Accepted as a speech
in session Academy of Finland session: Novel Applications of AI in Physical Sciences and Engineering research
in Hall 6 on March 6th, 16:15

# MACHINE LEARNING ANALYSIS OF EXTREME EVENTS IN OPTICAL FIBRE MODULATION INSTABILITY

### L. Salmela1, M. Närhi1, J. Toivonen1, C. Billet2, J. M. Dudley2, G. Genty1

lauri.salmela@tuni.fi
1 Photonics Laboratory, Physics Unit, Tampere University, Tampere, Finland
2 Institut FEMTO-ST, Université Bourgogne Franche-Comté CNRS UMR 6174, Besançon, France

Modulation instability (MI) is a universal process in nonlinear physics that describes the exponential growth of weak perturbations or noise on top of a continuous wave input signal. When seeded by noise, MI leads to the emergence of high intensity localized breather structures that show complex dynamics with random statistics. It has been also suggested that MI may be linked with the formation of rogue waves on the surface of the ocean [1]. Despite the recent developments in real-time measurement techniques both in the spectral and temporal domain [2], the study of instabilities in nonlinear fibre optics still remains limited in various ways. For example, in addition to limitations on measurement power and bandwidth, the limited dynamic range of the spectral measurements restricts the type of dynamics that can be observed [3]. Here, we overcome these restrictions by combining techniques of machine learning with a novel high-dynamic range ($>$50 dB) real-time spectral intensity measurement scheme to yield qualitative information about the temporal characteristics of a random MI field.

Figure 1 shows a schematic of the experimental setup along with a selection of recorded single-shot spectra when pulses (3 ps duration, 175 W peak power) from a Ti:Sapphire laser at 825 nm are injected into a 68 cm long photonic crystal fibre (PCF) in the anomalous dispersion regime to generate a random MI field. By using a rapidly-rotating mirror, sequential pulses are focused on different vertical positions of the entrance slit of a Czerny-Turner (C-T) spectrograph. Spectral windowing and differential attenuation are used to take advantage of the full dynamic range of an EMCCD camera, yielding a single-shot dynamic range exceeding 50 dB and with 1 nm spectral resolution. The experimental spectra are then analyzed using a neural network (NN) trained for relating the temporal properties of the noisy MI field with the corresponding spectral intensity characteristics. The NN trained from generalized nonlinear Schrödinger equation simulations parameterized to our experiments is capable of accurately predicting the temporal shot-to-shot statistics of the maximum temporal intensity solely based on spectral intensity measurements. Additionally, an unsupervised clustering analysis was used for classifying the spectra into subsets with distinct temporal structures (not shown here). Our results are highly significant since they are the first demonstration of spectral measurements combined with machine learning to predict the occurrence extreme events in a nonlinear optical system.

References
[1] D.R. Solli, C. Ropers, P. Koonath and B. Jalali, "Optical rogue waves", Nature 450, 1054-1057 (2007).
[2] P. Ryczkowski, et al., "Real-time full-field characterization of transient dissipative soliton dynamics in a mode-locked laser", Nat. Photonics 12, 221–227 (2018).
[3] N. Akhmediev, et al., "Rogue wave early warning through spectral measurements?", Phys. Lett. A 375.3, 541- 544 (2011).

Figure 1: (a) Schematic of the experimental setup. Ti:Sa: Titanium-Sapphire mode-locked laser, AOM: acousto-optic modulator, PCF: photonic crystal fibre, ND: neutral density. (b) Example of recorded single-shot spectra with $>$50 dB dynamic range (blue) and the mean spectrum (black).