All-Optical Stabilization of Soliton Microcomb via CW Laser Injection - INVITED

. Repetition-rate locking in soliton microcombs via the injection of a weak second continuous-wave laser in the spectral wing of the soliton is studied experimentally, resulting in all-optical control and reduction of phase noise through optical division.


Introduction
Dissipative Kerr solitons (DKSs) in continuous-wave (CW) laser-driven microresonators provide access to ultrashort pulses and frequency combs (microcombs) with ultra-high repetition rates up to THz.They have found applications in sensing, communication, and signal processing [1].Their comb spectra are characterized by two degrees of freedom, the repetition rate (i.e. the line spacing) and an offset frequency.While the offset frequency is directly defined by the CW pump laser, the repetition rate, approximately defined by the resonator's freespectral range (FSR), fluctuates due to technical and fundamental noise source.For many advanced applications, such as precision spectroscopy, optical communication or low-noise signal generation, reducing the noise is essential and stabilization if often required.Besides approaches of controlling and stabilizing the repetition rate actively [2], all-optical stabilization based on injecting a CW laser into the wing of the comb, many modes away from the pump, has been studied theoretically [3], describing a locking of the closest DKS comb line to the CW laser, an effect similar to parametric seeding [4] observed experimentally in four-wave mixing spectra.
Here we study experimentally the locking of the DKS comb lines to a second (auxiliary) laser and observe a drastic reduction of the solitons repetition rate phase noise, through optical division of the frequency interval defined by the pump laser and the second CW laser.Notably, this optical division does not require any active feedback or control.

Results
Using ∼100 mW of on-chip pump power at a wavelength of 1557.5 nm, we generate a single dissipative Kerr soliton (DKS) inside an integrated silicon nitride ring resonator with an FSR of 300 GHz.The soliton spectrum has a 3 dB bandwidth of 5.19 THz corresponding to a transformlimited pulse length of 60 fs.In order to record the soliton repetition rate f rep , we use a scheme similar to ref. [5] whereby the interval between two neighbouring comb lines is optically down-mixed using electro-optic modulation.The resulting beatnote is recorded from which f rep can readily be recovered.
In order to lock the soliton repetition rate f rep , a continuously-tunable laser (CTL) with ∼250 µW of on-  chip power is combined with the pump and subsequently scanned across the wings of the soliton comb spectrum during single-DKS operation.When the CTL is sufficiently close to a line of the soliton comb, this line is observed to lock onto the CTL.With the soliton microcomb pinned to both the pump and CTL, the repetition rate is effectively locked to an integer fraction of the pump-to-CTL spacing: f rep = |ν ctl − ν pump |/µ, where µ is the relative comb line number to which the CTL is injected (with regard to the pumpe line).The recorded spectrogram of f rep as the CTL is swept across the comb line µ = 12 is shown in Fig. 1a, where a locking range of ∼4 MHz is observed, corresponding to ∼48 MHz of tuning of the CTL.Furthermore we record the phase noise (PN) in the free-running and locked states (Fig. 1b) and investigate the evolution of the PN as the CTL is gradually injected further away from the pump line.A reduction in PN consistent with optical frequency division is observed (∼32.5 dB reduction from µ = 1 to µ = 42): indeed as when locked, f rep is an integer fraction of the frequency interval defined by the two lasers, its phase noise is also reduced (with regard to the lasers' phase noise) and given by S rep = (S pump + S ctl )/µ 2 .
We study the locking range as a function of the comb line number µ by running a frequency-calibrated scan of the CTL from 1510 nm to 1630 nm and recording the chip transmission (Fig. 2a and b).When crossing a comb line, the transmission follows a profile similar to that of the beatnote in Fig. 1a enabling easy identification of the locking range.Interestingly, the CTL also probes the neighbouring resonances enabling real-time measurement of the effective pump detuning.

Conclusion
Robust locking of the DKS repetition rate to an integer fraction of the frequency interval defined by the pump laser and a second auxiliary laser is observed.Although only free-running lasers are used, this effect results in a significant reduction of DKS repetition rate phase noise.The locking range (tuning range of the second laser) is on the order of the resonator's linewidth and exceeds by far the frequency drift of the free-running lasers, permitting long-term operation.The presented experimental observations may lead to simplified schemes for DKS-based optical clocks, ultra-high repetition rate pulse with ultra-low timing jitter, high-coherence sources for optical communication, and may also be of interest for dual-comb systems where lines of different mode number phase-coherently lock [6].

Figure 1 .
Figure 1.a, Spectrogram of the soliton repetition rate microwave signal as the auxiliary CTL laser is swept across DKS comb line µ = 12.b, Phase noise of the of DKS repetition rate in the freerunning and lock states, as the CTL is gradually injected further from the pump line (µ = 1 to µ = 42).

fFigure 2 .
Figure 2. a, Chip transmission as function of CTL frequency and comb line number µ. b, Zoom-in on the comb region of a, showcasing the evolution of locking range as a function of comb line number µ.