APPLIED OPTICS

Photonic chip–based opticalfrequency comb using solitonCherenkov radiationV. Brasch,1 M. Geiselmann,1 T. Herr,1* G. Lihachev,2,3 M. H. P. Pfeiffer,1

M. L. Gorodetsky,2,3 T. J. Kippenberg1†

Optical solitons are propagating pulses of light that retain their shape because nonlinearityand dispersion balance each other. In the presence of higher-order dispersion, opticalsolitons can emit dispersive waves via the process of soliton Cherenkov radiation.This process underlies supercontinuum generation and is of critical importance in frequencymetrology. Using a continuous wave–pumped, dispersion-engineered, integrated siliconnitride microresonator, we generated continuously circulating temporal dissipative Kerrsolitons.The presence of higher-order dispersion led to the emission of red-shifted solitonCherenkov radiation.The output corresponds to a fully coherent optical frequency comb thatspans two-thirds of an octave andwhose phasewewere able to stabilize to the sub-Hertz level.By preserving coherence over a broad spectral bandwidth, our device offers the opportunity todevelop compact on-chip frequency combs for frequency metrology or spectroscopy.

Optical solitons are propagating pulses oflight that retain their temporal and spec-tral shape as the result of a balance be-tween nonlinearity and dispersion (1). Inthe presence of higher-order dispersion,

optical solitons can emit soliton Cherenkov ra-diation (2, 3). This process, also known as disper-sive wave generation, is one of the key nonlinearfrequency conversion mechanisms of coherentsupercontinuum generation (4), which allowsa substantial increase in the spectral bandwidthof pulsed laser sources. The generation of a cohe-rent supercontinuum from a pulsed laser prop-agating through a photonic crystal fiber hasenabled the first self-referenced optical frequencycombs (5, 6) and has given access to coherentbroadband spectra for frequency combs with rep-etition rates up to ~10 GHz.One route to broadband frequency combs

with higher repetition rates was establishedwith the discovery of microresonator (Kerr) fre-quency combs (7, 8). Since then, the field ofmicroresonator frequency combs has made sub-stantial advances (9–11), including frequencycomb generation in complementary metal-oxidesemiconductor (CMOS)–compatible silicon ni-tride (Si3N4, henceforth SiN) photonic chips(12, 13) and a detailed understanding of thecomb formation process (14–17). However, it hasbeen a challenge to achieve broadband frequencycombs that are coherent (18, 19). Recently, tem-poral dissipativeKerr solitons (DKSs)—analogousto dissipative cavity solitons (20, 21) in fiberloop cavities—have been observed in crystal-

line microresonators (19), leading to coherentfrequency combs. These solitons, which bal-ance dispersion and loss via the Kerr non-linearity, can be generated spontaneously fromchaotic Kerr frequency combs when tuning thepump laser through the cavity resonance (19).Recent numerical simulations (16, 17, 19) havepredicted that such solitons in the presence ofsoliton Cherenkov radiation (3, 16, 22) can pro-vide a path to the reliable generation of broad-band and coherent frequency combs, which caneven span a full octave.The resonance frequencies of one mode fam-

ily in a microresonator can be approximatedaround w0 as a Taylor series:

wm ¼ w0 þXj¼1

Djmj

j!ð1Þ

where m ∈ Z is the relative mode number, D1/2pis the free spectral range of the resonator, D2

is related to the group velocity dispersion(GVD) parameter b2 by D2 ¼ −ðc=nÞD2

1b2, andD3, D4, … are related to higher-order dis-persion. Figure 1E shows the integrated disper-sion Dint(m) relative to the pump mode at m = 0;that is,

DintðmÞ ≡ wm − ðw0 þ D1mÞ¼ D2m2

2!þ D3m3

3!þ… ð2Þ

When pumping a microresonator with a contin-uous wave (CW) laser with frequency wP near w0,the dynamics of this system can be described by amaster equation,

@A

@tþ i

Xj¼2

Dj

j!

