Hertz-linewidth semiconductor lasers using CMOS-ready ultra-high- Q microresonators
Warren Jin, Qi-Fan Yang, Lin Chang, Boqiang Shen, Heming Wang, Mark A. Leal, Lue Wu, Avi Feshali, Mario Paniccia, Kerry J. Vahala, John E. Bowers
aa r X i v : . [ phy s i c s . op ti c s ] S e p Hertz-linewidth semiconductor lasers using CMOS-ready ultra-high- Q microresonators Warren Jin , ∗ , Qi-Fan Yang , ∗ , Lin Chang , ∗ , Boqiang Shen , ∗ , Heming Wang , ∗ ,Mark A. Leal , Lue Wu , Avi Feshali , Mario Paniccia , Kerry J. Vahala , † , and John E. Bowers , † ECE Department, University of California Santa Barbara, Santa Barbara, CA 93106, USA T. J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, CA 91125, USA Anello Photonics, Santa Clara, CA ∗ These authors contributed equally to this work. † Corresponding authors: [email protected], [email protected]
Driven by narrow-linewidth bench-top lasers, coherent optical systems spanning opticalcommunications, metrology and sensing provide unrivalled performance. To transferthese capabilities from the laboratory to the real world, a key missing ingredient is amass-produced integrated laser with superior coherence. Here, we bridge conventionalsemiconductor lasers and coherent optical systems using CMOS-foundry-fabricated mi-croresonators with record high Q factor over 260 million and finesse over 42,000. Fiveorders-of-magnitude noise reduction in the pump laser is demonstrated, and for thefirst time, fundamental noise below 1 Hz Hz − is achieved in an electrically-pumpedintegrated laser. Moreover, the same configuration is shown to relieve dispersion re-quirements for microcomb generation that have handicapped certain nonlinear plat-forms. The simultaneous realization of record-high Q factor, highly coherent lasers andfrequency combs using foundry-based technologies paves the way for volume manufac-turing of a wide range of coherent optical systems. The benefits of high coherence lasers extend to manyapplications. Hertz-level linewidth is required to inter-rogate and manipulate atomic transitions with long co-herence times, which form the basis of optical atomicclocks . Furthermore, linewidth directly impacts per-formance in optical sensing and signal generation appli-cations, such as laser gyroscopes , light detection andranging (LIDAR) systems , spectroscopy , optical fre-quency synthesis , microwave photonics , and coher-ent optical communications . In considering the fu-ture transfer of such high coherence technologies to amass manufacturable form, semiconductor laser sourcesrepresent the most compelling choice. They are directlyelectrically pumped, wafer-scale manufacturable and ca-pable of complex integration with other photonic devices.Indeed, their considerable advantages have made theminto a kind of ‘photonic engine’ for nearly all modern dayoptical source technology, including commercial benchtoplaser sources. Nonetheless, mass manufacturable semi-conductor lasers, such as used in communications sys-tems, have linewidths ranging from 100 kHz to a fewMHz , which is many orders of magnitude too large forthe above mentioned applications.A powerful method to narrow the linewidth of a laseris to apply optical feedback through an external reflector,for which the degree of noise suppression scales with thesquare of the Q factor of the reflector . Ultra-high- Q microresonators are excellent candidates to achievesubstantial linewidth narrowing and have been demon-strated across a wide range of materials as discrete or integrated components . While sub-Hertz fun-damental linewidth has been realized in semiconduc-tor lasers that are self-injection-locked to discrete crys-talline microresonators , retaining ultra-high Q factor when moving to higher levels of integration is both ofparamount importance and challenging. As a measure ofthe level of difficulty, current demonstrations of narrow-linewidth integrated lasers, despite many years of effort,feature fundamental linewidths of 40 Hz to 1 kHz, aslimited by their Q factors .In this work, we present critical advances in siliconnitride waveguides, fabricated in a high-volume com-plementary metal-oxide-semiconductor (CMOS) foundry.We achieve a Q factor over 260 million – a record amongall integrated resonators. By self-injection locking aconventional semiconductor distributed-feedback (DFB)laser to these ultra-high- Q microresonators, we reducenoise by five orders of magnitude, yielding frequencynoise below 1 Hz Hz − , which is a previously unattain-able level for integrated lasers. Within the same configu-ration, a new regime of Kerr comb operation in microres-onators is supported. Specifically, the comb both oper-ates turnkey and attains coherent comb operation un-der conditions of normal dispersion without any specialdispersion engineering. The comb’s line spacing is suit-able for dense (DWDM) communications systems. More-over, each comb line benefits from the exceptional fre-quency noise performance of the disciplined pump, rep-resenting a significant advance for DWDM source tech-nology. The microwave phase noise performance of thecomb is also comparable to that of existing commercialmicrowave oscillators. Overall, experiment and theoryreveal an ultra-low-noise regime in integrated photonics. ResultsCMOS-ready ultra-high- Q microresonators The ultra-high Q factor resonators use high-aspect-ratioSi N waveguides as shown in Fig. 1a. The sam-ples are fabricated in a high-volume CMOS foundry on ba dc MeasurementFitting N o r m a li z ed a m p li t ude ( a r b . un i t. ) t =124 nsQ L =150 M0.51-4 -2 0 2 4Frequency (MHz) T r an s m i ss i on ( a r b . un i t. ) FittingMeasurementQ O =220 MQ L =150 M 1 mm 1 mm FSR =30 GHz
FSR =10 GHz
Cross section
SiThermal SiO (14.5 m m)LPCVD Si N (100 nm)LPCVD SiO (2 m m) 1480 1500 1520 1540 1560 1580 1600 1620 1640Wavelength (nm)100150200250300 Q f a c t o r ( M ) Intrinsic QLoaded Q10015050 1450 1470 1490 1510 1530 1550 1570 1590 1610 1630 1650Intrinsic QLoaded Q 2.8 m m8 m m FSR =30 GHz
FSR =5 GHz
Fig. Ultra-high- Q Si N microresonators. a, Cross sectional diagram of the ultra-low loss waveguide, consisting of Si N as the core material, silica as the cladding, and silicon as the substrate (not to scale). b, Top view of the Si N microresonatorswith 30 GHz F SR (ring, left panel) and 10 GHz
F SR (racetrack, right panel). c, Transmission spectrum (upper panel) of ahigh- Q mode at 1560 nm in a 30 GHz ring resonator. Interfacial and volumetric inhomogeneities induce Rayleigh scattering,causing resonances to appear as doublets due to coupling between counter-propagating modes. Intrinsic Q of 220 M and loaded Q of 150 M is extracted by fitting the asymmetric mode doublet. The ring-down trace of the mode (lower panel) shows 124 nsphoton lifetime, corresponding to a 150 M loaded Q . d, Measured intrinsic Q factors plotted versus wavelength in a 30 GHzring resonator with 8 µ m wide Si N core (upper panel) and a 5 GHz racetrack resonator with 2.8 µ m wide Si N core (lowerpanel). Insets: simulated optical mode profile.
