Abstract
Modulational instability in passive optical resonators, the triggering mechanism of frequency comb and pulse train generation, is shown to exhibit transitions between regimes involving period-one (P1) versus period-two (P2) dynamical evolutions. The latter is a signature of parametric resonance occurring in the system, which can arise either from intrinsic cavity periodicity or from spatial modulation of the cavity parameters. We characterize the P1-P2 transition for both cases employing a fiber resonator where the intra-cavity fiber can be either uniform or dispersion modulated. The key element of our setup is a time lens which we exploit to resolve the temporal dynamics over successive round-trips, allowing crystal clear evidence of the existence of P1-P2 transitions for suitable changes of cavity parameters, as well as for the successful characterization of the relative temporal patterns. Our findings reveal new regimes where the averaged model known as Lugiato-Lefever equation turns out to be inadequate to explain the dynamics, whereas the results are correctly predicted and described on the basis of the full Ikeda map.
Highlights
The generation of frequency combs has attracted a lot of attention during the last decades since these ultraprecise optical rulers have a wealth of applications including astrophysics, metrology, or spectroscopy to name a few [1,2]
Characteristics of the frequency comb strongly depend on these early stages of formation, and a perfect knowledge of the modulation instability (MI) dynamics is essential to understand their formation in order to optimize their performances [8]
For the sake of simplicity, we focus on the specific case where only the group velocity dispersion (GVD) is modulated along the cavity length with a piecewise constant dispersion profile, corresponding to almost all realistic fiber optics configurations [45]
Summary
The generation of frequency combs has attracted a lot of attention during the last decades since these ultraprecise optical rulers have a wealth of applications including astrophysics, metrology, or spectroscopy to name a few [1,2]. The general importance of such types of measurements stands on the fact that the P2 regime is a well-known mechanism in nonlinear systems supporting bistable states, first predicted by Ikeda et al [28], which was identified as a first step in a universal route to chaos It has been observed in modulationaly stable passive fiber cavities [29,30,31] and investigated in active lasers in theory [32,33,34] and in experiments [35,36].
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