@

i@φ

� �j

A− ig 1þ iD1

w0

@

@φ

� �jAj2A

¼ −k2þ iðw0 − wPÞ

h iAþ

ffiffiffiffiffiffiffiffiffiffiffikhPin

ℏw0

rð3Þ

(14, 17, 22), where

Aðφ; tÞ ¼Xm

Amexp½imφ − iðwm − w0Þt� ð4Þ

is the slowly varying field amplitude; φ is theazimuthal angular coordinate inside the resona-tor, corotating with a soliton; g ¼ ℏw2

0cn2=n2Veff

is the nonlinear (per photon) Kerr coupling co-efficient [where ħ is Planck’s constant divided by2p, c is the speed of light in vacuum, n and n2 arethe linear and nonlinear (Kerr) refractive indicesof the material, and Veff = AeffL is the effectivenonlinear mode volume (where Aeff is the ef-fective nonlinear mode area and L is the cavitylength)]; k is the cavity decay rate; h is the cou-pling efficiency; and Pin is the pump power insidethe bus waveguide. Formally, this equation isidentical to the Lugiato-Lefever equation (16, 17)(a damped, driven nonlinear Schrödinger equa-tion). For anomalous GVD and in the absence ofthird- and higher-order dispersion, approximatesolutions can correspond to bright temporalsolitons superimposed on a CW background:

AðφÞ ≈ ACW

þ A1

XNj¼1

sech

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ðw0 − wPÞ

D2

sðφ − φjÞ

" #expðiy0Þ

ð5Þ

with φj corresponding to the relative angularposition of the jth soliton. Amplitude A1, phasey0, and background ACW are determined by thesystem’s parameters. The minimal pulse dura-tion is given by

Dtmin ≈ 2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffinD2

cD21

1

gFPin

sð6Þ

(19), where F is the resonator finesse and g =wn2/cAeff. These temporal dissipative Kerr sol-itons have been generated in fiber cavities (21)and have been observed in crystalline micro-resonators recently (19). When higher-order dis-persion terms are present, the shape and velocityof the stationary solitons change as they developradiative tails (3, 23, 24). The spectrum of such aperturbed soliton becomes asymmetric, with itsmaximum shifted away from the pump frequencyand an additional, local maximum (Fig. 1E) isgenerated (also called a dispersive wave). Becausethe radiative tail is emitted from the soliton, ananalogy to Cherenkov radiation can be drawn (3).The spectral position of the Cherenkov radia-

tion is approximately given by the linear phase-matching condition (2, 25) Dint(mDW) = 0 atmDW = (–3D2/D3) for D4 = 0. In the presence of D4,two peaks of Cherenkov radiation may occur at

mDW ¼ −2D3

D4T

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2D3

D4

� �2−12D2

D4

sð7Þ

Our experimental platform is based on siliconnitride optical microresonators, which are verysuitable for nonlinear optical applications (13, 26).We used SiN ring resonators (thickness 800 nm,diameter 238 mm) embedded in SiO2 (Fig. 1, A to

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1École Polytechnique Fédérale de Lausanne (EPFL), CH-1015Lausanne, Switzerland. 2Russian Quantum Center, Skolkovo143025, Russia. 3Faculty of Physics, M. V. LomonosovMoscow State University, Moscow 119991, Russia.*Present address: Centre Suisse d’Electronique et MicrotechniqueSA (CSEM), CH-2002 Neuchâtel, Switzerland. †Correspondingauthor. E-mail: tobias.kippenberg@epfl.ch

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D), resulting in anomalous GVD for wavelengthsaround 1.5 mm. The microresonator fabricationwas optimized so as to mitigate avoided cross-ings of different mode families that can locallyalter dispersion (27, 28). Measurements of the dis-persion (28) revealed that around the pump wave-

length, the mode structure closely approachesa purely anomalous GVD (Fig. 2B and fig. S2),with a measured D2/2p = 2.4 ± 0.1 MHz, in closeagreement with finite element method modelingthat yields D2/2p = 2.6 MHz (28). When pumpingthe resonator’s TM00 mode family at 1560 nm via

the bus waveguide, we observed discontinuities inthe cavity transmission and converted fre-quency comb light (figs. S1 and S5A) as wellas a narrowing of the repetition rate beat note(fig. S1, C and D), signatures previously associatedwith dissipative Kerr soliton formation (19).