200 mm wafers following the process of Bauters et al. ,but we increase the thickness of the Si N core from40 nm to 100 nm. Thicker Si N enables a bendingradius below 1 mm , allowing higher integration den-sity than the centimeter-sized resonators demonstratedpreviously . Furthermore, a top cladding thicknessof 2 µ m is sufficient, which obviates the need for com-plex chemical-mechanical polishing and bonding of ad-ditional thermal SiO on top . Microresonators hav-ing three different free spectral ranges ( F SR ) were fab-ricated. Those resonators having 30 GHz FSR were ina whispering-gallery-mode ring geometry while single-mode racetrack resonators with 5 GHz and 10 GHz
F SR were fabricated to reduce footprint (Fig. 1b). All deviceswere fabricated on the same wafer. Transmission spectra scans using a tunable exter-nal cavity laser (calibrated by a separate interferome-ter) were measured to study the resonator linewidth andto infer loaded, coupled and intrinsic optical Q factors.Cavity ring down was also performed as a separate checkof these Q measurments. Spectra were observed to oc-cur in doublets on account of both the ultra-high-Q andthe presence of waveguide backscattering (Fig. 1c) . Byfitting the doublet line shape of the 30 GHz ring res-onator, intrinsic Q of 220 M and loaded Q of 150 Mare extracted at 1560 nm, which are further confirmedby measuring the ring-down trace of the resonance asshown in Fig. 1c. The spectral dependences of Q -factorsin ring- and racetrack-resonators (Fig. 1d) provide in-sight into the origins of loss. A reduction in the value Frequency offset (Hz)10 F r equen cy N o i s e ( H z H z - ) Free running DFB laser30 GHz resonator10 GHz resonator5 GHz resonator10 ab AOM -55 MHz1 kmPC PD O sc ill o sc ope ISO
Linewidth measurement setup
TRN (30 GHz resonator)TRN (10 GHz resonator)TRN (5 GHz resonator)<1 Hz Hz -1 III-V DFB laser Ultrahigh-Q Si ! N " resonator Hybrid-integrated narrow-linewidth laser chip
Free-runningInjection-lockedS n (f) Fig. Hybrid-integrated narrow-linewidth laser based on ultra-high- Q Si N microresonator. a, Schematic ofthe hybrid laser design (not to scale) and linewidth test setup. The red (yellow) arrow denotes the forward (backscattered) lightfield. ISO: optical isolator; AOM: acousto-optic modulator; PC: polarization controller; PD: photodetector. b, Measurementof single-sideband frequency noise of the free-running and self-injection locked DFB laser. The white-frequency-noise levels are1 Hz Hz − , 0.8 Hz Hz − , 0.5 Hz Hz − for resonators with 20 GHz, 10 GHz and 5 GHz F SR , respectively. The dashed linesgive the simulated thermorefractive noise (TRN). of Q around 1510 nm is due to absorptive N-H bondsin the Si N core. Beyond this wavelength, the intrin-sic Q factor increases monotonically versus wavelength,likely limited by Rayleigh scattering. The highest Q fac-tor is obtained using the 30 GHz FSR resonator (meanvalue of 260 M and standard deviation of 13.5 M over 34modes) and observed in the 1630 nm to 1650 nm wave-length range. The overall lower Q factor of the 5 GHzracetrack resonator suggests excess propagation loss inits single mode waveguides. This is possibly caused byhigher scattering loss from increased modal overlap withthe waveguide sidewall as compared to the whispering-gallery mode waveguide. Hertz-linewidth integrated laser
The hybrid-integrated laser comprises a commercial DFBlaser butt-coupled to the bus waveguide of the Si N res-onator chip (Fig. 2a). The laser chip, which is mounted on a thermoelectric cooler to avoid long-term drift, isable to deliver power up to 30 mW at 1556 nm into theSi N bus waveguide. Optical feedback is provided to thelaser by backward Rayleigh scattering in the microres-onator, which spontaneously aligns the laser frequency tothe nearest resonator mode. As the phase accumulatedin the feedback is critical to determining the stability ofinjection-locking , we precisely control the feedbackphase by adjusting the air gap between the chips. Thelaser output is taken through the bus waveguide of themicroresonator, and directed to a self-heterodyne setupfor linewidth characterization. Two photodetectors and across-correlation technique are used to improve detectionsensitivity (see Methods).The frequency noise spectra of the self-injectionlocked laser system using the 30 GHz ring, and the10 GHz and 5 GHz racetrack resonators (respective in- P o w e r ( d B pe r d i v i s i on ) Wavelength (nm) a bd -150 -100 -50 50 100 150-10-300 -200 -100 0 100 200 300-10 0 I n t eg r a t ed d i s pe r s i on D i n t / p ( G H z ) D /(2 p) = - D /(2 p) = - m Time (ms)-2-1012 F r equen cy ( M H z + . G H z ) C o m b po w e r ( a r b . un i t. ) RF Power (arb. unit.)0 1Laser on
FSR = 5 GHz
FSR = 10 GHz
FSR = 5 GHz
FSR = 10 GHz f r =10.873 GHz e
10 20 300 40 50 100 Normalized detuning02 N o r m a li z ed i n t r a c a v i t y po w e r q p p I n t r a c a v i t y po w e r ( a r b . un i t ) O p t i c a l po w e r ( d B pe r d i v i s i on ) Mode number0 50-50
Kerr combsc.w. state c Kerr combs Steady state
Frequency offset (Hz)10 P ha s e no i s e ( d B c H z - ) -140-120-100-80-60-40-200 5.4 GHz10.8 GHz Frequency (kHz + 5437.07 MHz) P o w e r ( d B pe r d i v i s i on ) -40 -20 0 4020-100 dBc Hz -1 -114 dBc Hz -1 RBW10 Hz-140 dBc Hz -1 -129 dBc Hz -1
10 20 300 40 50 1552 1554 1556 1558 1560 f Fig. Formation of mode-locked Kerr combs. a,
Measured mode family dispersion is normal. The plot shows theintegrated dispersion defined as D int = ω µ − ω o − D µ where ω µ is the resonant frequency of a mode with index µ and D is the F SR at µ = 0. The wavelength of the central mode ( µ = 0) is around 1550 nm. The dashed lines are parabolic fits( D int = D µ /
2) with D / π equal to − . − . F SR , respectively.Note: D = − cD β /n eff where β is the group velocity dispersion, c the speed of light and n eff the effective index of themode. b, Experimental comb power (upper panel) and detected comb repetition rate signal (lower panel) with laser turn-onindicated at 5 ms. c, Measured optical spectra of mode-locked Kerr combs with 5 GHz (upper panel) and 10 GHz (lowerpanel) repetition rates. The background fringes are attributed to the DFB laser. d, Single-sideband phase noise of dark solitonrepetition rates. Dark solitons with repetition rate 10.8 GHz and 5.4 GHz are characterized. Inset: electrical beatnote showing5.4 GHz repetition rate. e, Phase diagram of microresonator pumped by an isolated laser. The backscattering is assumed weakenough to not cause mode-splittings. The detuning is normalized to one half of microresonator linewidth, while the intracavitypower is normalized to parametric oscillation threshold. Green and red shaded areas indicate regimes corresponding to the c.w.state and Kerr combs. The blue curve is the c.w. intracavity power, where stable (unstable) branches are indicated by solid(dashed) lines. Simulated evolution of the unisolated laser is plotted as the solid black curve, and