenergy is estimated to be 0.1 nJ inside the resonator.Third, a striking attribute is the sharp feature around1930 nm (155 THz) that corresponds to the soliton in-duced Cherenkov radiation[16]. Figure 2b shows themeasured dispersion and the dispersion simulated withthe aforementioned finite element modeling (cf. Meth-ods). The spectral position of the Cherenkov radiation

5

at µ = 195 is in very good agreement with the linearphase matching condition that occurs at µDW ≈ 200 forthe simulated parameters D2/2π = 2.6 MHz, D3/2π =24.5 kHz, D4/2π = −290 Hz.

We compared the measured single soliton spectrumto numerical simulations of the soliton dynamics[26] us-ing dispersion parameters derived from FEM simula-tions. The resulting spectrum is shown as the envelope inFig. 2a and again, good agreement is attained. From thesimulations we can also calculate the temporal shape ofthe soliton inside the microresonator, which agrees wellwith the estimate based on the measured spectrum as-suming flat phases (cf. Fig. 2f). The good agreementwith experimental data therefore establishes numericalsimulations[16, 29] as a powerful predictive tool for soli-ton dynamics in microresonators. Noticeable differencesbetween the experimental spectrum and the theoreticalsimulation are the reduced intensity of the Cherenkov ra-diation and the absence of an observable soliton recoil inthe experiment. We attribute the former to experimen-tally confirmed higher optical losses in the setup for theselong wavelengths and the latter to possible variations inthe quality factor versus wavelength and nonlinear terms(Raman shift[59], frequency dependence of the nonlin-ear coefficient), which are not taken into account in oursimulation.

A key property of a frequency comb, the coherence ofits spectrum, has to be investigated separately. First, therepetition rate beat note of the generated soliton spec-trum was measured on a high-speed photodiode at a fre-quency of 189.2 GHz using amplitude modulation down-mixing[60] (cf. Methods and SI Fig. 9b). Figure 2c showsthe resulting resolution bandwidth limited beat note (res-olution bandwidth of 1 kHz) which exhibits a signal tonoise ratio (SNR) of 40 dB in 100 kHz bandwidth. Thisdemonstrates the low noise nature of the temporal soli-ton state. In addition, we record the low frequency am-plitude noise of the soliton state and find no excess noisecompared to the pump laser noise (cf. SI Fig. 8). Thesemeasurements demonstrate that the soliton componentof the spectrum centered around the pump exhibits lownoise and is fully coherent.

Given that in theory an interaction of the soliton andits radiation tail was studied[61], potentially leading toloss of coherence, it demands for a detailed analysis ofthe coherence of the soliton Cherenkov radiation in themicroresonator case. To do so we carry out additionalCW heterodyne beat note measurements with a thuliumfiber laser (wavelength 1907 nm). To reduce the effectof frequency jitter of the pump on the measurements, westabilize the pump laser onto an absolute frequency refer-ence. Figure 2e shows the beat of the thulium fiber laserat 1907 nm with one frequency comb component of thesoliton induced Cherenkov radiation, exhibiting a nar-row linewidth ∼ 1 MHz and > 20 dB high SNR in 2 MHzbandwidth. Simultaneously with the beat at 1907 nmwe measure the beat with an erbium fiber laser close tothe pump at 1552 nm. The resulting CW beat is simi-

lar in width to the in-loop beat of the stabilized pumplaser (∼ 300 kHz). We attribute the difference betweenthe widths of the beat at 1552 nm and 1907 nm to theeffect of the non-stabilized repetition rate. The narrowbeat note for the line spacing together with the two het-erodyne measurements proof that the entire spectrum iscoherent over its full span of 2/3 of an octave, in con-trast to earlier reports[35, 38]. We note that this spec-trum constitutes the broadest coherent spectrum gener-ated directly on chip to date and that its bandwidth canbe increased further by dispersion engineering[29].

It is insightful to contrast the coherent single solitonstate to the incoherent high noise state that can be gen-erated when tuning the pump laser continuously into theresonance, a tuning mechanism that has been widely em-ployed in Kerr frequency comb generation experiments.We observe in this case a spectrum that markedly de-viates in its shape from the single soliton spectrum (seeSI Fig. 8a). While the overall bandwidth is only slightlyreduced the spectrum is not coherent and a degradationof the beat note to a width of the order of GHz is mea-surable in CW heterodyne measurements (SI Fig. 8b), inagreement with the formation of sub-combs[11]. In thishigh noise regime the height of the Cherenkov radiation issignificantly lower (by approx. 10 dB) and the spectrumdevelops two characteristic lobes symmetric around thepump. Also this low coherence state is in good agree-ment with our numerical simulations (cf. SI Fig. 8a) andrecent theoretical predictions[49].

