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Abstract 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.

Abstract 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 $$\sim$$ ∼ 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.

Abstract 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.

Two-octave supercontinuum generation in the femtosecond regime from the visible to mid-infrared and self-cleaning dynamics are reported in a non-silica graded-index multimode fiber with nanostructured design and enhanced nonlinearity.

In this work the authors perform a combined numerical and experimental study of noise-like pulse multiscale instabilities in dissipative laser systems. They reveal an underlying multiscale dynamics and report the observation of rogue wave events.

Abstract 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.

Abstract 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.

Real-time characterisation of nonlinear processes in the time domain is challenging. Here, Närhi et al. show that machine learning techniques can help overcome this limitation and use them to infer time-domain properties of optical fibre modulation instability from spectral intensity measurements.

Low amplitude noise on an otherwise constant-intensity wave can grow exponentially and induce nonlinear dynamical behaviour. Here, the authors present time-domain measurements of a phenomenon arising from such modulation instability: the emergence of highly localised breathers in an optical fibre.