Spontaneous symmetry breaking and trapping of temporal Kerr cavity solitons by pulsed or amplitude-modulated driving fields

Abstract

We report on a systematic study of temporal Kerr cavity soliton dynamics in the presence of pulsed or amplitude modulated driving fields. In stark contrast to the more extensively studied case of phase modulations, we find that Kerr cavity solitons are not always attracted to maxima or minima of driving field amplitude inhomogeneities. Instead, we find that the solitons are attracted to temporal positions associated with specific driving field values that depend only on the cavity detuning. We describe our findings in light of a spontaneous symmetry breaking instability that physically ensues from a competition between coherent driving and nonlinear propagation effects. In addition to identifying a new type of Kerr cavity soliton behaviour, our results provide valuable insights to practical cavity configurations employing pulsed or amplitude modulated driving fields.

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

“…We first recall CS trapping behaviour in the absence of de-synchronization (d = 0). In the presence of driving field amplitude inhomogeneities, a CS positioned at τ CS will (to first order) experience a drift in (fast) time with a rate [33]:…”

“…If the peak amplitude of the driving pulses satisfy S 0 < S c , the former (dS/dτ = 0) trapping position is stable and the latter [a(S c , ∆) = 0] trapping positions do not exist. As the peak amplitude S 0 increases past the critical value S c , the dS/dτ = 0 trapping position becomes unstable through a pitchfork bifurcation, concomitant with the emergence of a pair of new asymmetric stable states that correspond to the a(S c , ∆) = 0 equilibria [33]. In this latter regime (where S 0 > S c ), a CS will be attracted to (and trapped at) positions τ c on the edge of the driving pulse, where S(τ c ) = S c .…”

“…In Ref. [33] it was shown that, for increasing detuning ∆, the critical driving level S c approaches the minimum driving level required for soliton existence [S min ≈ (8∆/π 2 ) 1/2 ]. As most (microresonator) experiments operate in the regime ∆ 1, where S c is very close to S min , it is reasonable to conclude that S 0 > S c in most experimental situations.…”

“…We have recently demonstrated that CSs in Kerr resonators driven with pulsed or amplitude modulated fields are attracted to (and subsequently pinned to) temporal positions associated with specific values of the driving field amplitude [33] -behaviour that is in stark contrast to the tendency of CSs to be attracted to the extrema of phase inhomogeneities [23,30,31]. Moreover, Tabbert et al have shown that amplitude inhomogeneities can affect the domains of soliton existence and stability [34].…”

“…The analyses reported in Refs. [33] and [34] were, however, performed under the assumption of perfect synchronization between the CS(s) and the periodic driving field, which is unlikely to hold true in general.…”