Source-linked AI summary
Predicting ultrafast nonlinear dynamics in fibre optics with a recurrent neural network
Lauri Salmela, Nikolaos Tsipinakis, Alessandro Foi, Cyril Billet, John M. Dudley, Goëry Genty
TL;DR
Computationally demanding NLSE simulations limit real-time design and optimization of nonlinear optical-fibre propagation. The paper uses an LSTM recurrent neural network trained on intensity-evolution data to forecast temporal and spectral dynamics, accurately reproducing soliton compression and supercontinuum generation with experimental agreement for soliton compression.
Problem
Sensitive dependence of nonlinear-fibre propagation on input pulses and fibre characteristics makes NLSE-based simulation computationally demanding for real-time design and optimization.
Method
An LSTM recurrent neural network forecasts temporal and spectral intensity evolution from transform-limited pulse intensity profiles using recent propagation profiles and recurrent states.
Results
The network accurately predicts higher-order soliton compression and supercontinuum generation, with soliton-compression predictions agreeing with experiments in temporal and spectral domains.
Takeaways & Limitations
The results support model-free prediction of nonlinear optical-fibre dynamics for pulse-compression and broadband-light-source applications.
Takeaways & Limitations
Using fewer consecutive profiles raises the relative prediction error from 0.097 to 0.174, while using more profiles increases training time.
Abstract
from arXiv · showhide
The propagation of ultrashort pulses in optical fibre displays complex nonlinear dynamics that find important applications in fields such as high power pulse compression and broadband supercontinuum generation. Such nonlinear evolution however, depends sensitively on both the input pulse and fibre characteristics, and optimizing propagation for application purposes requires extensive numerical simulations based on generalizations of a nonlinear Schrödinger-type equation. This is computationally-demanding and creates a severe bottleneck in using numerical techniques to design and optimize experiments in real-time. Here, we present a solution to this problem using a machine-learning based paradigm to predict complex nonlinear propagation in optical fibres with a recurrent neural network, bypassing the need for direct numerical solution of a governing propagation model. Specifically, we show how a recurrent neural network with long short-term memory accurately predicts the temporal and spectral evolution of higher-order soliton compression and supercontinuum generation, solely from a given transform-limited input pulse intensity profile. Comparison with experiments for the case of soliton compression shows remarkable agreement in both temporal and spectral domains. In optics, our results apply readily to the optimization of pulse compression and broadband light sources, and more generally in physics, they open up new perspectives for studies in all nonlinear Schrödinger-type systems in studies of Bose-Einstein condensates, plasma physics, and hydrodynamics.
1 Introduction
The paper targets the computational bottleneck of simulating sensitive nonlinear pulse propagation by extending model-free machine-learning forecasting to optical-fibre dynamics. It demonstrates LSTM-based prediction for soliton compression and supercontinuum generation, including agreement with experiments for soliton evolution.
- NLSE-based simulations are computationally demanding because propagation depends sensitively on both the input pulse and fibre characteristics.
- The paper proposes a recurrent neural network to predict complex nonlinear propagation without directly solving the governing propagation model.
- An LSTM network reproduces ultrashort-pulse dynamics in optical fibre governed by an NLSE system.
- The study covers higher-order soliton compression, Peregrine-soliton formation, and broadband supercontinuum generation from transform-limited intensity profiles.
- For soliton compression, predicted temporal and spectral evolutions agree with reported experimental measurements.
2 Model-free modeling of nonlinear propagation dynamics
The model-free approach replaces direct numerical propagation with an LSTM recurrent network trained on simulated temporal or spectral intensity evolution. It uses recent profiles and recurrent state information to forecast subsequent profiles, with dense layers refining predictions.
- Direct numerical propagation integrates an NLSE model over many elementary steps and can be extremely time-consuming.
- The RNN forecasts propagation from sequential intensity data, using internal memory to account for long-term dependencies.
- The LSTM separately forecasts temporal and spectral intensity evolution using only the initial transform-limited pulse condition.
- Training uses numerically generated NLSE or GNLSE evolution maps across varied input-pulse characteristics, with downsampling to reduce computational load.
- Ten consecutive intensity profiles sampled at interval ∆z are fed to the RNN to predict the profile at the next propagation distance.
