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Supercontinuum generation in optical fiber involves complex nonlinear dynamics, making optimization challenging, and typically relying on trial-and-error or extensive numerical simulations. Machine learning and metaheuristic algorithms offer more efficient optimization approaches. We report here an experimental study of supercontinuum spectral shaping by tuning the phase of the input pulses, different optimization approaches including a genetic algorithm, particle swarm optimizer, and simulated annealing. We find that the genetic algorithm and particle swarm optimizer are more robust and perform better, with the particle swarm optimizer converging faster. Our study provides valuable insights for the systematic optimization of supercontinuum and other optical sources., Competing Interests: Declarations. Competing interests: The authors declare no competing interests., (© 2024. The Author(s).)

High-order solitons exhibit fascinating dynamics during their propagation in anomalous dispersion media. High-order soliton dynamics have been intensively exploited for extreme pulse compression and coherent ultra-broadband spectrum generation. Despite recent advances, most previous studies have been restricted to soliton propagation external to a laser cavity, leaving the intracavity generation and evolution of high-order solitons less explored. Here, we numerically demonstrate that by carefully optimizing the cavity parameters, intracavity coherent supercontinuum could be generated via high-order soliton dynamics in a dissipative soliton fiber laser. In particular, a positively chirped dissipative soliton is formed in normal dispersion gain fiber, which acts as a robust nonlinear attractor. After dechirping, a high (∼8.5) order soliton was formed in a 1.1 m highly nonlinear fiber, which subsequently experienced significant intracavity temporal self-compression and spectral broadening. The shortest pulse duration was ∼14 fs, corresponding to ∼2.7 optical cycles at 1551 nm, with the spectrum spanning over 600 nm at the -30 dB level. The generated supercontinuum maintains high coherence under quantum noise injection. In addition, the supercontinuum bandwidths were further optimized via a genetic algorithm, demonstrating the great promise of machine learning tools in optimizing complicated nonlinear systems. This work opens new possibilities for constructing compact and highly coherent supercontinuum light sources. Additionally, it provides valuable insights into the self-consistent evolution dynamics of high-order solitons within a fiber laser cavity.

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.

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.

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., (© 2023. The Author(s).)

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., (© 2023. The Author(s).)

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.

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., (© 2022. The Author(s).)

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 k x -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 10 2 . 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., (© 2022. The Author(s).)

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 μ m, 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.

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.

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., (© 2022. The Author(s).)

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

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.

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., (© 2021. The Author(s).)

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.

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.

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.

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.

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.

Numerical simulations of a dissipative soliton-similariton laser are shown to reproduce a range of instabilities seen in recent experiments. The model uses a scalar nonlinear Schrödinger equation map, and regions of stability and instability are readily identified as a function of gain and saturable absorber parameters. Studying evolution over multiple round trips reveals spectral instabilities linked with soliton molecule internal motion, soliton explosions, chaos, and intermittence. For the case of soliton molecules, the relative phase variation in the spectrum is shown to be due to differences in nonlinear phase evolution between the molecule components over multiple round trips.

The concepts of Fourier optics were established in France in the 1940s by Pierre-Michel Duffieux, and laid the foundations of an extensive series of activities in the French research community that have touched on nearly every aspect of contemporary optics and photonics. In this paper, we review a selection of results where applications of the Fourier transform and transfer functions in optics have been applied to yield significant advances in unexpected areas of optics, including the spatial shaping of complex laser beams in amplitude and in phase, real-time ultrafast measurements, novel ghost imaging techniques, and the development of parallel processing methodologies for photonic artificial intelligence.

The study of dissipative solitons in mode-locked lasers reveals a rich landscape of interaction dynamics resulting from the interplay of nonlinearity, dispersion and dissipation. Here, we characterize a range of instabilities in a dissipative soliton fibre laser in a regime where both conventional soliton and similariton propagation play significant roles in the intracavity pulse shaping. Specifically, we use the Dispersive Fourier Transform technique to perform real-time spectral measurements of buildup dynamics from noise to the generation of stable single pulses, phase evolution dynamics of bound state "similariton molecules", and several examples of intermittent instability and explosion dynamics. These results show that the instabilities previously seen in other classes of passively mode-locked fibre lasers are also observed in the presence of strong nonlinear attraction of similariton evolution in an optical fibre amplifier.