Our system also allows to study multiple temporal soli-tons in the cavity which are stable for hours, as the singlesoliton state, (Fig. 3d) allowing for the analysis of theircoherence properties. Figure 3a–c show the optical spec-tra of three multi-soliton states, which we find again tobe coherent (cf. SI Fig. 7). The generated spectra showpronounced variations in the spectral envelope, that arisefrom the interference of the Fourier components of the in-dividual solitons. The spectral envelope function of thisinterference is given by

I(µ) =

∣∣∣∣∣∣N∑j=1

exp(iφjµ)

∣∣∣∣∣∣2

,

where φj corresponds to the relative angular position ofthe jth soliton. The insets of Fig. 3a–c show the recon-structed relative positions of the solitons inside the res-onator for the different spectra (cf. Methods). Figure 3bshows the case where two solitons are almost perfectlyopposite to each other in the resonator (differing by 180degrees). This results in a spectrum that exhibits twicethe line spacing of the single soliton case. Figure 3c showsthat a higher number of cavity solitons (N = 3) can resultin a spectrum with more complex spectral modulations.Using the soliton positions, we can retrieve successfullythe equivalent single soliton spectrum (solid green enve-lope in Fig. 3c).

To prove the usability of our system for metrologicalapplications we implement a full phase stabilization of

6

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FIG. 3. Multi-soliton states in a planar microres-onator and their stability. a,b,c Spectra for multi-solitonstates and the relative phase position of the solitons insidethe microresonator, sketched in the insets according to thefield autocorrelation (Fourier transform of the intensity spec-trum). a,b Two soliton states and c three soliton state withthe derived single soliton spectral envelope (solid green line).d, The color-coded field autocorrelation of a two-soliton stateversus laboratory time. The peaks (bright blue and red hori-zontal lines) give directly the positions of the two solitons withrespect to each other. The position jitters only very little anddoes not drift over the time of one hour. The panel to theright shows the field autocorrelation after 50 min indicated bythe white line.

the spectrum by phase locking the pump laser and therepetition rate of the SiN comb to a common RF ref-erence. For the absolute frequency stabilization of thepump laser we use an offset lock to a self-referenced fiberlaser frequency comb. The actuation for the repetitionrate is achieved via the pump power[35] (cf. Methods).In Fig. 4b we show the modified Allan deviation of the in-loop signals, i.e. the repetition rate and offset lock respec-tively for a two soliton based Cherenkov radiation combstate. To verify the stabilization we record an out-of-loop

123

1719 18

0

frep = 189.2GHz

1361213614 13613

fool = 57.6 MHz

18

fo� = 70MHz

012

frep,fc = 250.1MHz

0

−40 −20 0 20 400

50

100

150fool: 57.59168095 MHz ± 558 mHz

Std dev: 8.28Hz

deviation (Hz)

coun

ts

188.5 189 189.5 190 190.5 191 191.5 192 192.5

−40

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frequency (THz)

inte

nsity

(dBm

)

18frep = 13613frep,fc+fo�–fool

10−3

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102

10−5

10−3

10−1

101

103

105

gate time (s)

mod

. Alla

n D

evia

tion

(Hz)

Out−of−loopRepetition ratePump osetReference

a b

c

FIG. 4. Full phase stabilization and absolute frequencyaccuracy measurement of dissipative Kerr solitons inSiN. a Histogram of the counter measurement for the out-of-loop beat of the stabilized microresonator frequency combwith a commercial fiber laser frequency comb. Gate time is1 s. The Gaussian fit gives the exact frequency of the beat(fool). The stabilized state shown here is a two soliton state.b The modified Allan deviation of the out-of-loop beat aswell as the in-loop signals for the two locks of the repetitionrate and the pump laser offset of the microresonator frequencycomb. All signals average down over the gate time as expectedfor coherent signals. c A scheme highlighting the principle ofthe absolute frequency accuracy measurement referenced to aself-referenced fiber frequency comb. The out-of-loop beat isthe beat between the 18th line on the red side of the pumpof the microresonator frequency comb and the 13613th line ofthe reference comb counted from the line that the pump laseris locked to. The exact frequencies are given in the Methodssection.

