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Identifying the underlying processes that locally dominate physical interactions is the key to understanding nonlinear dynamics. Machine-learning techniques have recently been shown to be highly promising in automating the search for dominant physics, adding important insights that complement analytical methods and empirical intuition. Here we apply a fully unsupervised approach to the search for dominant balance during nonlinear and dispersive propagation in an optical fiber and show that we can algorithmically identify dominant interactions in cases of optical wavebreaking, soliton fission, dispersive wave generation, and Raman soliton emergence. We discuss how dominant balance manifests both in the temporal and spectral domains.
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We investigate the spectral phase characteristics of dual-pumped Kerr frequency combs generated in a bichromatic Brillouin fiber laser architecture with normal dispersion, producing square-like pulse profiles. Using a pulse shaper, we measure the relative phase between the pump Stokes and adjacent lines, revealing a symmetric phase relationship. Our results highlight good phase coherence of the comb. By manipulating spectral amplitudes and phases, we demonstrate the transformation into various optical waveforms. The stability of our low-noise frequency comb ensures reliable performance in practical settings.
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We demonstrate that the dynamic mode decomposition technique can effectively reduce the amount of noise in the dispersive Fourier transform dataset and allow for finer quantitative analysis of the experimental data. We therefore show that the oscillation pattern of a soliton molecule actually results from the interplay of several elementary vibration modes.
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We report on the experimental and numerical observations of synchronization and desynchronization of bound states of multiple breathing solitons (breathing soliton molecules) in an ultrafast fiber laser. In the desynchronization regime, although the breather molecules as wholes are not synchronized to the cavity, the individual breathers within a molecule are synchronized to each other with a delay (lag synchronization). An intermediate regime between the synchronization and desynchronization phases is also observed, featuring self-modulation of the synchronized state. This regime may also occur in other systems displaying synchronization. Breathing soliton molecules in a laser cavity open new avenues for the study of nonlinear synchronization dynamics.
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Neural networks have been recently shown to be highly effective in predicting time-domain properties of optical fiber instabilities based only on analyzing spectral intensity profiles. Specifically, from only spectral intensity data, a suitably trained neural network can predict temporal soliton characteristics in supercontinuum generation, as well as the presence of temporal peaks in modulation instability satisfying rogue wave criteria. Here, we extend these previous studies of machine learning prediction for single-pass fiber propagation instabilities to the more complex case of noise-like pulse dynamics in a dissipative soliton laser. Using numerical simulations of highly chaotic behaviour in a noise-like pulse laser operating around 1550 nm, we generate large ensembles of spectral and temporal data for different regimes of operation, from relatively narrowband laser spectra of 70 nm bandwidth at the -20 dB level, to broadband supercontinuum spectra spanning 200 nm at the -20 dB level and with dispersive wave and long wavelength Raman extension spanning from 1150-1700 nm. Using supervised learning techniques, a trained neural network is shown to be able to accurately correlate spectral intensity profiles with time-domain intensity peaks and to reproduce the associated temporal intensity probability distributions.
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The dynamics of ideal four-wave mixing in optical fiber is reconstructed by taking advantage of the combination of experimental measurements together with supervised machine learning strategies. The training data consist of power-dependent spectral phase and amplitude recorded at the output of a short fiber segment. The neural network is shown to be able to accurately predict the nonlinear dynamics over tens of kilometers, and to retrieve the main features of the phase space topology including multiple Fermi-Pasta-Ulam recurrence cycles and the system separatrix boundary.
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We show that subwavelength Si-rich nitride waveguides efficiently sustain high-speed transmissions at 2 µm. We report the transmission of a 10 Gbit/s signal over 3.5 cm with negligible power penalty. Parametric conversion in the pulsed pump regime is also demonstrated using the same waveguide structure with an efficiency as high as -18 dB.
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Simple photonic fiber-based workbenches have been able to emulate well-known nonlinear wave dynamics occurring in deep or shallow water conditions. Here, by investigating the nonlinear reshaping of a flat-top pulse upon propagation in an anomalous dispersive optical fiber, we observe that typical signatures of focusing dam break flows and Peregrine-like breather events can locally coexist in spontaneous pattern formations. The experimental measurements are in good agreement with our numerical predictions.
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We propose and experimentally demonstrate a new approach to dramatically reduce the spectral broadening induced by self-phase modulation occurring in a Kerr medium. By using a temporal sinusoidal phase modulation, we efficiently cancel to a large extent the chirp induced by the nonlinear effect. Experimental validation carried out in a passive or amplifying fiber confirms the interest of the technique for the mitigation of the spectral expansion of long pulses.
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Metal grating couplers embedded into a titanium dioxide layer are proposed. A coupling efficiency better than 20% is experimentally demonstrated with a 3 dB bandwidth of 86 nm which is in agreement with simulation results. This allowed us to perform error-free transmissions of 10 Gbit/s wavelength multiplexed signals in the C-band.
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We theoretically and experimentally investigate the design of a high-repetition rate source delivering well-separated optical pulses due to the nonlinear compression of a dual-frequency beat signal within a cavity-less normally dispersive fiber-based setup. This system is well described by a set of two coupled nonlinear Schrödinger equations for which the traditional normally dispersive defocusing regime is turned in a focusing temporal lens through a degenerated cross-phase modulation process (XPM). More precisely, the temporal compression of the initial beating is performed by the combined effects of normal dispersion and XPM-induced nonlinear phase shift provided by an intense beat signal on its weak out-of-phase replica co-propagating with orthogonal polarizations. This adiabatic reshaping process allows us to experimentally demonstrate the generation of a 40 GHz well-separated 3.3 ps pulse train at 1550 nm in a 5 km long normally dispersive fiber.