We demonstrate experimentally ghost optical coherence tomography using a broadband incoherent supercontinuum light source with shot-to-shot random spectral fluctuations. The technique is based on ghost imaging in the spectral domain where the object is the spectral interference pattern generated from an optical coherence tomography interferometer in which a physical sample is placed. The axial profile of the sample is obtained from the Fourier transform of the correlation between the spectrally resolved intensity fluctuations of the supercontinuum and the integrated signal measured at the output of the interferometer. The results are in excellent agreement with measurements obtained from a conventional optical coherence tomography system.

We present a simultaneous study of the phase properties of rational breather waves generated in a water wave tank and in an optical fiber platform, namely, the Peregrine soliton and related second-order solution. Our analysis of experimental wave measurements makes use of standard demodulation and filtering techniques in hydrodynamics and more complex phase retrieval techniques in optics to quantitatively confirm analytical and numerical predictions. We clearly highlight a characteristic phase shift that is a multiple of π between the central pulsed part and the continuous background of rational breathers at their maximum compression. Moreover, we reveal a large longitudinal phase shift across the point of maximum compression.

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.

Ghost imaging is a technique that generates high-resolution images by correlating the intensity of two light beams, neither of which independently contains useful information about the shape of the object. Ghost imaging has been demonstrated in both the spatial and temporal domains, using incoherent classical light sources or entangled photon pairs. Here we exploit the recent progress in ultrafast real-time measurement techniques to demonstrate ultrafast, scan-free, ghost imaging in the frequency domain using a continuous spectrum from an incoherent supercontinuum light source with random spectral fluctuations. We demonstrate the application of this technique to broadband spectroscopic measurements of methane absorption performed with sub-nanometer resolution. Our results offer novel perspectives for remote sensing in low light conditions, or in spectral regions where sensitive detectors are lacking.

Ultrafast lasers have revolutionized material processing, opening a wealth of new applications in many areas of science. A recent technology that allows the cleaving of transparent materials via non-ablative processes is based on focusing and translating a high-intensity laser beam within a material to induce a well-defined internal stress plane. This then enables material separation without debris generation. Here, we use a non-diffracting beam engineered to have a transverse elliptical spatial profile to generate high-aspect-ratio elliptical channels in glass of a dimension 350  nm×710  nm and subsequent cleaved surface uniformity at the sub-micron level.

During ultrafast laser pulse propagation in dielectrics, the nonlinear generation of new spatial frequencies can be deleterious to reach high intensities and to generate uniform plasma channels. In this context, diffraction-free Bessel beams have attracted major recent interest because of their enhanced stability when compared to conventional Gaussian beams. However, Bessel beams can still suffer from significant modulation instability arising from noise-induced nonlinear four-wave mixing (FWM). In this Letter we report control of the nonlinear instability growth by shaping the longitudinal intensity profile of the incident field. Our results show that tailored longitudinal intensity shaping of a nondiffracting Bessel beam can strongly reduce FWM-induced oscillations and stabilize nonlinear propagation at ablation-level intensities.

We report experimental confirmation of the universal emergence of the Peregrine soliton predicted to occur during pulse propagation in the semiclassical limit of the focusing nonlinear Schrödinger equation. Using an optical fiber based system, measurements of temporal focusing of high power pulses reveal both intensity and phase signatures of the Peregrine soliton during the initial nonlinear evolution stage. Experimental and numerical results are in very good agreement, and show that the universal mechanism that yields the Peregrine soliton structure is highly robust and can be observed over a broad range of parameters.

Modulation instability is a fundamental process of nonlinear science, leading to the unstable breakup of a constant amplitude solution of a physical system. There has been particular interest in studying modulation instability in the cubic nonlinear Schrödinger equation, a generic model for a host of nonlinear systems including superfluids, fibre optics, plasmas and Bose-Einstein condensates. Modulation instability is also a significant area of study in the context of understanding the emergence of high amplitude events that satisfy rogue wave statistical criteria. Here, exploiting advances in ultrafast optical metrology, we perform real-time measurements in an optical fibre system of the unstable breakup of a continuous wave field, simultaneously characterizing emergent modulation instability breather pulses and their associated statistics. Our results allow quantitative comparison between experiment, modelling and theory, and are expected to open new perspectives on studies of instability dynamics in physics.