signal, by counting the heterodyne beat of an indepen-dent comb teeth of the SiN comb with the reference comb.For all three signals the modified Allan deviation averagesdown with increasing gate time. The slope of the modi-fied Allan deviation for the out-of-loop data in Fig. 4b is−0.83. Similar results have been measured for a singlesoliton state as well (cf. SI Fig. 10). These measurementsdemonstrate that the soliton induced Cherenkov radia-tion state is stable against pump and laser fluctuationsand allows a full phase stabilization.

The out-of-loop measurement also allows to comparethe absolute frequency accuracy of the soliton Cherenkovradiation based comb state with the fiber laser refer-ence comb. To assess the absolute accuracy we com-pare the 18th soliton comb teeth to the fiber laser comb(with approximately 250 MHz mode spacing). After nu-merically infering that the beat with the fiber comboriginates from the 13613th comb teeth (relative to thepump) we can measure the absolute frequency differ-ence ∆ of the two intervals, and thus access the soliton

7

comb accuracy. Taking into account all locked frequen-cies as shown in Fig. 4c and extracting the center fre-quency of the out-of-loop signal from counter measure-ments shown in Fig. 4a, we derive a frequency differenceof ∆ = 18 ·frep−13613 ·frep,fc−foff +fool = 25±558 mHzfor the 1000 s long measurement. We therefore validatethe accuracy (and thereby also the equidistance) of theSiN soliton frequency comb to sub-Hz level and verify therelative accuracy (with respect to the optical carrier) to3 · 10−15.

The observation of broadband and coherent spec-tra created by soliton formation and soliton inducedCherenkov radiation in a photonic chip based microres-onator provides an essential novel ingredient to realizeon chip frequency combs for two reasons. First, themechanisms are well understood which makes quantita-tive predictions of the generated coherent spectra possi-ble. Second, they expand the frequency comb bandwidthto the normal GVD window which can extend the fre-quency comb bandwidth to the visible wavelength range,a regime in which most materials have normal GVD.The presently achieved coherent 2/3 of an octave withdetectable mode spacing can be self-referenced with the2f -3f technique[1, 2] without any additional broadeningand can be extended to a full octave with a modifieddispersion design, as previously predicted[29]. From atime domain perspective, the approach enables the syn-thesis of few cycle light pulses, that are already at presentshorter than conventional fiber laser technology based onerbium. The generated broadband frequency comb spec-tra with multi-GHz mode spacing can be directly used forastrophysical spectrometer calibration, meeting the spec-ifications for e.g. the SPIROU spectrometer, employedfor the search of earth like exoplanets. In conjunctionwith the ability to integrate lasers and detectors on thesame chip our results provide a key step towards the longterm goal of a fully integrated, on-chip RF-to-optical link.

ACKNOWLEDGMENTS

This work was supported by the DARPA ProgramQuASAR, an ESA TRP and the Swiss National Sci-ence Foundation. MLG acknowledges support from theRFBR grant 13-02-00271. Correspondence and requestsfor materials should be addressed to TJK (email: to-bias.kippenberg@epfl.ch).

METHODS

A. Nanofabrication

Starting with a silicon wafer with 4µm of thermal sili-con dioxide (SiO2) we deposit close to stoichiometric sil-icon nitride (SiN) for the waveguide cores as a 800 nm

thick film in a low-pressure chemical vapor deposition(LPCVD) process. After some auxiliary steps the waveg-uides are patterned in a 100 kV electron beam lithogra-phy system using ZEP520 as resist. After developmentthe resist is re-flown. The following reactive ion etchis the critical etch step. It uses CHF3 and SF6 gasesand transfers the pattern into the SiN. This is followedby a photolithography step to define auxiliary structures.The wafer is thoroughly cleaned before an additional thinlayer of SiN is deposited with the same process as before.Afterwards the wafer is annealed and the 3µm thick SiO2cladding is deposited with a CVD process on top. Thelast steps are the definition and separation of the chipsand a second anneal.