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We show that the amplitude and phase shaping of only four sidebands of the optical spectrum is sufficient to synthesize parabolic, triangular, or flat-top pulse trains at high repetition rates. Selection of the symmetric carrier-suppressed waveform is easily achieved by changing the phase difference between the inner and outer spectral lines. Experiments carried out at a repetition rate of 40 GHz confirm the high quality of the intensity profiles that are obtained.
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By using a highly nonlinear, dispersion oscillating optical fiber operating in the telecom C band, we experimentally demonstrate the splitting experienced by quasi-phase matched gain sidebands in the strongly dispersion managed regime of a dispersion oscillating fiber as the power of a continuous-wave pump laser is increased over a certain threshold value. Very good agreement is found between the theoretical predictions and our experimental measurements.
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We numerically show the possibility of pulse shaping in a passively mode-locked fiber laser by inclusion of a spectral filter into the laser cavity. Depending on the amplitude transfer function of the filter, we are able to achieve various regimes of advanced temporal waveform generation, including ones featuring bright and dark parabolic-, flat-top-, triangular- and saw-tooth-profiled pulses. The results demonstrate the strong potential of an in-cavity spectral pulse shaper for controlling the dynamics of mode-locked fiber lasers.
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We experimentally study the dynamics of the generation of multiple sidebands by means of a quasi-phase-matched four-wave mixing (FWM) process occurring in a dispersion-oscillating, highly nonlinear optical fiber. The fiber under test is pumped by a ns microchip laser operating in the normal average group-velocity dispersion regime and in the telecom C band. We reveal that the growth of higher-order sidebands is strongly influenced by the competition with cascade FWM between the pump and the first-order quasi-phase matched sidebands. The properties of these competing FWM processes are substantially affected when a partially coherent pump source is used, leading to a drastic reduction of the average power needed for sideband generation.
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We experimentally investigate the nonlinear reshaping of a continuous wave that leads to chirp-free and flat-top intense pulses or flaticons exhibiting strong temporal oscillations at their edges and a stable self-similar expansion upon propagation of their central region. This study was performed in the normal dispersion regime of a nonzero dispersion-shifted fiber and involved a sinusoidal phase modulation of the continuous wave. Our fiber optics experiment is analogous to considering the collision between oppositely directed currents near the beach, and it may open the way to new investigations in the field of hydrodynamics.
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We demonstrate the existence of the spectral phase shift a pulse experiences when it is subjected to spectral focusing. This π/2 phase shift is the spectral analog of the Gouy phase shift a 2D beam experiences when it crosses its focal plane. This spectral Gouy phase shift is measured using spectral interference between a reference pulse and a negatively chirped parabolic pulse experiencing spectral focusing in a nonlinear photonic crystal fiber. To avoid inherent phase instability in the measurement, both reference and parabolic pulses are generated with a 4-f pulse shaper and copropagate in the same fiber. We measure a spectral phase shift of π/2, reaffirming its generality as a consequence of wave confinement in the spatial, temporal and spectral domains.
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We analyze the dynamics of modulation instability in optical fiber (or any other nonlinear Schrödinger equation system) using the machine-learning technique of data-driven dominant balance. We aim to automate the identification of which particular physical processes drive propagation in different regimes, a task usually performed using intuition and comparison with asymptotic limits. We first apply the method to interpret known analytic results describing Akhmediev breather, Kuznetsov-Ma, and Peregrine soliton (rogue wave) structures, and show how we can automatically distinguish regions of dominant nonlinear propagation from regions where nonlinearity and dispersion combine to drive the observed spatio-temporal localization. Using numerical simulations, we then apply the technique to the more complex case of noise-driven spontaneous modulation instability, and show that we can readily isolate different regimes of dominant physical interactions, even within the dynamics of chaotic propagation.
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The noise-like pulse regime of optical fiber lasers is highly complex, and associated with multiscale emission of random sub-picosecond pulses underneath a much longer envelope. With the addition of highly nonlinear fiber in the cavity, noise-like pulse lasers can also exhibit supercontinuum broadening and the generation of output spectra spanning 100's of nm. Achieving these broadest bandwidths, however, requires careful optimization of the nonlinear polarization rotation based saturable absorber, which involves a very large potential parameter space. Here we study the spectral characteristics of a broadband noise-like pulse laser by scanning the laser operation over a random sample of 50,000 polarization settings, and we quantify that these broadest bandwidths are generated in only [Formula: see text] 0.5% of cases. We also show that a genetic algorithm can replace trial and error optimization to align the cavity for these broadband operating states.
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We propose a new concept of a fiber laser architecture supporting self-similar pulse evolution in the amplifier and nonlinear spectral pulse compression in the passive fiber. The latter process allows for transform-limited picosecond pulse generation, and improves the laser's power efficiency by preventing strong spectral filtering from being highly dissipative. Aside from laser technology, the proposed scheme opens new possibilities for studying nonlinear dynamical processes. As an example, we demonstrate a clear period-doubling route to chaos in such a nonlinear laser system.