it converges to the steadystate as marked by the black dot. The initial condition is set within the self-injection locking bandwidth , while feedbackphase is set to 0. f, Simulated intracavity field (upper panel) and optical spectrum (lower panel) of the unisolated laser steadystate in panel e. trinsic Q factors of 250 M, 56 M and 100 M) are comparedin Fig. 2b. The ultra-high-Q factors enable the frequencynoise of the free-running DFB laser to, in principle, besuppressed by up to 80 dB (see Methods). In practice,however, the noise suppression over a broad range of off-set frequencies (10 kHz to 2 MHz) is limited to 50 dBby the presence of thermorefractive noise in the mi-croresonator. Consistent with theory, microresonatorswith larger mode volume, i.e. smaller F SR , experiencea lower thermorefractive fluctuation and exhibit reducedfrequency noise (Fig. 2b). At low frequency offset (below10 kHz), frequency noise is primarily limited by temper- ature drift and coupling stability between chips. Thiscan be suppressed by improved device packaging. Athigh offset frequencies (above 5 MHz), frequency noiserises with the square of offset frequency, as the maxi-mum noise suppression bandwidth of injection locking islimited to the bandwidth of the resonator . Thus,minimum frequency noise below 1 Hz Hz − is observedat about 5 MHz offset frequency, where the contributionsof rising laser noise and falling thermorefractive noise areapproximately equal. To achieve an ultra-low white fre-quency noise floor at high offset frequencies, the laseroutput may be taken from a resonator featuring a drop- ab F r equen cy N o i s e ( H z H z - ) Frequency offset (MHz)10 -1 Pump (1555.438 nm)<1 Hz Hz -1 c P o w e r ( d B m ) -60-40-200 Wavelength (nm)1550 1552 1554 1556 1558 1560Wavelength (nm)1554 1555 1556 1557 F unda m en t a l L i ne w i d t h ( H z ) Fig. Coherence of integrated mode-locked Kerrcombs. a,
Optical spectrum of a mode-locked comb with43.2 GHz repetition rate generated in a microresonator with10.8 GHz
F SR . b, Single-sideband optical frequency noise ofthe pump and comb lines as indicated in panel a, selected us-ing a tunable fiber-Bragg-grating (FBG) filter. c, Wavelengthdependence of white frequency noise linewidth of comb linesin panel a. port. The drop port would provide low-pass filtering ac-tion and is studied further in the Supplement . Mode-locked Kerr comb
The ultra-high Q of the microresonators enables strongresonant build-up of the circulating intensity, providingaccess to nonlinear optical phenomena at low input powerlevels . As an example, optical frequency combs havebeen realized in continuously pumped high- Q optical mi-croresonators due to the Kerr nonlinearity and they arefinding a wide range of applications . To explore thenonlinear operating regime of the hybrid-integrated laserin pursuit of highly-coherent Kerr combs, the mode dis-persion of racetrack resonators with 5 GHz and 10 GHz F SR was characterized. Their mode families are mea-sured to have normal dispersion across the telecommuni-cation C-band (Fig. 3a). Also, the dispersion curves ex-hibit no avoided-mode-crossings, which is consistent withthe single-mode nature of the waveguides. As distinctfrom microresonators with anomalous dispersion wherein bright soliton pulses are readily generated, comb forma-tion is forbidden in microresonators with normal disper-sion, unless avoided-mode-crossings are introduced to al-ter mode family dispersion so as to allow formation ofdark solitons . Surprisingly, however, it was nonethe-less possible to readily form coherent combs in these de-vices without either of the aforementioned conditions be-ing satisfied.Indeed, deterministic, turnkey comb formation wasexperimentally observed when the DFB laser wasswitched-on to a preset driving current (see Fig. 3b). Aclean and stable beatnote of the comb is established 5 msafter turning on the laser, indicating that mode-lockinghas been achieved (see Fig. 3b). Plotted in Fig. 3c are op-tical spectra of the mode-locked Kerr combs in resonatorswith 5 GHz and 10 GHz F SR , where the typical spectralshape of dark soliton pulses is observed . The stabil-ity of mode-locking is characterized by measurement ofthe comb beat note phase noise (Fig. 3d). For Kerr combswith 10.8 (5.4) GHz
F SR , the phase noise reaches -100(-114) dBc Hz − at 10 kHz and -129 (-140) dBc Hz − at 100 kHz offset frequencies. We note that in order tosuppress noise at high-offset frequencies, the pump is ex-cluded in the photodetection using a fiber Bragg gratingfilter, as suggested by previous works .This unexpected result is studied theoretically in theSupplement. Here, results from that study are brieflysummarized. A phase diagram of the microcomb systemis given in Fig. 3e, and separates resonator operation intocontinuous-wave (c.w.) and Kerr comb regimes based onthe viability of parametric oscillation . The intracavitypower exhibits a typical bi-stable behavior as a functionof cavity-pump frequency detuning when pumped by alaser with optical isolation . In contrast, a recent studyshows that the feedback from a nonlinear microresonatorto a non-isolated laser creates an operating point for thecompound laser-resonator system in the middle branch .The operating point is induced through a combination ofself- and cross-phase modulation, and is associated withturnkey operation of soliton combs operating under con-ditions of anomalous dispersion . Here, we have vali-dated through simulation that the same operating pointallows access to dark solitons (normal dispersion) withoutthe requirement for extra dispersion engineering providedby avoided mode crossings. The black curve in Fig. 3egives the dynamics of the compound laser-resonator sys-tem when initialized at a point that is within the lock-ing bandwidth of the system. It converges to a steadystate located in the Kerr comb regime. The spectral andtemporal profile of the steady state solutions show thatflat-top pulses are formed in the microresonator with nor-mal dispersion (Fig. 3f). The possible presence of darksoliton formation in microresonators pumped by a self-injection locked laser has been observed, but has not yetbeen clarified previously .The combs generated in these devices exhibit sev-eral important properties. In Fig. 4a, the spectrum ofa 43.2 GHz repetition rate comb is presented. Curiously, Table 1 | Current integrated ultra-high- Q microresonators and narrow-linewidth lasers Material Q (M) FSR (GHz) Finesse Si N (this work) Cladding Si N (low confinement)Si N (high confinement)SiO AirOxideOxideOxideSi LiNbO Phosphorous-doped silica OxideOxideDoped-oxide 2608137652166723205221031 303.32002.72.7631015.25.441 42,6001,40038,4009103,00021,7001,20015,800630210170
Operation principle Linewidth (Hz)
Self-injection locking (this work)
Configuration
External cavity Hybrid III-V/Si N N Heterogeneous III-V/Si 4,000External cavity Heterogeneous III-V/Si N Microresonators
Ref
Lasers
Ref
TABLE I.
