Coexistence of dark vector soliton Kerr combs in normal dispersion resonators

Abstract

We investigate the formation of dark vector dissipative solitons in the presence of nonlinear polarization mode coupling in optical resonators subject to a coherent optical injection in the normal dispersion regime. This simple device is described by coupled Lugiato-Lefever equations. The stabilization of dark dissipative solitons is attributed to a front locking mechanism in the bistable regime as shown in a recent communication [B. Kostet et al., OSA Continuum 4, 1564]. Here, we focus on a tristable homogeneous steady state regime. We show that two branches of dark dissipative solitons can coexist for a fixed value of the system parameters. These coexisting solutions possess different polarization states and different peak powers in the microresonator. We characterize their formation by drawing their bifurcation diagrams in regimes far from any modulational instability. It is shown that both branches of localized structures exhibit a heteroclinic collapsed snaking type of behavior. The coexistence of two vectorial branches of dark localized states is not possible without taking into account polarization degrees of freedom.

Discrete vector light bullets in coupled χ3 nonlinear cavities

“…2 (a) shows the distribution of the total intensity or the Stokes 𝑆 0 parameter, which is used for the normalization of the 𝑠 1 , 𝑠 2 and 𝑠 3 parameters (c.f., e.g. [49]). If the discrete LBs were scalar, i.e.…”

“…𝛥𝛽 1 = (𝛽 1,𝑥 − 𝛽 1,𝑦 )∕2 corresponds to the group velocity mismatch, associated with the first-order dispersion. The group velocity mismatch has been shown to result in a drift motion of the vector localized structures along the cavity [49]. In the following, we present results in the limit of zero group velocity mismatch between the field components.…”

“…Dissipative solitons described by the vector Maxwell equations often called vector dissipative solitons have been observed in broad area VCSELs [45,46], predicted theoretically for the LLE in [47] and consequently confirmed experimentally in [48]. The coexistence of dark vector soliton Kerr combs in normal dispersion resonators has recently been analyzed in [49]. Quite recently, vector LBs have also been considered for the LLEs coupled by the cross-phase modulation terms [50].…”

Rogue waves in nonlinear optics

“…When polarization degree of freedom is taken into account within Kerr resonators, new MIs appear [170][171][172] and vector LSs are predicted [173][174][175][176]. However, when the Kerr resonator is operating in a dispersion regime, another class of LSs resulting from interactions may be generated in scalar [177][178][179][180][181][182] and vectorial cases [183,184].…”

Breathing of dissipative light bullets of nonlinear polarization mode in Kerr resonators

“…The Kerr resonators support stationary localized structures in 1D and 2D settings [30,31], as well as breathing of localized structures [32], in the scalar case where polarisation degree of freedom is ignored. However, in one dimesnional setting, the stability of localized structures are strongly dependent on the polarization of the incident light as they acquire a distinct ellipticity [27,33,34]. These dissipative localized structures can undergo breathing, which is a periodic variation in their duration and intensity [35][36][37][38].…”