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- ItemRaman-Kerr Comb Generation Based on Parametric Wave Mixing in Strongly Driven Raman Molecular Gas Medium(2020) Benoît, Aurélien; Husakou, Anton; Beaudou, Benoît; Debord, Benoît; Gérôme, Frédéric; Benabid, FetahWe report on experimental and theoretical demonstrations of an optical comb spectrum based on a combination of cascaded stimulated Raman scattering and four-wave mixing mediated by Raman-induced nonresonant Kerr-type nonlinearity. This combination enabled us to transform a conventional quasiperiodic Raman comb into a comb with a single and smaller frequency spacing. This phenomenon is achieved using a hollow-core photonic crystal fiber filled with 40 bars of deuterium and pumped with a high-power picosecond laser. The resultant comb shows more than 100 spectral lines spanning over 220 THz from 800 nm to 1710 nm, with a total output power of 7.1 W. In contrast to a pure Raman comb, a 120 THz wide portion of the spectrum exhibits denser and equally spaced spectral lines with a frequency spacing of around 1.75 THz, which is much smaller than the lowest frequency of the three excited deuterium Raman resonances. A numerical solution of the generalized nonlinear Schrödinger equation in the slowly varying envelope approximation provides very good agreement with the experimental data. The additional sidebands are explained by cascaded four-wave mixing between preexisting spectral lines, mediated by the large Raman-induced optical nonlinearity. The use of such a technique for coherent comb generation is discussed. The results show a route to the generation of optical frequency combs that combine large bandwidth and high power controllable frequency spacing.
- ItemTiming of transients: Quantifying reaching times and transient behavior in complex systems(Bristol : Institute of Physics Publishing, 2017) Kittel, T.; Heitzig, J.; Webster, K.; Kurths, J.In dynamical systems, one may ask how long it takes for a trajectory to reach the attractor, i.e. how long it spends in the transient phase. Although for a single trajectory the mathematically precise answer may be infinity, it still makes sense to compare different trajectories and quantify which of them approaches the attractor earlier. In this article, we categorize several problems of quantifying such transient times. To treat them, we propose two metrics, area under distance curve and regularized reaching time, that capture two complementary aspects of transient dynamics. The first, area under distance curve, is the distance of the trajectory to the attractor integrated over time. It measures which trajectories are 'reluctant', i.e. stay distant from the attractor for long, or 'eager' to approach it right away. Regularized reaching time, on the other hand, quantifies the additional time (positive or negative) that a trajectory starting at a chosen initial condition needs to approach the attractor as compared to some reference trajectory. A positive or negative value means that it approaches the attractor by this much 'earlier' or 'later' than the reference, respectively. We demonstrated their substantial potential for application with multiple paradigmatic examples uncovering new features.