Upper: Best-to-date integrated ultra-high- Q ( >
10 M) microresonators with integrated waveg-uides. Lower: Best-to-date integrated narrow-linewidth lasers. this spectrum was generated in a microresonator hav-ing a 10.8 GHz
F SR . The appearance of rates thatare different from the
F SR rate has been observed fordark solitons . This line spacing is compatible withDWDM channel spacings and 10 comb teeth feature on-chip optical power over -10 dBm, which is a per chan-nel power that is readily usable in DWDM communica-tion systems . However, most significant, is that thewhite-frequency-noise-level floor for each of these opti-cal lines (Fig. 4b) is measured to be on the order of1 Hz Hz − . We note that these spectra are truly white,i.e., not rising for higher offset as discussed above for thelaser source. The corresponding fundamental linewidthsof the comb teeth are plotted in Fig. 4c. One of thelines exhibits degraded linewidth of approximately 30 Hz,which is suspected to be due to its coincidence with asub-lasing-threshold side-mode of the DFB laser. No-tably, certain comb teeth are quieter than the pumpdue to the filtering of pump noise by the ultra-high- Q modes. These results represent a two order-of-magnitudeimprovement as compared to previously demonstrated in-tegrated microcombs . Performance Comparison
For devices with both integrated waveguide coupler andresonator, a few platforms have emerged as able to pro-
Intrinsic Q (M)10
10 10010 F i ne ss e This workLow-confinementSi N SilicaLiNbO High-confinementSi N SiliconPhosphorous-doped Silica
Fig. Comparison of finesse and intrinsic Q factorsof state-of-the-art integrated microresonators. vide ultra-high Q ( Q >
10 M). In silica ridge resonators,a Q factor of 205 M has been demonstrated , while inlow-confinement silicon nitride, a Q factor of 216 M hasbeen demonstrated . However, these platforms posechallenges to photonic integration with large scale andhigh density, e.g. the use of suspended structures or therequirement for centimeter-level bending radius . Whilethese limitations are not present in high-confinement sili-con nitride resonators, the highest demonstrated Q factoris lower, 67 M . In Table I, we list key figures of meritfor integrated microresonators with ultra-high- Q factors.In addition to record-high Q factor, owing to their com-pact footprint, the current resonators stand out amongultra-high Q resonators for having the highest finesse aswell. Fig. 5 provides a comparison as a plot of the Q andfinesse of the current work with the state-of-the-art.We further compare the current hybrid-integratedlaser linewidth to state-of-the-art results in Table I. TheLorentzian linewidth of monolithic III-V lasers is gener-ally limited to the 100 kHz to 1 MHz range by passivewaveguide losses well above 1 dB cm − , with best demon-strated linewidth below 100 kHz . Phase and amplitudenoise scale according to the square of cavity losses .Thus, hybrid integration, where the active III-V andpassive photonic chips are assembled post-fabrication,and heterogeneous integration , where III-V material isdirectly bonded to the passive chip during fabrication,have emerged as primary technologies to create narrow-linewidth integrated lasers. As shown in Table I, hybridand heterogeneous integration can produce fundamentallinewidth well below 1 kHz. In this work, fundamentalfrequency noise is suppressed to 0.5 Hz Hz − , or equiv-alently, a 3 Hz linewidth, which is more than an order ofmagnitude improvement over the best results to date . Discussion
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Experimental details
The Q is obtained by frequency-down-scanning aexternal-cavity-diode-laser (ECDL) across a mode, withfrequency calibrated using a Mach-Zehnder interferom-eter (MZI). Measured transmission spectra at variouswavelengths are shown in the Supplement . Similarly,the mode family dispersion is extracted from the broad-band transmission spectrum of the resonator, with cali-bration provided by the MZI as well.The laser switch-on test is performed by rapidly mod-ulating its driving current with square wave functions.The real-time evolution of comb repetition rate is ob-tained by down-mixing the photodetected beatnote witha local microwave oscillator. The trace, which is recordedusing a high-speed oscilloscope, is Fourier transformed togive the spectrograph. Multiple turnkey tests are shownwith 100 percent success rate (see Supplement ). Thephase noise of comb repetition rates is characterized us-ing a Rohde & Schwarz phase noise analyzer. Laser linewidth measurement
The noise in the photodetection, e.g., shot noise, ther-mal noise and dark current, limit the sensitivity of self-heterodyne method especially at high-offset frequencies.To overcome such limit, we use two photodetectors tomeasure the self-heterodyne signals simultaneously. Theinstantaneous frequency is extracted using Hilbert trans-formation, and their cross correlation C ν ( f ) is given by C ν ( f ) = 2 h − (1 − τ BW) + cos(2 πf τ ) i S ν ( f ) − h − τ BW) + cos(2 πf τ ) i × f ( S I ( f c + f ) + S I ( f c − f )) (1)where S ν ( f ) and S I ( f ) are the single-sideband powerspectral density of frequency and relative intensity noise(RIN) of the laser, τ the delay between the two arms,and x + = max(0 , x ) the ramp function. The resolutionbandwidth of the cross-correlator BW is set as 20 kHzso that τ BW ≪
1. To reduce the contribution of RINas well as enhance the detection sensitivity of frequencynoise, at high-offset frequencies ( f > πf τ ) ≈ −
1. The enhancementof sensitivity equals √ BW ∗ T with T the recording time.In this measurement T is set 200 ms, corresponding to18 dB enhancement of sensitivity. Thermorefractive noise
Constant heat exchange between the microresonator andits ambient results in thermodynamic fluctuations, whichcould induce changes in the refractive index throughthermo-optic effect, giving rise to thermorefractive noiseof the resonant frequencies . The variance of the ther- morefractive noise (TRN) is given by < δω c > = n ω c n k B T ρCV . (2)where n T is the thermo-optic coefficient, ω c the resonantfrequency, n eff the effective index of the mode, k B theBoltzmann’s constant, T the temperature of the heatbath, ρ the density, C the specific heat and V the volume.Owing to their larger mode volumes, the low-confinementresonators in this work feature notably smaller TRNthan those of high-confinement resonators . The spec-tral density of the TRN is computed using finite-element-method (FEM) based on fluctuation-dissipationtheorem , as plotted in Fig. 2b in the maintext. Linewidth-reduction factor