B. Finite element simulations

Using the commercial Comsol Multiphysics package forFEM simulations, we implemented a 2D simulation whichtakes into account the cylindrical symmetry of the systemin the third dimension. Material dispersion is taken intoaccount via an iterative approach which takes the valuesof the refractive index from measured values for our SiNfilms. The values for dispersion parameters are obtainedfrom fitting appropriate polynomials to the absolute fre-quencies of the modes around our pump wavelength of192.2 THz. The relative magnitude of the values for thefree spectral range in the simulation is used to identifythe mode families (TE and TM) inside the resonator.

C. Implementation of the numerical simulation

For the numerical simulation we used coupled modeequations which are propagated in time using an adap-tive step size Runge-Kutta algorithm[14]. The calcu-lation of the nonlinear mixing terms is efficiently cal-culated in the Fourier-domain[62]. An additional self-steepening term[29] was added to better model the be-havior of few-cycles pulses. To allow for determinis-tic simulations of required states one, two or three-soliton states were seeded as initial waveform, startingthe simulation with a detuning that allows for stablesolitons. The parameters used for the simulation pre-sented in Fig. 2a are: D2/2π = 2.2 MHz, D3/2π = 25 kHz,D4/2π = −300 Hz, detuning ζ = 12, Qint = 1.5 · 106,Qext = 8 · 105, Ppump = 1 W.

D. Multi-soliton and single-soliton spectra

When N identical solitons circulate around the res-onator they produce a frequency comb spectrum S(N)(µ)with a structured envelope which results from interfer-ence of single soliton Fourier spectra S(1)(µ):

8

S(N)(µ) =

∣∣∣∣∣∣F

N∑j=1

Aµ(φ− φj)

∣∣∣∣∣∣2

= S(1)(µ)I(µ) = S(1)(µ)

N + 2∑j 6=l

cos(µ(φj − φl))

. (3)

If now the Fourier transform of this optical spectrum(sometimes transformed initially by picking only the fre-quency comb lines) is taken, it will result in the fieldautocorrelation function of the waveform according tothe Wiener-Khinchin theorem. In the case of N soli-tons it contains two peaks at 0 and 2π and in additionN(N − 1) single-soliton autocorrelation peaks at posi-tions in the interval (0..2π) symmetric around π, corre-sponding to pairwise distances between circulating soli-tons (cf. Fig. 3d). Using simple peak-finding it is possibleto obtain these distances and define the trigonometricmultiplier of the spectrum. To reconstruct the single-soliton spectrum we simply divide the initial spectrum by

N + 2∑Nj 6=l cos(µ(φj − φl)). Note that in the degenerate

case when all the distances are related as integer numbers(like in Fig. 3b) the trigonometric sum may turn to zeroat some points, which should be dropped from consider-ation. With the measured or reconstructed single-solitonspectrum and assuming flat phases it is possible to es-timate an approximate symmetrized form of the solitonand its duration, assuming that the asymmetry of thepulses is small (Fig. 2f). From the 3–dB width of thespectrum the pulse duration can be derived via the time-bandwidth product for soliton pulses of 0.315[26].

E. Sample characterization

The dispersion of our resonators was measured bysweeping a widely tunable external cavity diode laser(ECDL) over the resonances and recording the transmit-ted power on a photodiode. Part of the power of theECDL is differed before the resonator and used to recordits beat signal with a commercial fiber laser frequencycomb (repetition rate around 250 MHz). By counting thecrossings of this beat at certain frequencies and interpo-lation the position of the laser and the relative positionsof the resonances can be determined with a precision ofa few MHz[58]. The average linewidth of 300 MHz ofthe mode family used for the generation of the frequencycomb is measured by determining the linewidths of manyresonances within the range from 1510 nm to 1580 nm. Todetermine the linewidth the laser is scanned over each res-onance and the polarization is optimized. The laser scanis calibrated by using the same technique that is used tocalibrate the laser scan for the dispersion measurementabove. To measure the parametric threshold an amplifieddiode laser is swept over the resonance while the pumplight is filtered out from the transmission using a tun-able fiber Bragg grating. The remaining converted lightwhich is the light at other frequencies than the pumpis detected on a photodiode. The power of the pump

is adjusted until a clear signature of converted light onthe photodiode is observed indicating that parametricfrequency conversion takes place. To take into accountasymmetric input and output losses from the chip thismeasurement is repeated with changed direction on thechip. The measured threshold is Pthres = 300 mW in thewaveguide. The coupling loss per chip facet is approxi-mately 3 dB.

