Machine learning for ultrafast nonlinear photonics

Recent years have seen the rapid growth of the field of smart photonics where the deployment of machine-learning strategies is the key to enhance the performance and expand the functionality of optical systems. Here, we review our recent results in the area by providing several examples of advances enabled by machine-learning tools such as neural networks (NNs). We describe the use of a supervised feedforward NN paradigm to solve the direct and inverse problems relating to nonlinear pulse shaping in optical fibres, bypassing the need for direct numerical solution of the governing propagation model. Specifically, we show how the network accurately predicts the temporal and spectral intensity profiles of the pulses. This data-driven approach reduces the computational time by two orders of magnitude. Further, we demonstrate the ability of the NN to determine the nonlinear propagation properties from the pulses observed at the fibre output, and to classify the output pulses according to the initial pulse shape. We also illustrate the use of a NN to study the temporal and spectral evolutions of periodic signals made of equally frequency-spaced components upon propagation in fibre. The phase and amplitude of the frequency comb structure resulting from multi-wave mixing are accurately predicted by the network along with the corresponding high-repetition rate temporal waveform. We also emphasize how the network can learn the physical model from an experimental dataset.