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.

References in corpus (9)

• Optical frequency comb generation from a monolithic microresonator
• Temporal solitons in optical microresonators
• Dynamics of localized and patterned structures in the Lugiato-Lefever equation determine the stability and shape of optical frequency combs
• From the Lugiato-Lefever equation to microresonator based soliton Kerr frequency combs
• Introduction: Localized Structures in Dissipative Media: From Optics to Plant Ecology
• Spontaneous symmetry breaking and trapping of temporal Kerr cavity solitons by pulsed or amplitude modulated driving fields
• Interaction of solitons and the formation of bound states in the generalized Lugiato-Lefever equation
• Experimental observation of the spontaneous breaking of the time-reversal symmetry in a synchronously-pumped passive Kerr resonator
• Delay-Induced Depinning of Localized Structures in a spatially inhomogeneous Swift-Hohenberg Model

Cited by in corpus (3)

• Impact of de-synchronization and drift on soliton-based Kerr frequency combs in the presence of pulsed driving fields
• Hybrid patterns and solitonic frequency combs in non-Hermitian Kerr Cavities
• Impact of phase modulation on the dynamics of temporal localized structures in injected Kerr microcavities