The amount of linewidth-reduction in self-injectionlocked laser depends on the spectral response and powerof the backscattered field, which has been derived inthe supplement based on a complete theory involvingboth laser and microresonator dynamics . We introducethe coupling between the clockwise and counterclockwisefield in the microresonator, β , which is normalized to onehalf of the cavity linewidth. In the case of weak backscat-tering ( β ≪ α ≈ α g ) T η | β | Q Q , (3)where Q R and Q d stand for the Q of the microresonatorand the laser diode, respectively. η = Q R /Q e is the mi-croresonator loading factor with Q e being the coupling Q between the bus waveguide and the resonator. T de-notes the power insertion loss between the facets of thelaser and the bus waveguide, while α g is the amplitude-phase coupling coefficient of the laser. In the presence ofa strong backscattered field ( β ≫ α ≈ α g ) T η Q Q , (4)which is independent of the backscattering coefficient.Typical values of these parameters in our systems are: α g = 2 . T = − η = 0 . Q d = 10 . For mode fea-turing loaded Q of 50 M and split resonances, the max-imum estimated noise reduction factor is around 70 dB,which is 20 dB higher than the noise suppression achievedin experiment. In the experiment, the locking point is in-tentionally offset from the exact resonance by adjustingthe feedback phase to avoid nonlinearity. Phase diagram
The phase diagram presented in Fig. 3b of the maintextis a powerful tool to interpret how self-injection lock-ing can deterministically lead to mode-locked Kerr combformation. Assuming homogeneous intracavity field, the0parametric gain of the ± l th modes relative to the pumpis given by Γ( ± l ) = Re n − p ρ − (∆ − ρ + d l ) o , (5)where ρ is the intracavity power normalized to the para-metric oscillation threshold , κ represents the modallinewidth, ∆ = 2 δω/κ the normalized detuning, δω thepump-cavity detuning, and d = D /κ the normalizeddispersion. To initiate parametric oscillation, Γ( ± l ) > l = 1, the regimecorresponding to Kerr comb is given by∆ > ρ + d − p ρ − . (6) Data availability
All data generated or analysed during this study areavailable within the paper and its supplementary ma-terials. Further source data will be made available onreasonable request.
Code availability
The analysis codes will be made available on reasonablerequest.
Acknowledgments
The authors gratefully acknowl-edge the Defense Advanced Research Projects Agency(DARPA) under DODOS (HR0011-15-C-055) programsand Anello Photonics.
Author contributions
Experiments were conceived byW.J., Q.-F.Y., L.C., B.S. and H.W. Devices were de-signed by W.J., and A.F. Measurements were performedby W.J., Q.-F.Y., L.C, B.S., H.W. with assistance fromM.A.L and L.W. Analysis of results was conducted byW.J., Q.-F.Y. and H. W. The project is coordinatedby Q.-F.Y. and L.C. under the supervision from J.B.,K.V. and M.P. All authors participated in writing themanuscript.
Competing interests
The authors declare no compet-ing financial interests.
Additional informationSupplementary information is available for thispaper.
Correspondence and requests for materials shouldbe addressed to K.V. and J.B. r X i v : . [ phy s i c s . op ti c s ] S e p Supplementary Information to Hertz-linewidth semiconductor lasers usingCMOS-ready ultra-high-Q microresonators
Warren Jin , ∗ , Qi-Fan Yang , ∗ , Lin Chang , ∗ , Boqiang Shen , ∗ , Heming Wang , ∗ ,Mark A. Leal , Lue Wu , Avi Feshali , Mario Paniccia , Kerry J. Vahala , † , and John E. Bowers , † ECE Department, University of California Santa Barbara, Santa Barbara, CA 93106, USA T. J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, CA 91125, USA Anello Photonics, Santa Clara, CA ∗ These authors contributed equally to this work. † Corresponding authors: [email protected], [email protected]
I. DEVICE DESIGN
Among the design parameters involved in achieving ultra-high Q factors, the choice of waveguide thickness is critical,as thinner cores will minimize the impact of scattering losses through lower modal confinement, at the expense oflarger bending radius and thus lower integration density. In Fig. S1, we compare simulated bending loss in waveguidesof 250 nm, 100 nm, and 40 nm thickness and 1.4 µ m, 2.8 µ m, and 5.6 µ m width, respectively, where width is chosen toguarantee single-mode propagation within the C band. Although the lowest propagation loss has been demonstratedin 40 nm thick cores , a radius of 1 cm is required to guarantee bending loss below 0.01 dB/m, which limits theintegration density to a single resonator per die for typical lithography stepper reticles of 2 cm by 2 cm dimension.On the other hand, 250 nm thick cores allow for highly compact resonators, with just 100 µ m bend radius. In thiswork, we focus on achieving ultra-low loss while maintaining moderate integration density. Thus, we select 100 nmas the optimal core thickness to allow bend radius as low as 700 µ m, permitting as many as 100 resonators to beintegrated on a single die while still suppressing the contribution of the waveguide sidewall roughness to scatteringloss. For the resonators designed in this work, the minimum bend radius is chosen as 1 mm, ensuring that bend lossesare entirely negligible.To achieve the highest Q factor, we use multi-mode ring resonators to further minimize the contribution of sidewallscattering. For 1 mm bend radius, the fundamental mode propagation constant is insensitive to waveguide width forwidth beyond 8 µ m. Hence, we choose a width of 8 µ m, which produces a whispering-gallery mode and free spectralrange ( F SR ) of 30 GHz. To ensure selective, low-loss coupling to the fundamental mode, a pulley coupler is used.The coupler waveguide width is chosen to precisely phase-match the propagation constant of the coupler waveguidemode with that of the ring waveguide for a 5 µ m width space between the waveguides. The length of the coupleris approximately 1 mm long, and is designed to be under-coupled to allow accurate measurement of the intrinsic Q factor. Measured resonator transmission spectra at various wavelength are provided in Fig. S2.To achieve larger mode volume and smaller F SR while retaining reasonable footprint and ultra-high Q , racetrack
100 1000 10000Bending radius ( m m)250 nm100 nm40 nm B end i ng l o ss ( d B m - ) -2 -1 Thickness of Si N FIG. S1.
