Thermal and Nonlinear Dissipative-Soliton Dynamics in Kerr-Microresonator Frequency Combs

We explore the dynamical response of dissipative Kerr solitons to changes in pump power and detuning and show how thermal and nonlinear processes couple these parameters to the frequency-comb degrees of freedom. Our experiments are enabled by a Pound-Drever-Hall (PDH) stabilization approach that provides on-demand, radio-frequency control of the frequency comb. PDH locking not only guides Kerr-soliton formation from a cold microresonator but opens a path to decouple the repetition and carrier-envelope-offset frequencies. In particular, we demonstrate phase stabilization of both Kerr-comb degrees of freedom to a fractional frequency precision below ${10}^{-16}$, compatible with optical-time-keeping technology. Moreover, we investigate the fundamental role that residual laser-resonator detuning noise plays in the spectral purity of microwave generation with Kerr combs.

Figure 1

(a) PDH approach for Kerr-soliton generation. An SSB-SC frequency shifter is driven by a high-bandwidth VCO for fast frequency control of the pump laser, and a servo locks one of the phase-modulation (PM) sidebands at resonance. A voltage-controlled optical attenuator (VOA) is used to control the pump power. (b) By adjusting the frequency sweep rate, we control the transition into the soliton regime. The waveform applied to the VCO is a simple, linear voltage sweep, and the $x$ axis is relative to the cold cavity resonance frequency. (c) Feedback is initiated at a predetermined instant of the frequency scan. The dashed line corresponds to the PDH lock point. (d) Generation of soliton frequency combs across the entire $C$ band.

Figure 2

(a) Shaded regions detail the signs of ${\nu }_p$ and ${\nu }_c$ tuning; their fixed points are marked by (i) and (ii), respectively. The red curve is the integral of Eq. (5). (b) Dependence of soliton repetition frequency with detuning. (c) Dependence of soliton repetition frequency with pump power. Red lines in (b),(c) are linear fits. (d) Soliton repetition-frequency response to detuning (blue line) and pump power (green line).

Figure 3

(a) Illustration of the experiment to characterize residual noise in our phase locks of $f_{\mathrm{rep}}$ and $f_{\mathrm{ceo}}$. The pump laser is phase-locked to a cavity-stabilized laser, which is electro-optically (EO) modulated to produce a reference comb. The repetition rates of both combs are derived from the same reference. (b) Setup used to fully stabilize the Kerr comb. (c) Allan deviations of three Kerr comb lines counted against neighboring EO teeth. Inset: Distribution of counted frequencies at 0.1 s gate time with a Gaussian fit (red line). The error between the mean and the expected value is 2 mHz.

Figure 4

Measured phase noise of $f_{\mathrm{rep}}$ (black traces) and predictions obtained from our model (red trace) and the PDH error signal (blue trace). The gray trace is the measurement-system floor.