Analysis of real-time spectral interference using a deep neural network to reconstruct multi-soliton dynamics in mode-locked lasers

Abstract

The dynamics of optical soliton molecules in ultrafast lasers can reveal the intrinsic self-organized characteristics of dissipative systems. The photonic time-stretch dispersive Fourier transformation (TS-DFT) technology provides an effective method to observe the internal motion of soliton molecules real time. However, the evolution of complex soliton molecular structures has not been reconstructed from TS-DFT data satisfactorily. We train a residual convolutional neural network (RCNN) with simulated TS-DFT data and validate it using arbitrarily generated TS-DFT data to retrieve the separation and relative phase of solitons in three- and six-soliton molecules. Then, we use RCNNs to analyze the experimental TS-DFT data of three-soliton molecules in a passive mode-locked laser. The solitons can exhibit different phase evolution processes and have compound vibration frequencies simultaneously. The phase evolutions exhibit behavior consistent with single-shot autocorrelation results. Compared with autocorrelation methods, the RCNN can obtain the actual phase difference and analyze soliton molecules comprising more solitons and almost equally spaced soliton pairs. This study provides an effective method for exploring complex soliton molecule dynamics.

Comparing Performance of Deep Convolution Networks in Reconstructing Soliton Molecules Dynamics from Real-Time Spectral Interference

“…The generation of simulated TS-DFT data of soliton bound state is considering factors such as bandwidth, sampling, and noise, which has been proven to be used for deep learning data sets [17]. The complex amplitude of the slowly varying envelope of soliton molecules is described by the superposition of solitons, which is given by [32]…”

“…However, the autocorrelation method cannot further quantitatively analyze all the dynamic evolution processes in complex molecular structures, such as relative phase of each soliton. When multisoliton molecules and soliton pairs with near equal spacing happen [11], it is almost impossible to obtain relative phase differences (PDs) evolution [17]. Therefore, the autocorrelation method is suitable for analyzing simple soliton molecule structures consisting of soliton pairs, unequally spacing three solitons [4], etc.…”

“…Therefore, the autocorrelation method is suitable for analyzing simple soliton molecule structures consisting of soliton pairs, unequally spacing three solitons [4], etc. Recent years have seen the rapid growth and development of the field of ultrafast photonics, where artificial intelligence algorithms are being applied in exploring complex dynamical processes of soliton molecules in PMLFLs [17], the extreme events in optical fibre modulation instability [18], and the generation and characterization of light pulses [19,20]. In order to solve the internal dynamics of complex soliton molecules, we introduced artificial intelligence combining with TS-DFT.…”

“…Although the residual networks (ResNets) [21] have been used for exploring complex dynamical processes in soliton molecules experimentally and numerically based on TS-DFT in passive mode-locked lasers (PMLs), emerging models continue to push the limits of what can be achieved. It also has proved that the data generated based on theory can be used to analyze experimental data [17]. It is necessary to consider whether the network structures outside the ResNets are more accurate and effective to analyze the internal dynamics of multisoliton molecules.…”

“…Recently, deep convolution networks (DCNs) have demonstrated a powerful ability to apply in mode-locked lasers [17,22], decompose the modes in few-mode fibers [23], recognize orbital angular momentum modes with fractional topological charges [24], mitigate fiber nonlinearity in optical communication [25], and the characterization and control of ultrafast propagation dynamics [26]. It is well known that convolutional neural networks (CNNs) have dominated machine-learning landscape in data-rich applications, such as VGG (Visual Geometry Group) [27], Residual Networks (ResNets) [21], Dense Convolutional Networks (DenseNets) [28], and other models.…”