Bending loss versus radius.
Simulated waveguide bending loss of single mode waveguides at three thicknesses ofSi N core. T r an s m i ss i on ( a r b . un i t ) =1460.2 nmQ =159 MQ L =147 M =1490.2 nmQ =155 MQ L =138 M =1520.2 nmQ =137 MQ L =118 M =1540.1 nmQ =157 MQ L =126 M00.51 T r an s m i ss i on ( a r b . un i t ) =1560.2 nmQ =199 MQ L =146 M =1580.3 nmQ =227 MQ L =151 M =1609.6 nmQ =233 MQ L =139 M =1640.2 nmQ =278 MQ L =128 M-10 0 Frequency (MHz) 10 -10 0
Frequency (MHz) 10 -10 0
Frequency (MHz) 10 -10 0
Frequency (MHz) 10 -10 0
Frequency (MHz) 10 -10 0
Frequency (MHz) 10 -10 0
Frequency (MHz) 10 -10 0
Frequency (MHz) 10
FIG. S2. Q factor measurement. Transmission of high- Q modes at various wavelength in a 30 GHz resonator for determina-tion of intrinsic and loaded Q factors (red). Fitted doublet lineshape is overlaid. The tuning rate of the laser is simultaneouslycalibrated by the transmission of an MZI with 14.3 MHz F SR , also pictured (blue). resonators with 5 GHz and 10 GHz
F SR are used. Racetrack resonators were designed for critical coupling at 1550 nmto ensure efficient delivery of power to the resonator. To convert the mode between straight and bending waveguides,a sine curve evaluated between 0 and π/ Q factor of the 10 GHz racetrackresonator as compared to the 5 GHz resonator of 56 M and 100 M at 1560 nm, respectively. Imperfect adiabaticity canalso cause coupling to higher-order waveguide modes. When those higher order modes are antiresonant, this couplingis suppressed, however strong coupling can occur at mode crossings. As the loss in higher-order modes typicallyexceeds that of the fundamental, the Q at a mode crossing can be further degraded. Furthermore, the location ofthese mode crossings can be highly variable due to fabrication variability. Thus, to simplify operation of the device,we use single-mode waveguides within all racetrack resonators, at the expense of lower Q factor. Nonetheless, the Q factor is still high enough that the frequency noise of the self injection-locked laser is limited by thermorefractivenoise, so the impact of reduced Q factor is negligible. II. THEORY: SELF-INJECTION LOCKING
In this section we apply the theory of self-injection locking to study the linewidth-reduction factor when the laser isstabilized to the microresonator. The hybrid-laser system can be split into three parts: the laser field A L , the forwardoptical field A F and the backscattered field A B in the microresonator. The complete set of equations of motion are : ∂A F ∂t = − ( κ iδω ) A F + i D ∂ A F ∂θ + ig (2 | A B | + | A F | ) A F + iβ κ A B − p T κ R κ L e iφ B A L ,∂A B ∂t = − ( κ iδω ) A B + i D ∂ A B ∂θ + ig (2 | A F | + | A B | ) A B + iβ κ A F ,dA L dt = i ( δω L − δω ) A L − γ L A L + g L iα g ) A L − p T κ R κ L e iφ B A B . (S1)Here κ and γ L are the damping rates of the microresonator mode and the laser, respectively. δω = ω c − ω o isthe detuning of the cold-cavity resonant frequency ω c relative to the injection-locked laser frequency ω o . Similarly, δω L = ω c − ω L with ω L being the free-running, cold laser frequency. The nonlinear coupling coefficient g = ω o cn /n V with c the speed of light, n the Kerr coefficient, n eff the effective index and V the effective mode volume. θ isthe polar angle of the resonator in rotational frame, and D is the group velocity dispersion. β stands for thedimensionless backscattering coefficient normalized to the mode linewidth κ/
2, which is chosen as a positive realnumber for simplicity. κ R and κ L denote the external coupling rate of the resonator and the laser facet, respectively. T is the energy coupling efficiency between the facets of the laser and the Si N waveguide, and φ B is the propagationphase delay between the resonator and the laser. g L is the intensity dependent gain of the laser, and α g is theamplitude-phase coupling coefficient. The average intracavity intensity | A F , B | = R π | A F , B | dθ/ π , while the averageamplitude A F , B = R π A F , B dθ/ π .Introducing the normalized amplitude ρ F , B , L = A F , B , L / √ E th with E th = κ/ (2 g ) the intracavity parametric oscilla-tion threshold, the equations of motion can be normalized to a dimensionless form ∂ρ F ∂τ = − (1 + i ∆) ρ F + id ∂ ρ F ∂θ + i (2 | ρ B | + | ρ F | ) ρ F + iβρ B + F,∂ρ B ∂τ = − (1 + i ∆) ρ B + id ∂ ρ B ∂θ + i (2 | ρ F | + | ρ B | ) ρ B + iβρ F ,dρ L dτ = i (∆ L − ∆) ρ L − Γ ρ L + G L (1 + iα g ) ρ L − p T η Λ e iφ B ρ B , (S2)where normalized coefficients τ = κt/
2, ∆ = 2 δω/κ , d = D /κ , ∆ L = 2 δω L /κ , η = κ R /κ , Λ = κ L /κ , Γ = γ L /κ and G L = g L /κ . The normalized pump term F = − √ T η Λ e iφ B ρ L . Note that if the Q of the laser diode is limited by thecoating on its emission end, then Λ = Q m /Q d with Q m the Q of the microresonator and Q d the Q of the laser diode.Expanding the laser field as ρ L = | ρ L | e iφ L , the dynamics of the amplitude and phase are given by1 | ρ L | d | ρ L | dτ = G L − Γ − Re[2 p T η Λ e iφ B ρ B ρ L ] , (S3) dφ L dτ = ∆ L − ∆ + α g G L − Im[2 p T η Λ e iφ B ρ B ρ L ] . (S4)In the presence of sufficient gain saturation, the laser dynamics can be adiabatically eliminated so that d | ρ L | /dτ = 0.Therefore the gain can be solved as G L = Γ + Re[2 p T η Λ e iφ B ρ B ρ L ] . (S5)Substituting Eq. S5 into Eq. S4, we obtain dφ L dτ = ∆ L − ∆ + α g Γ − Im[2(1 − iα g ) p T η Λ e iφ B ρ B ρ L ]= ∆ L − ∆ + α g Γ + 4
