Stabilization of localized structures by inhomogeneous injection in Kerr resonators

Abstract

We consider the formation of temporal localized structures or Kerr comb generation in a microresonator with inhomogeneities. We show that the introduction of even a small inhomogeneity in the injected beam widens the stability region of localized solutions. The homoclinic snaking bifurcation associated with the formation of localized structures and clusters of them with decaying oscillatory tails is constructed. Furthermore, the inhomogeneity allows not only to control the position of localized solutions, but strongly affects their stability domains. In particular, a new stability domain of a single peak localized structure appears outside of the region of multistability between multiple peaks of localized states. We identify a regime of larger detuning, where localized structures do not exhibit a snaking behavior. In this regime, the effect of inhomogeneities on localized solutions is far more complex: they can act either attracting or repelling. We identify the pitchfork bifurcation responsible for this transition. Finally, we use a potential well approach to determine the force exerted by the inhomogeneity and summarize with a full analysis of the parameter regime where localized structures and therefore Kerr comb generation exist and analyze how this regime changes in the presence of an inhomogeneity.

Oscillatory motion of dissipative solitons induced by delay-feedback in inhomogeneous Kerr resonators

“…The paper is organized as follows, after a brief introduction, we discuss in Section 2 , the formation of dissipative solitons in the presence of inhomogeneities. This effect has been discussed in [17] for a small and positive defect, here we investigate more systematically the effect of inhomogeneities including the case when the amplitude of the defect is negative. We analyze this effect by using the tools of bifurcation theory, showing that depending on the system parameters, the inhomogeneity can attract or repeal dissipative solitons.…”

“…When the Kerr resonators are driven by an inhomogeneous injected beam such as a modulated beam [13][14][15] or Gaussian [16] , dissipative solitons can be stabilized through the front pinning mechanism. When the cavity is operating close to the modulational instability, it has been shown that the inhomogeneity impacts strongly the stability domains, as well as the homoclinic snaking bifurcation associated with the formation of dissipative solitons [17] . In particular, the stability domain of a single peak dissipative solitons is much larger than the pinning region where the system exhibits multistability between multiple peaks of dissipative solitons [17] .…”

“…When the cavity is operating close to the modulational instability, it has been shown that the inhomogeneity impacts strongly the stability domains, as well as the homoclinic snaking bifurcation associated with the formation of dissipative solitons [17] . In particular, the stability domain of a single peak dissipative solitons is much larger than the pinning region where the system exhibits multistability between multiple peaks of dissipative solitons [17] . Dissipative soliton and localized pattern formation are an important issue not only in the context of nonlinear optics and laser physics but constitute a multidisciplinary area of research in many far from equilibrium extended systems involving physics, chemistry, biology, plant ecology, and mathematics (see overviews on this issue [18][19][20][21][22][23][24] ).…”

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

“…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.…”

“…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.…”