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Fig. 1. Temporal soliton generation and solitonCherenkov radiation in a planar SiN microresonator ona photonic chip. (A) Colored scanning electron micros-copy images of a SiN optical microresonator with thesame geometry as the one used but without the SiO2

encapsulation. Blue, silicon substrate; magenta, SiO2

pedestal; orange, SiN waveguide. (B) An image of reso-nators at lower magnification. (C) A close-up of thecoupling region between bus waveguide and resonator(similar geometry as used, but the two waveguides havethe same width in the sample used in this work). (D) Across section of a device that also shows the top clad-ding (SiO2, colored purple). (E) A schematic of the inte-grated dispersion Dint(m) and the associated solitondynamics with the Cherenkov radiation at Dint = 0.Regions with positive curvature have anomalous groupvelocity dispersion (GVD); regions with negative curva-ture have normal GVD. Around the pump Dint(m) can beapproximated by a parabola (red dashed line) as it isdominated by quadratic, anomalous GVD.

Fig. 2. Single optical dissipative Kerr soliton andsoliton Cherenkov radiation in a SiN chip basedoptical microresonator. (A) The optical spectrumshows the sech2 shape of a single soliton (with a3-dB width of 10.8 THz) and the soliton Cherenkovradiation at 155 THz.The green dashed lines marka span of two-thirds of an octave. The green solidline denotes the simulated spectral envelope.Thedifferent blue colors indicate measurements donewith twodifferent optical spectrumanalyzers. (B) Theintegrated dispersionDint from finite elementmethodsimulations for the measured resonator geometry(gray solid line). The gray dashed line indicates thezero dispersion point. The blue dots around 0 (insetshows a zoom-in) are measured positions of around80 resonances which show good agreement withthe simulated dispersion. (C) The repetition rate beatnote of the frequency comb at the line spacing of189.22 GHz shows a narrow linewidth of ~1 kHz.(D andE) Themeasuredbeat note of the generatedfrequency combwith a narrow linewidth referencelaser positioned at 1552.0 nm [(D), orange line in(A)] and at 1907.1 nm [(E), red line in (A)]. (F) Theintensity profile of the soliton pulse inside the reso-nator estimated from the measured spectrum (blue)and taken directly from the numerical simulation,with full width at halfmaximum(FWHM)below30 fs.The red profile shows a small asymmetry due to theeffect of the Cherenkov radiation.

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To access the soliton states in a steady state,we developed a laser tuning technique to over-come instabilities associated with the discon-tinuous transitions of the soliton states (28),allowing stable soliton operation for hours (fig.S7). The optical single-soliton spectrum withPin ≈ 2 W shown in Fig. 2A has several salientfeatures: (i) It covers a bandwidth of two-thirdsof an octave. (ii) It exhibits the characteristicsech2 spectral envelope near the pump that isassociated with temporal solitons. The 3-dBbandwidth of 10.8 THz corresponds to 29-fsoptical pulses. (iii) The sharp feature around1930 nm (155 THz) corresponds to the solitonCherenkov radiation (16, 22). Figure 2B showsthe measured and simulated dispersion. Thespectral position of the Cherenkov radiationat m = –195 is in good agreement with thelinear phase-matching condition that occursfor Dint(mDW) = 0 at mDW = −200 with the sim-ulated parameters D2/2p = 2.6 MHz, D3/2p =24.5 kHz, and D4/2p = –290 Hz (fig. S8).Also shown in Fig. 2A is a numerically sim-

