Supercontinuum generation in a graded-index multimode tellurite fiber.

We report the generation of a broadband supercontinuum (SC) from 790 to 2900 nm in a tellurite graded-index (GRIN) multimode fiber with a nanostructured core. We study the SC dynamics in different dispersion regimes and observe near-single-mode spatial intensity distribution at high input energy values. Numerical simulations of the (3 + 1)D generalized nonlinear Schrödinger equation are in good agreement with our experiments. Our results open a new avenue for the generation of high-power mid-infrared SC sources in soft-glass fibers.

Tailored supercontinuum generation using genetic algorithm optimized Fourier domain pulse shaping.

We report the generation of a spectrally tailored supercontinuum using Fourier-domain pulse shaping of femtosecond pulses injected into a highly nonlinear fiber controlled by a genetic algorithm. User-selectable spectral enhancement is demonstrated over the 1550-2000-nm wavelength range, with the ability to both select a channel with target central wavelength and bandwidth in the range of 1-5 nm. The spectral enhancement factor relative to unshaped input pulses is typically ∼5-20 in the range 1550-1800 nm and increases for longer wavelengths, exceeding a factor of 160 around 2000 nm. We also demonstrate results where the genetic algorithm is applied to the enhancement of up to four spectral channels simultaneously.

Machine learning analysis of instabilities in noise-like pulse lasers.

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.

Two octave supercontinuum generation in a non-silica graded-index multimode fiber.

The generation of a two-octave supercontinuum from the visible to mid-infrared (700-2800 nm) in a non-silica graded-index multimode fiber is reported. The fiber design is based on a nanostructured core comprised of two types of drawn lead-bismuth-gallate glass rods with different refractive indices. This yields an effective parabolic index profile and ten times increased nonlinearity when compared to silica fibers. Using femtosecond pulse pumping at wavelengths in both normal and anomalous dispersion regimes, a detailed study is carried out into the supercontinuum generating mechanisms and instabilities seeded by periodic self-imaging. Significantly, suitable injection conditions in the high power regime are found to result in the output beam profile showing clear signatures of beam self-cleaning from nonlinear mode mixing. Experimental observations are interpreted using spatio-temporal 3+1D numerical simulations of the generalized nonlinear Schrödinger equation, and simulated spectra are in excellent agreement with experiment over the full two-octave spectral bandwidth. Experimental comparison with the generation of supercontinuum in a silica graded-index multimode fiber shows that the enhanced nonlinear refractive index of the lead-bismuth-gallate fiber yields a spectrum with a significantly larger bandwidth. These results demonstrate a new pathway towards the generation of bright, ultrabroadband light sources in the mid-infrared.

Feed-forward neural network as nonlinear dynamics integrator for supercontinuum generation: erratum.

We present an erratum to our Letter [Opt. Lett.47, 802 (2022)10.1364/OL.448571]. This erratum corrects an error in the sign of one of the higher-order dispersion coefficient used in the simulations of Figs. 2 and 4, as well as in Figs. S1 and S3. The simulations in the original Letter were performed using the correct value, and therefore this correction does not affect any of the results and conclusions of the original Letter.

Feed-forward neural network as nonlinear dynamics integrator for supercontinuum generation.

The nonlinear propagation of ultrashort pulses in optical fibers depends sensitively on the input pulse and fiber parameters. As a result, the optimization of propagation for specific applications generally requires time-consuming simulations based on the sequential integration of the generalized nonlinear Schrödinger equation (GNLSE). Here, we train a feed-forward neural network to learn the differential propagation dynamics of the GNLSE, allowing emulation of direct numerical integration of fiber propagation, and particularly the highly complex case of supercontinuum generation. Comparison with a recurrent neural network shows that the feed-forward approach yields faster training and computation, and reduced memory requirements. The approach is generic and can be extended to other physical systems.

Low-noise octave-spanning mid-infrared supercontinuum generation in a multimode chalcogenide fiber.

We demonstrate the generation of a low-noise, octave-spanning mid-infrared supercontinuum from 1700 to 4800 nm by injecting femtosecond pulses into the normal dispersion regime of a multimode step-index chalcogenide fiber with 100 µm core diameter. We conduct a systematic study of the intensity noise across the supercontinuum spectrum and show that the initial fluctuations of the pump laser are at most amplified by a factor of three. We also perform a comparison with the noise characteristics of an octave-spanning supercontinuum generated in the anomalous dispersion regime of a multimode fluoride fiber with similar core size and show that the normal dispersion supercontinuum in the multimode chalcogenide fiber has superior noise characteristics. Our results open up novel perspectives for many practical applications such as long-distance remote sensing where high power and low noise are paramount.

Machine learning analysis of rogue solitons in supercontinuum generation.

Supercontinuum generation is a highly nonlinear process that exhibits unstable and chaotic characteristics when developing from long pump pulses injected into the anomalous dispersion regime of an optical fiber. A particular feature associated with this regime is the long-tailed "rogue wave"-like statistics of the spectral intensity on the long-wavelength edge of the supercontinuum, linked to the generation of a small number of "rogue solitons" with extreme red-shifts. Whilst the statistical properties of rogue solitons can be conveniently measured in the spectral domain using the real-time dispersive Fourier transform technique, we cannot use this technique to determine any corresponding temporal properties since it only records the spectral intensity and one loses information about the spectral phase. And direct temporal characterization using methods such as the time-lens has resolution of typically 100's of fs, precluding the measurement of solitons which possess typically much shorter durations. Here, we solve this problem by using machine learning. Specifically, we show how supervised learning can train a neural network to predict the peak power, duration, and temporal walk-off with respect to the pump pulse position of solitons at the edge of a supercontinuum spectrum from only the supercontinuum spectral intensity without phase information. Remarkably, the network accurately predicts soliton characteristics for a wide range of scenarios, from the onset of spectral broadening dominated by pure modulation instability to near octave-spanning supercontinuum with distinct rogue solitons.

Machine learning analysis of extreme events in optical fibre modulation instability.

A central research area in nonlinear science is the study of instabilities that drive extreme events. Unfortunately, techniques for measuring such phenomena often provide only partial characterisation. For example, real-time studies of instabilities in nonlinear optics frequently use only spectral data, limiting knowledge of associated temporal properties. Here, we show how machine learning can overcome this restriction to study time-domain properties of optical fibre modulation instability based only on spectral intensity measurements. Specifically, a supervised neural network is trained to correlate the spectral and temporal properties of modulation instability using simulations, and then applied to analyse high dynamic range experimental spectra to yield the probability distribution for the highest temporal peaks in the instability field. We also use unsupervised learning to classify noisy modulation instability spectra into subsets associated with distinct temporal dynamic structures. These results open novel perspectives in all systems exhibiting instability where direct time-domain observations are difficult.