- The LSTM output enters two dense layers, and the predicted profile is compared with NLSE or GNLSE simulations for backpropagation-based parameter updates.
3 Results
The RNN reproduces higher-order soliton compression and supercontinuum evolution across temporal and spectral domains, matching NLSE or GNLSE simulations and, for soliton compression, experiments. Performance remains strong across varied inputs, including complex soliton fission, dispersive-wave emission, and Raman-shifted solitons.
- Higher-order soliton compression: N = 6 soliton compression is visually reproduced by the RNN, including the distance and profile of maximum temporal compression.The comparison uses a 1.1 ps, 26.3 W pulse propagated through 13 m of highly nonlinear fibre.
- Higher-order soliton compression: RMS error was 0.04 for one temporal evolution and 0.097 across 100 varied input conditions.The varied inputs span the simulated parameter range.
- Higher-order soliton compression: RNN temporal profiles agree remarkably with NLSE simulations and measurements, reproducing the compressed centre and Peregrine-soliton side lobes near 10 m.Third-order dispersion was included in the training simulations for this comparison.
- Higher-order soliton compression: Spectral predictions reproduce self-phase-modulation broadening, higher-order-soliton breathing, and narrowing and re-expansion, with RMS error R = 0.106.The relative discrepancy remains within a few dB over the full spectral evolution.
- Higher-order soliton compression: Across 100 input spectra, spectral evolution remained accurate over a 25 dB dynamic range, with RMS error R = 0.161.The detailed comparisons were made near maximum temporal compression and spectral broadening.
- Supercontinuum generation: Supercontinuum RMS errors were 0.097 and 0.049 for the two temporal cases, 0.176 across 50 temporal tests, and 0.12 across 50 spectral tests.The predictions remained within a few dB down to the -30 dB bandwidth in the temporal comparisons.
4 Conclusion
The study demonstrates that an LSTM recurrent neural network predicts nonlinear ultrashort-pulse propagation in optical fibres from pulse intensity profiles. The approach reproduces temporal and spectral dynamics and agrees closely with experiments for higher-order soliton compression, with proposed applications in ultrafast-optics design and optimization.
- An LSTM recurrent neural network reproduces higher-order soliton compression and supercontinuum-generation dynamics using only the pulse intensity profile as input.
- The network predicts nonlinear propagation in both temporal and spectral domains, and soliton-compression maps agree excellently with experiments.
- The authors anticipate neural networks becoming tools for analysing ultrafast dynamics, optimizing broadband spectra and frequency combs, and designing ultrafast-optics experiments.
- Future extensions could include nonlinear fibre parameters as training variables and prediction of the complex field rather than intensity alone.
Methods
The methods train LSTM-based recurrent networks on numerically generated NLSE or GNLSE propagation maps to forecast temporal or spectral intensity profiles. Performance is evaluated against simulations using normalized RMS error, while the number of input profiles trades prediction accuracy against training time.
- Simulation setup: The simulations use NLSE or GNLSE models for slowly varying optical-field envelopes in nonlinear fibres, covering soliton compression and supercontinuum generation.The two cases model 13 m and 20 cm fibres with different pulse and fibre regimes.
- Evaluation: Prediction quality is measured with average normalized RMS error over intensity profiles, propagation steps, and distinct realizations.The metric compares simulated profiles xm with RNN predictions x̂m.
- RNN architecture and training: The soliton-compression networks use 161-node LSTM and hidden layers, while temporal and spectral supercontinuum networks use 300-node and 250-node layers, respectively.Outputs use sigmoid activations; hidden layers use ReLU activations.
- RNN architecture and training: The LSTM receives ten consecutive temporal or spectral intensity profiles and feeds its output to two dense layers that predict the next profile.Weights and biases are adjusted by backpropagation to reduce the difference from NLSE or GNLSE profiles.
- Evaluation: Reducing the input history from ten to five profiles increases temporal soliton-evolution error from 0.097 to 0.174, while longer histories increase training time.The number of consecutive profiles is therefore a compromise between prediction accuracy and training duration.
- Simulation setup: For supercontinuum generation, 1,300 simulations provide 1,250 training and 50 testing realizations, sampled into 200 propagation profiles per evolution.Spectral profiles are filtered to 251 bins spanning 550–1050 nm.