T η Λ q α g Im[ e iψ ρ B F ] , (S6)where ψ = 2 φ B − arctan( α g ) . (S7)Note that Eq. S6 resembles the form of Adler’s equation , whose stationary solution gives the frequency of theself-injection locked laser as ∆ = ∆ L + α g Γ + K Im[ e iψ ρ B F ] . (S8)It should be noted that, the locking strength K = 4 T η Λ q α g , is usually much greater than 1 ( > in this work).The linewidth-reduction factor is derived as follows. For simplicity, we ignore all nonlinear terms by assuminghomogeneous intracavity field, i.e., ρ F , B = ρ F , B . Therefore, at steady state, the backscattered field is given by ρ B = iβF (1 + i ∆) + | β | . (S9)Substituting Eq. S9 into Eq. S8, we have∆ = ∆ L + α g Γ + K Im[ ie iψ β (1 + i ∆) + | β | ] = ∆ L + α g Γ +
Kχ. (S10)The equation has two solutions. However, stable self-injection locking is established only when ∂χ/∂ ∆ <
0. Assumingthe system is operating at steady state, the linewidth-reduction factor at low offset frequencies can be calculated using α = ( ∂ ∆ L ∂ ∆ ) , (S11)which can be solved analytically in the two following regimes: Weak backscattering ( β ≪ ): In this case, the mode will remain as a singlet. Stable locking occurs when ψ ≈ − π/
2. Assuming the laser is locked to the center of the mode, i.e., ∆ = 0, the linewidth-reduction factor yields α ≈ α g ) T η Λ | β | = 64(1 + α g ) T η | β | Q Q , (S12)where Q R and Q d stand for the Q of the microresonator and the laser diode, respectively. Strong backscattering ( β ≫ ): In this case, the mode will split as doublets. When ψ ≈ π ), the laser will belocked to the mode at the red (blue) side. Assuming the laser is locked to the center of a split mode, i.e., ∆ = ±| β | ,the linewidth-reduction factor yields α ≈ α g ) T η Λ = 4(1 + α g ) T η Q Q , (S13)which is irrelevant to the backscattering coefficient β .Typical values of these parameters in our systems are: α g = 2 . T = − η = 0 . Q d = 10 . For mode featuringloaded Q of 50 M and split resonances, the maximum estimated noise reduction factor is around 70 dB, which is 20dB higher than the noise suppression achieved in experiment. Under single-mode operation, we expect the lockingpoint to be detuned from resonance center to avoid nonlinearity. III. THEORY: SPECTRAL DEPENDENCE OF NOISE SUPPRESSION FACTOR
In this section, we derive the spectral dependence of the noise suppression factor, where the frequency responseof the microresonator is taken into consideration. For simplicity, the backscattering is assumed weak enough to notcause mode splitting ( β ≪ α g are also ignored. The steady state solutions from Eq. S2now read ρ F = Rρ L ,ρ B = iβRρ L , (S14)where R = − √ T η Λ e iφ B . The fluctuation of laser can be introduced using a Langevin term f , which includesspontaneous emission and carrier density fluctuations. As a result, the system will fluctuate in the vicinity of thesteady state, as denoted by field perturbation u F , u B and u L . With proper linearization, the dynamics of perturbationterms are formulated as ˙ u F = − u F + iβu B + Ru L , ˙ u B = − u B + iβu F , ˙ u L = i ∆ L u L + ( G L − Γ) u L − ǫG L A u ρ L + Ru B + f ( t ) , (S15)where u L = ρ L (1 + A u ) e iφ u − ρ L ≈ ρ L A u + iρ L φ u . (S16)The gain saturation effect is described by G L = G o / (1 + ǫ | ρ L | ). The amplitude and phase perturbations of the lasercan be studied separately as˙ A u = − L φ u + ( G L − Γ) A u − ǫG L A u + 12 ( Ru B + fρ L + c . c . ) , ˙ φ u = ∆ L A u + ( G L − Γ) φ u + 12 i ( Ru B + fρ L − c . c . ) . (S17)Assuming the gain saturation is large, i.e., ǫ ≫
1, the amplitude fluctuation diminishes ( A u ≈ φ u = − iβ ( R − R ∗ )2 φ u + 12 i ( Ru B + fρ L − c . c . ) . (S18)Applying Fourier transform, the spectral density of φ u yields iω f φ u = − iβ ( R − R ∗ )2 f φ u + 12 i ( R f u B ρ L − R ∗ f u ∗ B ρ ∗ L ) + 12 i ( f fρ L − f f ∗ ρ ∗ L ) . (S19)The spectrum of u B can be derived from Eq. S15 as iω f u F = − f u F + iβ f u B + iRρ L f φ u ,iω f u B = − f u B + iβ f u F , (S20)where f u L ≈ iρ L f φ u is used. Therefore, we have f u B = − iω ) βRρ L f φ u , (S21)where β ≪ ω with − ω , the spectrum of u ∗ B is given by f u ∗ B = − iω ) βR ∗ ρ ∗ L f φ u . (S22)Substituting Eqs. S21 and S22 into Eq. S19, we have iω f φ u = − iβ ( R − R ∗ )(2 iω − ω )2(1 + iω ) f φ u + e s, (S23)where s = i ( f fρ L − f f ∗ ρ ∗ L ). If the feedback phase ψ = 2 φ B = π/
2, we have R − R ∗ = − iT η Λ . (S24)Therefore, the phase noise of the self-injection locked laser can be written as | f φ u | = | e s | ω | βT η Λ(2+ iω )(1+ iω ) | . (S25)Compared with the free-running laser noise (obtained by setting β = 0), the spectrum of noise reduction factor isgiven by α ( ω ) = | βT η Λ(2 + iω )(1 + iω ) | . (S26)It is noted that at low offset frequencies, Eq. S26 resembles the form of Eq. S12 except for correction from amplitude-phase coupling term, which is set to be 0 in the derivation. Plotted in Fig. S3 is a typical spectral dependence ofthe noise reduction factor, which decreases at the rate of 1 /ω at frequencies exceeding the resonator linewidth. Suchineffectiveness at high-offset frequencies can be resolved by introducing a drop-port to the microresonator. For a laser -4 -3 -2 -1 drop portthrough port -5 Normalized frequency offset ( k /2) N o i s e r edu c t i on f a c t o r R e s ona t o r li ne w i d t h ab Laser Resonator Drop portThrough port
FIG. S3.
