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.

Analysis of interaction dynamics and rogue wave localization in modulation instability using data-driven dominant balance.

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.

Genetic algorithm optimization of broadband operation in a noise-like pulse fiber laser.

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.

Phase space topology of four-wave mixing reconstructed by a neural network.

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.

Data-driven model discovery of ideal four-wave mixing in nonlinear fibre optics.

We show using numerical simulations that data driven discovery using sparse regression can be used to extract the governing differential equation model of ideal four-wave mixing in a nonlinear Schrödinger equation optical fibre system. Specifically, we consider the evolution of a strong single frequency pump interacting with two frequency detuned sidebands where the dynamics are governed by a reduced Hamiltonian system describing pump-sideband coupling. Based only on generated dynamical data from this system, sparse regression successfully recovers the underlying physical model, fully capturing the dynamical landscape on both sides of the system separatrix. We also discuss how analysing an ensemble over different initial conditions allows us to reliably identify the governing model in the presence of noise. These results extend the use of data driven discovery to ideal four-wave mixing in nonlinear Schrödinger equation systems.

Time diffraction-free transverse orbital angular momentum beams.

The discovery of optical transverse orbital angular momentum (OAM) has broadened our understanding of light and is expected to promote optics and other physics. However, some fundamental questions concerning the nature of such OAM remain, particularly whether they can survive from observed mode degradation and hold OAM values higher than 1. Here, we show that the strong degradation actually origins from inappropriate time-delayed kx-ω modulation, instead, for transverse OAM having inherent space-time coupling, immediate modulation is necessary. Thus, using immediate x-ω modulation, we demonstrate theoretically and experimentally degradation-free spatiotemporal Bessel (STB) vortices with transverse OAM even beyond 102. Remarkably, we observe a time-symmetrical evolution, verifying pure time diffraction on transverse OAM beams. More importantly, we quantify such nontrivial evolution as an intrinsic dispersion factor, opening the door towards time diffraction-free STB vortices via dispersion engineering. Our results may find analogues in other physical systems, such as surface plasmon-polaritons, superfluids, and Bose-Einstein condensates.

Noise in supercontinuum generated using PM and non-PM tellurite glass all-normal dispersion fibers.

Intensity fluctuations in supercontinuum generation are studied in polarization-maintaining (PM) and non-PM all-normal dispersion tellurite photonic crystal fibers. Dispersive Fourier transformation is used to resolve the shot-to-shot spectra generated using 225-fs pump pulses at 1.55 µm, with experimental results well reproduced by vector and scalar numerical simulations. By comparing the relative intensity noise for the PM and non-PM cases, supported by simulations, we demonstrate the advantage of the polarization-maintaining property of the PM fibers in preserving low-noise dynamics. We associate the low-noise in the PM case with the suppression of polarization modulation instability.

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.

Ultra-flat, low-noise, and linearly polarized fiber supercontinuum source covering 670-1390 nm: publisher's note.

This publisher's note contains a correction to Opt. Lett.46, 1820 (2021)10.1364/OL.420676.

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.

Intracavity incoherent supercontinuum dynamics and rogue waves in a broadband dissipative soliton laser.

Understanding dynamical complexity is one of the most important challenges in science. Significant progress has recently been made in optics through the study of dissipative soliton laser systems, where dynamics are governed by a complex balance between nonlinearity, dispersion, and energy exchange. A particularly complex regime of such systems is associated with noise-like pulse multiscale instabilities, where sub-picosecond pulses with random characteristics evolve chaotically underneath a much longer envelope. However, although observed for decades in experiments, the physics of this regime remains poorly understood, especially for highly-nonlinear cavities generating broadband spectra. Here, we address this question directly with a combined numerical and experimental study that reveals the physical origin of instability as nonlinear soliton dynamics and supercontinuum turbulence. Real-time characterisation reveals intracavity extreme events satisfying statistical rogue wave criteria, and both real-time and time-averaged measurements are in quantitative agreement with modelling.

Ultra-flat, low-noise, and linearly polarized fiber supercontinuum source covering 670-1390 nm.

We report an octave-spanning coherent supercontinuum (SC) fiber laser with excellent noise and polarization properties. This was achieved by pumping a highly birefringent all-normal dispersion photonic crystal fiber with a compact high-power ytterbium femtosecond laser at 1049 nm. This system generates an ultra-flat SC spectrum from 670 to 1390 nm with a power spectral density higher than 0.4 mW/nm and a polarization extinction ratio of 17 dB across the entire bandwidth. An average pulse-to-pulse relative intensity noise down to 0.54% from 700 to 1100 nm was measured and found to be in good agreement with numerical simulations. This highly stable broadband source could find strong potential applications in biomedical imaging and spectroscopy where an improved signal-to-noise ratio is essential.

Experimental demonstration of spectral domain computational ghost imaging.

We demonstrate computational spectral-domain ghost imaging by encoding complementary Fourier patterns directly onto the spectrum of a superluminescent laser diode using a programmable spectral filter. Spectral encoding before the object enables uniform spectral illumination across the beam profile, removing the need for light collection optics and yielding increased signal-to-noise ratio. In addition, the use of complementary Fourier patterns allows reduction of deleterious of parasitic light effects. As a proof-of-concept, we measure the wavelength-dependent transmission of a Michelson interferometer and a wavelength-division multiplexer. Our results open new perspectives for remote broadband spectral measurements.

Spectral correlation of four-wave mixing generated in a photonic crystal fiber pumped by a chirped pulse.

We report the spectral distribution of the parametric process generated in a photonic crystal fiber pumped by a chirped pulse. The spectral correlation of four-wave mixing has been measured using the dispersive Fourier transform method. From statistical analysis of multiple shot-to-shot spectral measurements, the spectral correlation between the signal and idler photons reveals physical insights into the particular portion of the pump spectrum responsible for generating the four-wave mixing. Therefore, the shape of the correlation map indicates directly the temporal and spectral links between the signal and the pump, which are highly important to design a four-wave mixing based amplifier.

Cross-phase modulation instability in PM ANDi fiber-based supercontinuum generation.

We demonstrate broadband supercontinuum generation in an all-normal dispersion polarization-maintaining photonic crystal fiber and report the observation of a cross-phase modulation instability sideband generated outside of the supercontinuum bandwidth. We demonstrate that this sideband is polarized on the slow axis and can be suppressed by pumping on the fiber's fast axis. We theoretically confirm and model this nonlinear process using phase-matching conditions and numerical simulations, obtaining good agreement with the measured data.

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.

Toward a self-driving ultrafast fiber laser.

Femtosecond pulses from an ultrafast mode-locked fiber laser can be optimized in real time by combining single-shot spectral measurements with a smart genetic algorithm to actively control and drive the intracavity dynamics.