ulated spectrum [based on coupled mode equa-tions (28)]. It shows only small deviations fromthe experimental spectrum, caused by effectsthat are not included in the simulations (28).In particular, the absence of the soliton recoil(Fig. 1E), which is associated with the forma-tion of a dispersive wave (23, 24), is attributedto the cancellation via the soliton Raman self-

frequency shift (28, 29). The good agreementwith the experimental data establishes numer-ical simulations as a powerful predictive tool forsoliton dynamics in microresonators.To investigate a key property of a frequency

comb, its coherence, we first measured therepetition rate beat note of 189.2 GHz on a photo-diode by means of amplitude modulation down-mixing (28, 30) (fig. S5B). Figure 2C shows theresulting beat note, which exhibits a narrowlinewidth and a signal-to-noise ratio of 40 dB in100 kHz bandwidth, demonstrating the coherentnature of the spectrum.We also recorded the low-frequency intensity noise of the transmittedlight of the soliton state and found no excessnoise relative to the pump laser noise (fig. S4). Tolocally investigate the coherence of the Cherenkovradiation, we carried out additional CW hetero-dyne beat note measurements at 1907 nm, whichexhibited a narrow linewidth around 1 MHz (Fig.2E). Simultaneously with the beat at 1907 nm, wemeasured the beat with a laser at 1552 nm. Theresulting beat note was similar in width to thein-loop beat of the frequency-stabilized pumplaser (~300 kHz). These measurements provethat the entire spectrum is coherent, in contrastto earlier reports (18). It is useful to contrast thesingle-soliton state to the incoherent high-noisestate; we observed in the high-noise case a spec-trum that markedly deviates from the single-soliton spectrum in terms of the shape of the

Cherenkov radiation peak and the shape of thespectrum around the pump (fig. S4K).Our system also allows us to access states with

multiple solitons in the resonator. Figure 3, A toC, shows the optical spectra of three multisolitonstates, which are coherent (fig. S3) and stable forhours (fig. S7). The generated spectra show pro-nounced variations in the spectral envelope thatarise from the interference of the Fourier com-ponents of the individual solitons, as describedby the spectral envelope function

IðmÞ ¼�����XNj¼1

expðiφjmÞ�����2

ð8Þ

The insets of Fig. 3, A to C, show the re-constructed relative positions of the solitonsinside the resonator for the different spectra(28). Figure 3B shows the case where twosolitons are almost perfectly opposite to eachother in the resonator, resulting in an effec-tively doubled line spacing. Figure 3C showsthat a higher number of cavity solitons (N = 3)results in a spectrum with more complex spec-tral modulations.To prove the usability of our system for metro-

logical applications, we implemented a full phasestabilization of the spectrum by phase-lockingthe pump laser and the repetition rate of theSiN comb to a common radio-frequency ref-erence. For absolute frequency stabilization of

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Fig. 3. Multisoliton states in a planar SiN micro-resonator on a photonic chip. (A to C) Spectrafor multisoliton states and the relative phase posi-tion of the solitons inside the microresonator shownin the insets according to the field autocorrelation(Fourier transform of the intensity spectrum). (A)and (B) show two-soliton states; (C) shows a three-soliton state with the derived single-soliton spectralenvelope (solid green line).