Spectral dependence of noise reduction factor. a,
Configuration of a laser butt-coupled to a microresonatorwith add-drop port. b, Calculated noise reduction factor of laser emission from through (red) and drop (blue) port. Thefrequency offset is normalized to κ/
2, one half of resonator linewidth. The term 4
T η
Λ is set to be 1000 in the plot. emitting from the drop-port of the microresonator, the phase is given by φ F = Im[ u F ρ F ] = 12 i ( u F ρ F − u ∗ F ρ ∗ F ) , (S27)whose spectrum yields f φ F = 12 i ( u F ρ F − u ∗ F ρ ∗ F ) = 11 + iω f φ u . (S28)Therefore, the noise reduction factor of the drop-port emission versus the free-running laser takes the form α drop ( ω ) = (1 + ω ) | βT η Λ(2 + iω )(1 + iω ) | . (S29)The additional noise suppression term at high-offset frequencies is attributed to the filtering effect of the high-Qmode. As a result, the noise reduction factor remains nearly constant across a wider frequency span. Strongernoise suppression at higher-frequencies is expected, though a model involving multiple longitudinal modes should beestablished at offset frequency on the order of the microresonator F SR . a b Evolution time (arb. unit) P o l a r ang l e q pp Polar angle q p p I n t r a c a v i t y po w e r ( a r b . un i t ) O p t i c a l po w e r ( d B pe r d i v i s i on ) Mode number0 50-50 Evolution time (arb. unit) P o l a r ang l e q pp Polar angle q p p I n t r a c a v i t y po w e r ( a r b . un i t ) O p t i c a l po w e r ( d B pe r d i v i s i on ) Mode number0 50-50 I n t r a c a v i t y po w e r ( a r b . un i t ) Singlet resonance Doublet resonance
FIG. S4.
Numerical simulation of Kerr comb formation in microresonators pumped by self-injection lockedlasers. a,
Evolution of intracavity field (upper panel), steady-state intracavity field (middle panel), and steady-state opticalspectrum (lower panel) when the mode is a singlet. The result is identical to that has been provided in Fig. 3 in the maintext.Parameters used in the simulation are: d = − . β = 0 . K = 2700, F = 10, ψ = − π/
2, ∆ L + α g Γ = 5. b, Evolution ofintracavity field (upper panel), steady-state intracavity field (middle panel), and steady-state optical spectrum (lower panel)when the mode splits into doublets. Parameters used in the simulation are: d = − . β = 5, K = 2700, F = 10, ψ = 0,∆ L + α g Γ = 5.
IV. THEORY: KERR COMB FORMATION
In this section we use the formalism in Section I to study the dynamics of Kerr comb formation in microresonatorspumped by self-injection locked laser. On account of Kerr nonlinearity and dispersion, the intracavity field is nolonger homogeneous. Since the Q of the laser cavity is much lower than the microresonator, the dynamics of the laserare much faster than the optical field in the microresonator, which can be assumed to operate at steady state as givenby Eq. S8. Therefore we can retrieve a set of coupled Lugiato-Lefever equations as ∂ρ F ∂τ = − (1 + i ∆) ρ F + id ∂ ρ F ∂θ + i (2 | ρ B | + | ρ F | ) ρ F + iβρ B + F,∂ρ B ∂τ = − (1 + i ∆) ρ B + id ∂ ρ B ∂θ + i (2 | ρ F | + | ρ B | ) ρ B + iβρ F , ∆ = ∆ L + α g Γ + K Im[ e iψ ρ B F ] . (S30)Numerical simulation based on the equations above is shown in Fig. S4, where two conditions are considered. Withweak backscattering, the mode remains a singlet. By setting the feedback phase as − π/
2, a spontaneous patternforms, leading to a flat-top pulse in the time domain as shown in Fig. S4a. Such a pulse is usually referred to asa dark soliton pulse or platicon . The optical spectrum is similar to the 10 GHz Kerr comb shown in Fig. 3C inthe maintext. When the backscattering is strong enough to cause mode splitting, spontaneous Kerr comb formationis also feasible by setting feedback phase ψ ≈
0, as shown in Fig. S4b. Compared with the case of weak-scattering,a pulse with shorter duration is formed, which is attributed to the increased effective detuning resulting from modesplitting. The simulated optical spectrum mimics the shape of the 5 GHz Kerr comb shown in Fig. 3c in the maintext.It should be noted that although stable injection can be established with feedback phase of π , spontaneous Kerr combformation is forbidden as imposed by the requirement of parametric oscillation. V. ADDITIONAL MEASUREMENT
Time (ms)-2-1012 F r equen cy ( M H z + . G H z ) C o m b po w e r ( a r b . un i t. ) RF Power (arb. unit.)0 1100 200 3000 400 500100 200 3000 400 500
FIG. S5.
Repeatability of turnkey Kerr comb generation.
Measured comb power (upper panel) and spectrographof comb repetition rate (lower panel) of 10 consecutive laser switching-on tests. The shaded region indicates the periodicswitching-on of lasers.[1] Bauters, J. F. et al.
Planar waveguides with less than 0.1 db/m propagation loss fabricated with wafer bonding.
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