F. Laser tuning procedure for soliton generationand beat note measurements

In order to achieve a stable soliton state we have toovercome the transient instability of the states withinthe steps. This is achieved by modulating the pumppower with a simple two step protocol. The first stepis to induce the soliton with a quick drop in power. Thesecond step is to stabilize the soliton state by increasingthe pump power. The two step process to obtain sta-ble soliton states is implemented using one acoustic opti-cal modulator (AOM) and one Mach-Zehnder amplitudemodulator (MZM). The only reason for the use of twomodulators is the required speed of the modulation whichcan not be obtained solely with the AOM. The first stepof a short dip in power is done with the MZM and typi-cally of 100 to 200 ns in length. The following increase inpump power is obtained with the AOM as a step functionthat remains at high power throughout the measurementsafterwards. In order to measure the electronic beat noteat 189 GHz with a photodiode, we suppress the pumpby around 30 dB using a fiber Bragg grating and mod-ulate sidebands of 40 GHz onto the lines of the remain-ing frequency comb using a MZM. The correspondingmodulation sidebands reduce the difference to 109 GHzamenable to direct detection with a commercial telecom-munication photodiode with an optical power of around1 mW. The electrical signal of 109 GHz as obtained fromthe photodiode is down mixed with a harmonic mixer onthe sixths harmonic before being detected with an electri-cal spectrum analyzer at a frequency of around 1.7 GHz.The two narrow linewidth fiber lasers used for the hetero-dyne beat note measurements are based on NKT Koherassources and have linewidths below 10 kHz and a very highfrequency stability.

G. Full stabilization

The repetition rate is detected as described above anddownmixed to 70 MHz. The 70 MHz signal of the rep-etition rate and the pump laser offset at the same fre-

9

quency are fed into two separate digital phase compara-tors with the same 70 MHz reference signal on both. Thephase comparators provide the error signal for two PIDcontrollers which provide the feedback which is used tomodulate the pump power via an AOM and the laser cur-rent for the repetition rate lock and the laser offset lockrespectively. All involved RF equipment in the scheme isreferenced to the atomic reference of the fiber frequencycomb that provides the absolute optical reference for thepump laser offset lock. To measure the modified Allandeviation, three counters of the Λ-type were used to mea-sure the frequencies of the laser offset, the repetition rateand the out-of-loop beat simultaneous. The result there-

fore does not agree perfectly with the modified Allandeviation but shows the same scaling for different noisesources[63].

The exact frequencies are for the repetition rateof the microresonator frequency comb (locked, frep):189179.658 MHz, for the repetition rate of the fiber laserfrequency comb used as a reference (locked, frep,fc):250.144820075 MHz, for the offset of the pump laser fromthe reference frequency comb (locked, foff): 70.000 MHzand for the out-of-loop beat between the two frequencycombs (unlocked, derived from fit in Fig. 4(a), fool):57.59168095 MHz.

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SUPPLEMENTARY INFORMATION

−0.4 −0.2 0 0.2

0

0.2

0.4

0.6

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time ( s−0.4 −0.2 0 0.2

0

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time ( s

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norm

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−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.80.7

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−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8

35

36

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freq

uenc

y (G

Hz)

scanning time ( s)

a

b

c

d

FIG. 5. SI – Signs of solitons in SiN microresonators. a, The typical triangular shape of the transmission for higherpower laser sweeps from the blue side to the red side of a resonance. b, The steps in the converted light at the end of thetriangle (marked with a red box in a) are strong signs for soliton states. Red and green are two traces from two consecutive lasersweeps, highlighting the changes in the step patterns. Resonators with different repetition rates, as noted inside the figures,show these steps. c, The step in the transmission of a 38 GHz sample with high time resolution at the position of the red boxin a. d, The collapse of the beat note at 38 GHz from around 1 GHz width to a width limited by the measurement techniquewithin the short step of c.

12

1620 1600 1580 1560 1540 1520 wavelength (nm)

186 188 190 192 194 196 198

−100

−50

0

50

DIn

t/2π

(GH

z)

186 188 190 192 194 196 198−1

0

1

2

3

frequency (THz)

DIn

t/2π

(GH

z)

186 188 190 192 194 196 1980

200

400

600

800

1000

frequency (THz)

κ/2π

(MH

z)

a

b

c

FIG. 6. SI – Sample characteristics. a,b Dint of resonances in the used sample. The red, horizontal mode is the pumpedTM11 mode (enlarged in b). The blue TE11 mode has a different FSR and therefore is a tilted line. The solid, green line in bis a quadratic fit yielding a value for D2/2π of 2.4 MHz. c, The full linewidth (κ/2π) of some resonances of the TM11 modefamily. The green vertical line in all plots represents the position of the pump laser for the frequency comb generation.

