The classical theory of modulation instability (MI) attributed to Bespalov-Talanov in optics and Benjamin-Feir for water waves is just a linear approximation of nonlinear effects and has limitations ...that have been corrected using the exact weakly nonlinear theory of wave propagation. We report results of experiments in both optics and hydrodynamics, which are in excellent agreement with nonlinear theory. These observations clearly demonstrate that MI has a wider band of unstable frequencies than predicted by the linear stability analysis. The range of areas where the nonlinear theory of MI can be applied is actually much larger than considered here.
Light flow in nonlinear media can exhibit quantum hydrodynamical features which are profoundly different from those of classical fluids. Here, we show that a rather extreme regime of quantum ...hydrodynamics can be accessed by exploring the piston problem (a paradigm in gas dynamics) for light, and its generalization, named after the celebrated mathematician Riemann, where the piston acts on a concomitant abrupt change of photon density. Our experiment reveals regimes featuring optical rarefaction (retracting piston) or shock (pushing piston) wave pairs, and most importantly the transition to a peculiar type of flow, occurring above a precise critical piston velocity, where the light shocks are smoothly interconnected by a large contrast, periodic, fully nonlinear wave. The transition to such extreme hydrodynamic state is generic for superfluids, but to date remained elusive to any other quantum fluid system. Our full-fiber setup used to observe this phenomenon in temporal domain proves to be a versatile alternative to other platforms currently employed to investigate the hydrodynamical properties of quantum fluids of light.
The discovery of the Fermi-Pasta-Ulam (FPU) recurrence phenomenon in the 1950 s was a major step in science that later led to the discovery of solitons in nonlinear physics. More recently, it was ...shown that optical fibers can serve as a medium for observing the FPU phenomenon. In the present work, we have found experimentally and numerically that in the low-dispersion region of an optical fiber, the recurrence is strongly influenced by the third-order-dispersion (TOD) term. Namely, the presence of TOD leads to several disappearances and recoveries of the FPU recurrence when the central frequency of the pump wave is varied. The effect is highly nontrivial and can be explained in terms of reversible and irreversible losses caused by Cherenkov radiations interacting with a multiplicity of modes sharing the optical energy in the process of its partition.
Optical frequency combs (OFCs), consisting of a set of phase-locked, equally spaced laser frequency lines, have enabled a great leap in precision spectroscopy and metrology since seminal works of ...Hänsch et al. Nowadays, OFCs are cornerstones of a wealth of further applications ranging from chemistry and biology to astrophysics and including molecular fingerprinting and light detection and ranging (LIDAR) systems, among others. Driven passive optical resonators constitute the ideal platform for OFC generation in terms of compactness and low energy footprint. We propose here a technique for the generation of OFCs with a tuneable repetition rate in externally driven optical resonators based on the gain-through-filtering process, a simple and elegant method, due to asymmetric spectral filtering on one side of the pump wave. We demonstrate a proof-of-concept experimental result in a fibre resonator, pioneering a new technique that does not require specific engineering of the resonator dispersion to generate frequency-agile OFCs.
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 intracavity 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 the 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.
In this Research Letter, using experimental data, we analyze the computational complexity of modulation instability of a light wave propagating in a single-mode optical fiber. We show that ...computational complexity is an excellent tool which provides an insight into the emergence from noise of modulation-instability-induced coherent structures in the linear stage, before they become fully developed in the temporal traces, and substantially anticipating other statistical methods. Furthermore, computational complexity captures qualitatively the statistical signature of the recurrences in the nonlinear stage of modulation instability too.
Abstract
Tricomb spectroscopy unveils a new dimension to standard linear and nonlinear spectroscopic analysis, offering the possibility to reveal the almost real-time evolution of complex systems ...with unprecedented accuracy. Current triple comb configurations are based on the use of mode-locked lasers, which impose constraints on the comb parameters, and require complex electronic synchronization, thus limiting potential applications. In this paper, we present the experimental demonstration of a new type of all-fiber, self-phase-locked, frequency-agile tri-comb light source. It is based on the nonlinear spectral broadening of three electro-optic modulator-based frequency combs in a three-core fiber. The exploitation of spatial multiplexing of light in optical fibers offers new possibilities to generate broadband-frequency combs that are highly coherent with each other. After characterizing the stability of the source and performing several dual-comb test measurements, we revealed the high mutual coherence between the three combs through the demonstration of a 2-D pump-probe four-wave mixing spectroscopy experiment.
Predicting complex nonlinear dynamical systems has been even more urgent because of the emergence of extreme events such as earthquakes, volcanic eruptions, extreme weather events (lightning, ...hurricanes/cyclones, blizzards, tornadoes), and giant oceanic rogue waves, to mention a few. The recent milestones in the machine learning framework o↵er a new prospect in this area. For a high dimensional chaotic system, increasing the system’s size causes an augmentation of the complexity and, finally, the size of the artificial neural network. Here, we propose a new supervised machine learning strategy to locally forecast bursts occurring in the turbulent regime of a fiber ring cavity.
Abstract
Modulation instability is one of the most ubiquitous phenomena in physics. Here we investigate the phase-sensitive properties of modulation instability with harmonic seeding in passive fiber ...resonators. Theoretical investigations based on the Lugiato−Lefever equation with time dependent pump and a three-wave truncation show that the dynamics of the system is sensitive to the relative phase between input signal, idler, and pump waves. The modulation instability gain can even vanish for a peculiar value of the initial relative phase. An advanced multi-heterodyne measurement technique had been developed to record the real time evolution, round-trip to round-trip, of the power and phase of the output cavity field to confirm these theoretical predictions.
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