On the spontaneous time-reversal symmetry breaking in synchronously-pumped passive Kerr resonators

Abstract

We study the spontaneous temporal symmetry breaking instability in a coherently-driven passive optical Kerr resonator observed experimentally by Xu and Coen in Opt. Lett. 39, 3492 (2014). We perform a detailed stability analysis of the Lugiato-Lefever model for the optical Kerr resonators and analyze the temporal bifurcation structure of stationary symmetric and the emerging asymmetric states as a function of the pump power. For intermediate pump powers a pitchfork loop is responsible for the destabilization of symmetric states towards stationary asymmetric ones while at large pump powers we find the emergence of periodic asymmetric solutions via a Hopf bifurcation. From a theoretical perspective, we use local bifurcation theory in order to analyze the most unstable eigenmode of the system. We also explore a non-conservative variational approximation capturing, among others, the evolution of the solution's amplitude, width and center of mass. Both methods provide insight towards the pitchfork bifurcations associated with the symmetry breaking. *

Interplay of Polarization and Time-Reversal Symmetry Breaking in Synchronously Pumped Ring Resonators

“…2(c). We note that a similar evolution can be obtained when the input power is swept while keeping the detuning fixed [12,14]. The manifestation of TSB is shown in Fig.…”

“…Instead, a solution where the peak of the soliton is shifted with respect to the extremum seems to be favoured. This phenomenon is referred to as a spontaneous symmetry breaking of the temporal pulse profile [11][12][13][14] and has been very recently identified in the context of cavity soliton dynamics as re- * francois.copie@npl.co.uk † pascal.delhaye@npl.co.uk sulting from a competition between the synchronous coherent driving and the nonlinear propagation inside the cavity [15]. On a different note, although a large fraction of the work done on nonlinear resonators addresses the case of one-dimensional and single polarization propagation, polarization-related effects can greatly widen the range of phenomena occuring in such systems related, for instance, to instabilities [16], pattern formation [17][18][19], soliton [20] and frequency comb generation [21] or symmetry breaking between the different polarization modes [4,22,[24][25][26].…”

“…Instead, a solution where the peak of the soliton is shifted with respect to the extremum seems to be favoured. This phenomenon is referred to as a spontaneous symmetry breaking of the temporal pulse profile [11][12][13][14] and has been very recently identified in the context of cavity soliton dynamics as re-sulting from a competition between the synchronous coherent driving and the nonlinear propagation inside the cavity [15].…”

Universal symmetry-breaking dynamics for the Kerr interaction of counterpropagating light in dielectric ring resonators

“…In the case of continuous symmetries, it allows for the modelling of magnetism and superconductivity [1], as well as the generation of mass via the Higgs mechanism [2]. It also plays a prominent role in systems that exhibit discrete symmetries, which are frequently found in optics, such as time-reversal [3,4] and parity-time symmetries [5], as well as the interplay between two types of symmetry breaking [6]. A novel type of discrete symmetry breaking has recently been demonstrated in bidirectionally-pumped whispering-gallery microresonators [7,8].…”

Kerr optical frequency comb generation using whispering-gallery-mode resonators in the pulsed-pump regime

“…A detailed mathematical analysis of that model was later on carried out in ref. [21], where the authors analyzed the bifurcation behavior of the system and the emergence of asymmetric states as a function of the pump power. For our numerical simulations, it is convenient to rewrite Eqs.…”