Impact of the frequency drift of a laser cooler on the phase noise of the microcomb repetition frequency

We study the repetition frequency phase-noise in an auxiliary laser cooler assisted soliton microcomb formed in a high-Q Si₃N₄ microresonator. We find that, below a 1-kHz offset from the carrier, this noise is dominated by the frequency drift of the laser cooler. We identify the dominant noise types in the phase-noise spectrum of the repetition frequency using the polynomial law and relate the underlying noise sources that lead to the phase instability. We find that the 1 𝑓³ ⁄ noise dominates the repetition frequency phase-noise over three decades, which we attribute to the frequency drift of the laser cooler and the uncompensated cavity-pump detuning. Since the laser cooler acts on the cavity-pump detuning via the thermo-optic effect, the thermal response time of the cavity limits the filtering of 1 𝑓³ ⁄ noise originating from the free-running pump laser. Hence, low-phase-noise operation that is obtained by using the auxiliary laser cooling scheme requires both the pump and cooler lasers to be locked to a stable frequency reference.