Femtosecond pulses provide an extreme degree of confinement of light matter-interactions in high-bandgap materials because of the nonlinear nature of ionization. It was recognized very early on that a highly focused single pulse of only nanojoule energy could generate spherical voids in fused silica and sapphire crystal as the nanometric scale plasma generated has energy sufficient to compress the material around it and to generate new material phases. But the volumes of the nanometric void and of the compressed material are extremely small. Here we use single femtosecond pulses shaped into high-angle Bessel beams at microjoule energy, allowing for the creation of very high 100:1 aspect ratio voids in sapphire crystal, which is one of the hardest materials, twice as dense as glass. The void volume is 2 orders of magnitude higher than those created with Gaussian beams. Femtosecond and picosecond illumination regimes yield qualitatively different damage morphologies. These results open novel perspectives for laser processing and new materials synthesis by laser-induced compression.

We report the first observation of Riemann (simple) waves, which play a crucial role for understanding the dynamics of any shock-bearing system. This was achieved by properly tailoring the phase of an ultrashort light pulse injected into a highly nonlinear fiber. Optical Riemann waves are found to evolve in excellent quantitative agreement with the remarkably simple inviscid Burgers equation, whose applicability in physical systems is often challenged by viscous or dissipative effects. Our method allows us to further demonstrate a viable novel route to efficiently control the shock formation by the proper shaping of a laser pulse phase. Our results pave the way towards the experimental study, in a convenient benchtop setup, of complex physical phenomena otherwise difficult to access.

Universal nonlinear scattering processes such as Brillouin, Raman, and Kerr effects are fundamental light-matter interactions of particular theoretical and experimental importance. They originate from the interaction of a laser field with an optical medium at the lattice, molecular, and electronic scale, respectively. These nonlinear effects are generally observed and analyzed separately, because they do not often occur concomitantly. In this article, we report the simultaneous excitation of these three fundamental interactions in mm-size ultra-high Q whispering gallery mode resonators under continuous wave pumping. Universal nonlinear scattering is demonstrated in barium fluoride and strontium fluoride, separately. We further propose a unified theory based on a spatiotemporal formalism for the understanding of this phenomenology.

Arbitrary shaping of the on-axis intensity of Bessel beams requires spatial modulation of both amplitude and phase. We develop a non-iterative direct space beam shaping method to generate Bessel beams with high energy throughput from direct space with a single phase-only spatial light modulator. For this purpose, we generalize the approach of Bolduc et al. to non-uniform input beams. We point out the physical limitations imposed on the on-axis intensity profile for unidirectional beams. Analytical, numerical and experimental results are provided.

There are many examples in physics of systems showing rogue wave behaviour, the generation of high amplitude events at low probability. Although initially studied in oceanography, rogue waves have now been seen in many other domains, with particular recent interest in optics. Although most studies in optics have focussed on how nonlinearity can drive rogue wave emergence, purely linear effects have also been shown to induce extreme wave amplitudes. In this paper, we report a detailed experimental study of linear rogue waves in an optical system, using a spatial light modulator to impose random phase structure on a coherent optical field. After free space propagation, different random intensity patterns are generated, including partially-developed speckle, a broadband caustic network, and an intermediate pattern with characteristics of both speckle and caustic structures. Intensity peaks satisfying statistical criteria for rogue waves are seen especially in the case of the caustic network, and are associated with broader spatial spectra. In addition, the electric field statistics of the intermediate pattern shows properties of an "optical sea" with near-Gaussian statistics in elevation amplitude, and trough-to-crest statistics that are near-Rayleigh distributed but with an extended tail where a number of rogue wave events are observed.

The nonlinear Schrödinger equation (NLSE) is a seminal equation of nonlinear physics describing wave packet evolution in weakly-nonlinear dispersive media. The NLSE is especially important in understanding how high amplitude "rogue waves" emerge from noise through the process of modulation instability (MI) whereby a perturbation on an initial plane wave can evolve into strongly-localised "breather" or "soliton on finite background (SFB)" structures. Although there has been much study of such structures excited under controlled conditions, there remains the open question of how closely the analytic solutions of the NLSE actually model localised structures emerging in noise-seeded MI. We address this question here using numerical simulations to compare the properties of a large ensemble of emergent peaks in noise-seeded MI with the known analytic solutions of the NLSE. Our results show that both elementary breather and higher-order SFB structures are observed in chaotic MI, with the characteristics of the noise-induced peaks clustering closely around analytic NLSE predictions. A significant conclusion of our work is to suggest that the widely-held view that the Peregrine soliton forms a rogue wave prototype must be revisited. Rather, we confirm earlier suggestions that NLSE rogue waves are most appropriately identified as collisions between elementary SFB solutions.