Third-order chromatic dispersion stabilizes Kerr frequency combs

Abstract

Using numerical simulations of an extended Lugiato-Lefever equation we analyze the stability and nonlinear dynamics of Kerr frequency combs generated in microresonators and fiber resonators, taking into account third-order dispersion effects. We show that cavity solitons underlying Kerr frequency combs, normally sensitive to oscillatory and chaotic instabilities, are stabilized in a wide range of parameter space by third-order dispersion. Moreover, we demonstrate how the snaking structure organizing compound states of multiple cavity solitons is qualitatively changed by third-order dispersion, promoting an increased stability of Kerr combs underlined by a single cavity soliton.

Coexistence of stable dark- and bright-soliton Kerr combs in normal-dispersion resonators

“…In the anomalous dispersion regime, such temporal oscillations, also called "breathers", were experimentally first observed in fiber resonators [12] and have recently also been measured in microresonators [48][49][50]. In the anomalous regime, it was furthermore shown that TOD, which leads to drift instabilities, could suppress such oscillatory and chaotic temporal dynamics of bright solitons [26,27].…”

“…6 is to be interpreted as a drift in the fast time scale of the resonator round trip (where τ is scaled by √ 2α/ √ |β 2 |l) per time unit t (where t depends on the photon lifetime as t × α/t r with t r the round-trip time) [12,35]. This drift velocity thus strongly depends on α and l, which can change significantly from device to device (see, e.g., [27]). As solitons of different widths travel at different speeds, they eventually collide in a periodic domain and are forced to interact with one another.…”

“…In particular, third-order dispersion (TOD) generates the emission of dispersive waves that can lead to the suppression of dynamical regimes such as oscillations and chaos [26,27]. As TOD also breaks reversibility, solitons move with a constant velocity [26][27][28][29][30].…”

“…In particular, third-order dispersion (TOD) generates the emission of dispersive waves that can lead to the suppression of dynamical regimes such as oscillations and chaos [26,27]. As TOD also breaks reversibility, solitons move with a constant velocity [26][27][28][29][30]. While recent work has numerically shown that TOD induces similar dispersive waves in dark solitons in both normal and anomalous dispersion regions [31], a complete understanding of the influence of TOD on the dynamics and bifurcation structure of dark pulse Kerr frequency combs is still lacking.…”

Nonlinear Cavity and Frequency Comb Radiations Induced by Negative Frequency Field Effects

“…There is currently an intense research activity aiming to maximise the spectral extent of the comb and its coherence, and to understand the experimentally obtained spectra from first principles. Due to the extremely complex dynamical behaviour and stability properties of the propagating CSs and patterns in the resonators, an intense theoretical activity on the mathematical properties of the traditionally used averaged propagation equation, called the temporal Lugiato-Lefever equation (LLE), has developed over the past years, with a frequent display of new and surprising results [3][4][5][6][7].…”