13

2000 1900 1800 1700 1600 1500 1400 1300 wavelength (nm)

150 160 170 180 190 200 210 220−80

−60

−40

−20

0193.16THz / 1552nm157.2THz / 1907.1nm

frequency (THz)

inte

nsity

(dBm

)

−40 −20 0 20 40

−100

−80

−60

frequency − o�set (MHz)

Beat at 157.2THz/1907nmRBW: 100 kHz

inte

nsity

(dBm

)

−20 0 20

−100

−80

−60 Beat at 193.16THz/1552nmRBW: 50 kHz

frequency − o�set (MHz)−0.4 −0.2 0 0.2

−130

−120

−110

−100

−90 Rep rate beatRBW: 1 kHz

frequency − 189.2 GHz (MHz)

a

b c d

FIG. 7. SI – Coherence of a two-soliton state in a SiN microresonator. a Optical spectrum of a two-soliton statemeasured under very similar conditions and in the same resonance as the data of Fig. 3. b, The beat note of a narrow linewidthfiber laser at 1907 nm with the nearest line of the generated frequency comb. c, The beat note of a narrow linewidth fiber laserat 1552 nm with the nearest line of the generated frequency comb. d, The repetition rate beat note of the generated frequencycomb.

14

150 160 170 180 190 200 210 220

−60

−40

−20

inte

nsity

(dB)

0 5 10 15−10

0

10

20

30

rela

tive

inte

nsity

(dB)

0 500 1000 1500−10

0

10

20

30

40

150 160 170 180 190 200 210 220

−60

−40

−20

inte

nsity

(dB)

0 5 10 15−10

0

10

20

30

rela

tive

inte

nsity

(dB)

0 500 1000 1500−10

0

10

20

30

40

150 160 170 180 190 200 210 220

−60

−40

−20

inte

nsity

(dB)

0 5 10 15−10

0

10

20

30

rela

tive

inte

nsity

(dB)

0 500 1000 1500−10

0

10

20

30

40

150 160 170 180 190 200 210 220

−60

−40

−20

inte

nsity

(dBm

)

0 5 10 15−10

0

10

20

30

rela

tive

inte

nsity

(dB)

RBW: 20kHz

0 500 1000 1500−10

0

10

20

30

40

rela

tive

inte

nsity

(dB)

RBW: 50kHz

150 160 170 180 190 200 210 220

−60

−40

−20

inte

nsity

(dBm

)

4.73 4.74 4.75

−120

−100

−80

−60

inte

nsity

(dBm

)

RBW: 20kHz

0 500 1000 1500−10

0

10

20

rela

tive

inte

nsity

(dB)

RBW: 50kHz

150 160 170 180 190 200 210 220

−60

−40

−20

frequency in THz

inte

nsity

(dBm

)

−0.0001 0 0.0001−130

−120

−110

−100

−90

−80

frequency (GHz)

inte

nsity

(dBm

)

RBW: 1kHz

0 500 1000 1500−10

0

10

20

frequency (MHz)

rela

tive

inte

nsity

(dB)

RBW: 10kHz

RBW: 20kHz

RBW: 20kHz

RBW: 20kHz

RBW: 50kHz

RBW: 50kHz

RBW: 50kHz

Hig

h N

oise

Low

Noi

se S

olit

on S

tate

s

rela

tive

inte

nsity

(dB)

rela

tive

inte

nsity

(dB)

rela

tive

inte

nsity

(dB)

