Double-seed stabilization of a continuum generated from fourth-order modulation instability

Summary form only given. Modulation instability (MI) is a ubiquitous process in which a weak field is exponentially amplified through a balance between dispersive and nonlinear effects. In single-mode scalar optical fibers, the positive Kerr nonlinearity phase-mismatch can be compensated by anomalous second-order dispersion, a process known as MI2. But phase-matched solutions can also exist in normal second-order dispersion region, thanks to negative even higher-order terms [1]. This process, that we label MI4, gives rise to a pair of narrow sidebands widely detuned far from the pump. MI may grow spontaneously from broadband noise and is usually the main process involved in the early stages of most supercontinuum (SC) generation. Because of its stochastic nature, MI creates strong fluctuations of spectral power, especially near the SC edges. In the time domain, these fluctuations manifest as so-called optical rogue waves, both in the MI2 [2] and MI4 [3] cases. Active methods based on stimulating the MI2 process have already been proposed [4]. However, in the configuration based on MI4, no experiments or numerical works have focused on the study of fluctuations and their reduction.For the first time, the large fluctuations of an SC generated from MI4 are highlighted and a method to mitigate them is proposed and validated. The experimental setup is sketched in Fig. 1(a) and relies on a Q-switch Nd-YAG laser emitting sub-nanosecond pulses. Pump pulses are combined with one or two continuous-wave seeds in the C-band corresponding to the Stokes MI-4 gain bandwidth of a 2 m long photonic crystal fiber. Output spectra as well as the statistical fluctuations after a narrowband filter are experimentally recorded and summarized in Fig. 1(b-c). Contrary to the MI2 case, stimulating the MI4 process with a single seed does not allow to significantly reduce fluctuations. We have found that this can be explained by the spontaneous cascaded MI2 process arising from the amplified seed in the vicinity of the MI4 gain band [5]. Therefore, two seeds are required to stimulate both the MI4 and the subsequent MI2, which results in an overall stabilization of the SC. This concept is validated from both experiments and numerical simulations. Fig 1(d) demonstrates that the spontaneous MI2-induced sideband (Fig. 1d2) can be efficiently mitigated by the double seeding scheme (Fig. 1d3). Consequently, the level of fluctuations affecting shot-to-shot records is drastically reduced (Figs. 1e) and numerical simulations based on the extended nonlinear Schrödinger equation reproduce the experimental stability improvement of the continuum source.