Uso de Redes Neurais Recorrentes para Modelagem de Propagação Não Linear de Pulsos Ópticos e Geração de Supercontínuos

Abstract

Optical fibers have become the backbone of modern telecommunication systems, linking countries, and continents through long submarine cables. Even with an attenuation of only 0.2 dB/km, this communication channel is not so transparent or passive, since its self-phase modulation and dispersive effects can be destructive for the communication system. Such effects are highly complex and require computationally demanding simulations based on the nonlinear Schrödinger equation (NLSE). The split-step Fourier state-of-the-art algorithm is a simple solution to evaluate the propagation of optical pulses, however, this method creates a severe bottleneck for real-time experiments, highly nonlinear cases, or with a great number of numerical simulations. This project uses recurrent neural networks to predict temporal and spectral evolution in the case of nonlinear pulse propagation, bypassing the need for numerical solutions. Due to the temporal characteristics of the propagation problem, it makes sense the use of recurrent networks such as the long short-term memory (LSTM). The first part of this work tested two networks, the LSTM and the convolutional LSTM (CLSTM). A range of hyperparameters was tested empirically in search of the best configuration that captures the optical transformations. Both networks presented good performance, with R² > 96%, however, in a deep analysis, we extended the initial conditions, and the pulse waveform, showing the CLSTM difficulty to adapt itself, highlighting the LSTM, with a maximum error of RMSE = 5.328 × 10−³ . In the second part, we tried to generalize the network applications also to the spectral domain. The bidirectional LSTM (BiLSTM) network is used, considering its bidirectional structure, allowing to learn long-term temporal dependencies and capture complex nonlinear patterns. The temporal and spectral domains are treated simultaneously here. The BiLSTM presented excellent performance, with R² > 97% to both domains, the RMSE = 4.39 × 10−³ for the temporal domain and RMSE = 1.21 × 10−² for the spectral domain, superior to the LSTM in the same conditions. Still, the same networks were applied to a supercontinuum generation case, more complex, and both networks showed good results. The BiLSTM, for example, returned an RMSE = 1.75 × 10−² for the temporal domain, and an RMSE = 1.32 × 10−² for the spectral domain. This work contributes to the applications of machine learning in nonlinear photonics, helping to build a neural model to get along with dynamics in optical pulse propagation, and supercontinuum generation.