a b c

d e f

g h j

k l m

n o p

q r s

FIG. 8. SI – Comparison of a high noise state and solition states in a SiN microresonator. a, d, g, k The opticalspectra of the high noise state for the same resonance as all other spectra and with similar pump power when tuning the pumpfurther into the resonance (from blue to red). The spectrum in k shows a clearly flattened maximum of the soliton inducedCherenkov radiation at around 156 THz and two maxima to the left and right of the pump at 192.2± 3 THz. The green solidline outlines the spectral envelope derived from simulations which agrees well with the experimental data. Reasons of thedeviation between simulation and experiment are explained in the main text. b, e, h, l The beat note of a comb line witha narrow linewidth fiber laser at 1552 nm (green vertical ine in a) in the RF domain (shifting from around 2.5 GHz in e toaround 11 GHz in l) is very broad and structured. c, f, j, m The amplitude noise of the light after the chip measured up to1.5 GHz is clearly elevated. n Optical spectrum of a four soliton state in the same resonance. Although a structure is visible(cf. Fig. 3) the state is low noise. o, The beat note with a narrow linewidth fiber laser at 1552 nm is well defined and limitedby the linewidth of the pump laser. p, The amplitude noise floor of the transmitted light shows no increase over the noisefrom the pump laser. q, The spectrum for a two-soliton state shows a clear pattern and is also of low noise. r, The repetitionrate beat note is narrow and well defined. The data is offset by 189.2 GHz. s, The amplitude noise in the transmission onlyshows technical noise at certain frequencies. For all axis labeled “relative intensity” the background has been subtracted. Theabsolute levels of the background are m: –99.6 dBm, p: –98.5 dBm, s: –110.8 dBm.

15

Frequency Comb Generation

Pump Laser Lock

Transmission Monitor

Heterodyne Measurement

RF Beatnote Measurement

ESA

ECDL

Fiber LaserComb

Laser Lock

OM & EDFA

AFGFPC

ESA

Local Oscillator17.9 GHz

VFPDRF Ref FPC

40 GHz HighPower RF

MZAMHM

×6

TLF

1907nmFiber Laser

1552nmFiber Laser

OBPFESA

FBG

Scope

ESA

FBG

OSA

PDs

SiN Microresonator

OBPF

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

norm

aliz

ed g

ener

ated

ligh

t int

ensi

ty

time in μs

a

b

12

34

56

78

FIG. 9. SI – Soliton steps and schematic experimental setup. a, A color-coded histogram (red denotes high probability,dark blue denotes zero probability) of the recorded steps in the intensity of the converted light (light that is not at thewavelength of the pump) versus laser detuning, revealing steps between different soliton states inside the cavity. The whitenumbers indicate the number of solitons for each state. The transmitted light from the resonator is filtered for the pump anddetected, while the laser is scanned through the cavity resonance of the SiN microresonator. b, The setup for microresonatorbased soliton generation. The microresonator is pumped with CW laser light from an external cavity diode laser (ECDL)that is amplified and modulated in power (bright red box). The remaining setup is for characterization and stabilization only.AFG, arbitrary function generator; EDFA, erbium-doped fiber amplifier; ESA, electrical spectrum analyzer; FBG, fiber Bragggrating; FPC, fiber polarization controller; HM, harmonic mixer; MZAM, Mach-Zehnder amplitude modulator; OBPF, opticalband-pass filter; OM, optical modulators; OSA, optical spectrum analyzer; PD, photodiode; TLF, tapered-lensed fiber; VFPD,very fast photodiode.

10−3

10−2

10−1

100

101

10−3

10−1

101

103

105

gate time (s)

mod

ified

Alla

n D

evia

tion

Out−of−loopRepetition ratePump offsetReference

−40 −20 0 20 400

50

100

150fool: 32.01250317 MHz ± 484mHz

Std dev: 8.2Hz

deviation (Hz)

coun

ts

a b

FIG. 10. SI – Full stabilization of a single dissipative Kerr soliton in SiN. a Same data as in Fig. 4a but for a singlesoliton state. Histogram of the counter measurement for the out-of-loop beat of the stabilized microresonator frequency combwith a commercial fiber laser frequency comb. The Gaussian fit gives the exact frequency of the beat. b The modified Allandeviation of the out-of-loop beat as well as the in-loop signals for the two locks of the repetition rate and the pump laser offsetof the microresonator frequency comb. All signals average down over the gate time as it should be for coherent signals.

Photonic chip based optical frequency comb using soliton induced Cherenkov radiationAbstractFigure 1Figure 2Figure 3Figure 4 Acknowledgments MethodsA NanofabricationB Finite element simulationsC Implementation of the numerical simulationD Multi-soliton and single-soliton spectraE Sample characterizationF Laser tuning procedure for soliton generation and beat note measurementsG Full stabilization

References Supplementary InformationFigure 5Figure 6Figure 7Figure 8Figure 9Figure 10