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Register a new userNoise-seeded spatio-temporal modulation instability in normal dispersion
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In optical second harmonic generation with normal dispersion, the virtually infinite bandwidth of the unbounded, hyperbolic, modulational instability leads to quenching of spatial multi-soliton formation and to the occurrence of a catastrophic spatio-temporal break-up when an extended beam is let to interact with an extremely weak external noise with coherence time much shorter than that of the pump.
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We derive analytical expressions for the coherence in the onset of modulation instability, in excellent agreement with thorough numerical simulations. As usual, we start by a linear perturbation analysis, where broadband noise is added to a continuous wave (CW) pump; then, we investigate the effect of adding a deterministic seed to the CW pump, a case of singular interest as it is commonly encountered in parametric amplification schemes. Results for the dependence of coherence on parameters such as fiber type, pump power, propagated distance, seed signal-to-noise ratio are presented. Finally, we show the importance of including higher-order linear and nonlinear dispersion when dealing with generation in longer wavelength regions (mid IR). We believe these results to be of relevance when applied to the analysis of the coherence properties of supercontinua generated from CW pumps.
We study modulational instability (MI) in optical fibers with random group velocity dispersion (GVD) generated by sharply localized perturbations of a normal GVD fiber that are either randomly or periodically placed along the fiber and that have random strength. This perturbation leads to the appearance of low frequency MI side lobes that grow with the strength of the perturbations, whereas they are faded by randomness in their position. If the random perturbations exhibit a finite average value, they can be compared with periodically perturbed fibers, where Arnold tongues appear. In that case, increased randomness in the strengths of the variations tends to affect the Arnold tongues less than increased randomness in their positions.
A simple analytical model is developed to analyze and explain the complex dynamics of the multi-peak modulation instability spectrum observed in dispersion oscillating optical fibers [M. Droques et al., 37, 4832-4834 Opt. Lett., (2012)]. We provide a simple expression for the local parametric gain which shows that each of the multiple spectral components grows thanks to a quasi-phase-matching mechanism due to the periodicity of the waveguide parameters, in good agreement with numerical simulations and experiments. This simplified model is also successfully used to tailor the multi-peak modulation instability spectrum shape. These theoretical predictions are confirmed by experiments.
The propagation of a continuous wave in the average anomalous dispersion region of a dispersion oscillating fiber is investigated numerically and experimentally. We demonstrate that the train of solitons arising from modulation instability is strongly affected by the periodic variations of the fiber dispersion. This leads to the emission of multiple resonant radiations located on both sides of the spectrum. Numerical simulations confirm the experimental results and the position of the resonant radiations is well predicted by means of perturbation theory.
Supercontinuum (SC) generation via femtosecond (fs) pumping in all-normal-dispersion (ANDi) fiber is predicted to offer completely coherent broadening mechanisms, potentially allowing for substantially reduced noise levels in comparison to those obtained when operating in the anomalous dispersion regime. However, previous studies of SC noise typically treat only the quantum noise, typically in the form of one-photon-per-mode noise, and do not consider other technical noise contributions, such as the stability of the pump laser, which become important when the broadening mechanism itself is coherent. In this work, we discuss the influence of the amplitude and pulse length noise of the pump laser, both added separately and combined. We show that for a typical mode-locked laser, in which the peak power and pulse duration are anticorrelated, their combined impact on the SC noise is generally smaller than in isolation. This means that the supercontinuum noise is smaller than the noise of the mode-locked pump laser itself, a fact that was recently observed in experiments but not explained. Our detailed numerical analysis shows that the coherence of ANDi SC generation is considerably reduced on the spectral edges when realistic pump laser noise levels are taken into account.
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