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the pump laser, we used an offset lock to a self-referenced fiber laser frequency comb (28, 31).In Fig. 4B, we show themodified Allan deviationof the in-loop signals and an out-of-loop signalthat consists of the beat of one comb tooth of theSiN comb (mode number –18) with one tooth ofthe reference comb. For all three signals, themodified Allan deviation averages down withincreasing gate time.The out-of-loopmeasurement also allows us to

compare the absolute frequency accuracy of thesolitonCherenkov radiation–based comb statewiththe fiber laser reference comb. Taking into accountall locked frequencies as shown in Fig. 4C, andextracting the center frequency of the out-of-loopsignal from frequency counter measurementsshown in Fig. 4A, we derive a frequency differ-ence of D = (18 × frep) – (13,613 × frep,fc) – foff + fol =25 ± 558 mHz for the 1000-s measurement. Wetherefore validate the accuracy of the SiN solitonfrequency comb to the sub-Hz level and verifythe relative accuracy (with respect to the opticalcarrier) to 3 × 10−15.The observation of soliton Cherenkov radia-

tion in a photonic chip–based microresonatorprovides a path to numerically predictable, fullycoherent frequency comb spectra, with increasedbandwidth that extends into the normal GVDregime.The currently achievedcoherent two-thirdsof an octave can be self-referenced by doubling andtripling the high and low end of the spectrum,respectively (2f-3f technique), and the band-width can be extended to a full octave withmodified dispersion designs.

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ACKNOWLEDGMENTS

Supported by European Space Agency contracts ESTEC CN4000108280/12/NL/PA and ESTEC CN 4000105962/12/NL/PA,the Swiss National Science Foundation, and contractW911NF-11-1-0202 from the Defense Advanced ResearchProjects Agency, Defense Sciences Office. This material isbased on work supported by the Air Force Office of ScientificResearch, Air Force Material Command, under awardFA9550-15-1-0099. M.L.G. and G.L. were supported by RussianFoundation for Basic Research grant 13-02-00271 and theMinistry of Education and Science of the Russian Federationproject 4.585.21.0005. M.G. acknowledges support fromthe Hasler foundation and the MSCA-COFUND program atEPFL. All samples were fabricated at the Centre forMicroNanotechnology (CMi) at EPFL.

SUPPLEMENTARY MATERIALS

www.sciencemag.org/content/351/6271/357/suppl/DC1Materials and MethodsSupplementary TextFigs. S1 to S8References (32–41)

18 September 2015; accepted 3 December 2015Published online 31 December 201510.1126/science.aad4811

360 22 JANUARY 2016 • VOL 351 ISSUE 6271 sciencemag.org SCIENCE

Fig. 4. Full phase stabilization and absolute fre-quency accuracy measurement of dissipativeKerr solitons in a SiN microresonator. (A) Histo-gram of the frequency counter measurement forthe out-of-loop beat of the stabilized microresona-tor frequency comb with a commercial fiber laserfrequency comb. Gate time is 1 s. The Gaussian fitgives the exact frequency of the beat (fol). Thestabilized state shown here is a two-soliton state.(B) The modified Allan deviation of the out-of-loopbeat as well as the in-loop signals for the two locksof the repetition rate and the pump laser offset ofthe microresonator frequency comb. All signalsaverage down over the gate time, as expected forcoherent signals. (C) A scheme highlighting theprinciple of the frequency accuracy measurementreferenced to a self-referenced fiber frequencycomb.The out-of-loop beat is between the 18th lineon the red side of the pump of the microresonatorfrequency comb and the 13,613th line of the refer-ence comb counted from the line to which thepump laser is locked.

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based optical frequency comb using soliton Cherenkov radiation−Photonic chipV. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky and T. J. Kippenberg

originally published online December 31, 2015DOI: 10.1126/science.aad4811 (6271), 357-360.351Science 

, this issue p. 357; see also p. 340Sciencebodes well for miniaturization of metrological technology and its adaption for widespread application.output light formed a coherent comb of frequencies spanning two-thirds of an octave. Such an on-chip demonstrationThey induced an optical soliton, or optical bullet, and propagated it in an engineered microcavity waveguide. The emitted

generated optical frequency combs on an optical chip (see the Perspective by Akhmediev and Devine).et al.Brasch Laser-induced optical frequency combs allow precision measurements and affect a broad range of technologies.

Timing on a chip

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