Impact of desynchronization and drift on soliton-based Kerr frequency combs in the presence of pulsed driving fields

Pulsed driving of Kerr microresonators represents a promising avenue for the efficient generation of soliton states associated with coherent optical frequency combs. The underlying physics has not, however, yet been comprehensively investigated. Here, we report on a numerical and theoretical study of the impact of desynchronization between the periodic pump field and the train of solitons circulating in the cavity. We show that desynchronization can affect the soliton configurations that can be sustained for given parameters, and that it can be leveraged to guarantee operation in the attractive single-soliton regime. We also reveal that the interplay between pump-resonator desynchronization and stimulated Raman scattering can give rise to rich dynamics that explain salient features observed in recent experiments. Our work elucidates the dynamics of Kerr cavity solitons in the presence of pulsed driving fields, and could facilitate the development of efficient microresonator frequency comb systems.

Figure 1

(a) Red dashed curve shows the drift velocity due to the amplitude inhomogeneity of a Gaussian driving field (blue solid curve) with amplitude $S_0=6$ and duration ${\tau }_{\mathrm{g}}=10$. The cavity detuning $\mathrm{\Delta }=7$. Red solid circles (black cross) highlight(s) stable (unstable) trapping positions. CSs do not exist in the gray shaded area, where the local driving field level is smaller than the minimum required for soliton existence. (b)–(d) Temporal profiles of the three possible soliton states that can manifest themselves for the parameters listed in (a). (e)–(g) Spectral profiles corresponding to (b)–(d), respectively.

Figure 2

(a) False color plot showing the evolution of the intracavity field intensity when desynchronization with $d=-0.1$ is abruptly introduced at slow time $t=50$ (highlighted by the horizontal dotted line). Other parameter as in Fig. 1. (b) Solid blue, dashed red, and solid green curves show the positions of CS solutions of Eq. (1) as a function of the drift coefficient $d$, obtained using a Newton continuation algorithm. The solid blue curve corresponds to stable solutions, the dashed red curve corresponds to the trivially unstable $dS/d\tau =0$ trapping position, while the solid green curves indicate more complex instabilities (see main text). An additional branch of trivially unstable CSs that connects the two end points is not shown for clarity. Open gray circles show trapping positions found by directly solving the roots of the equation $v=0$, where $v$ is given by Eq. (3).

Figure 3

Simulated intracavity dynamics of unstable CSs for (a) $d=0.15$ and (b) $d=0.06$ with other parameters as in Fig. 1. Both simulations use an initial condition comprised of a solitonlike perturbation close to its predicted trapping position. The inset in (a) shows the evolution over a smaller range of slow time so as to highlight the oscillatory nature of the instability. The dotted vertical line in (b) indicates the temporal position ${\tau }_{\min }$ which satisfies $S\left({\tau }_{\min }\right)=S_{\min }$. The inset in (b) shows the evolution of the normalized soliton amplitude ${\left|E\right|}^2=|E(t,{\tau }_{\min }){|}^2/\text{max}\left[\right|E(t,{\tau }_{\min }){|}^2]$ from slow time $t=150$ onwards. Note the different $x$ axes in (a) and (b).

Figure 4

Numerical results for a cavity detuning of $\mathrm{\Delta }=4$, driving pulse amplitude $S_0=3$, and driving pulse width ${\tau }_{\mathrm{g}}=10$. (a) Evolution of the intracavity field intensity when desynchronization with $d=-0.07$ is abruptly introduced at slow time $t=300$ (highlighted by the horizontal dotted curve). (b) As in Fig. 2, blue, green, and red curves show the positions of stable and unstable CS solutions of Eq. (1) as a function of the drift coefficient $d$. Open gray circles show trapping positions found by directly solving the roots of the equation $v=0$, where $v$ is given by Eq. (3).

Figure 5

(a)–(c) Average intracavity power as the detuning is scanned over the cavity resonance for different drift coefficients $d$ as indicated. (d) Dynamical evolution of the intracavity field intensity as the detuning is scanned over the resonance for $d=0$. (e) False color plot of scan traces as in (a)–(c) for a range of different drift coefficients $d$. Solid white curves highlight the maximum desynchronization that a CS can tolerate when excited by scanning the detuning (as described in the main text). The dashed vertical white line corresponds to the absolute maximum detuning of CS existence, i.e., ${\mathrm{\Delta }}_{\max }={\pi }^2{S}_0^2/8$. Simulations use $S_0=\sqrt{15}$ and ${\tau }_{\mathrm{g}}=4$.

Figure 6

(a) Soliton steps as a function of the drift coefficient $d$ when SRS is included in the model. Note the different axes limits compared to Fig. 5. (b), (c) Dynamical evolutions of the intracavity field intensity for drift coefficients as indicated. The Raman response function used in the simulations corresponds to fused silica [49], with $f_{\mathrm{R}}=0.18$. Other parameters as in Fig. 5.