Passively mode-locked fiber lasers are typical nonlinear systems with abundant physical phenomena such as soliton collisions, soliton molecules, and soliton explosions. With the rise of ultrafast detection technologies such as the time-stretching dispersion Fourier transform (TS-DFT), the number of soliton dynamics phenomena has increased, generating large amounts of analyzable data. Laser self-tuning is an important method for optimizing laser mode-locking; however, traditional algorithms limit the efficiency of laser self-tuning. Thus, it is necessary to reduce the dimensions of high-dimensional data and extract features to reduce irrelevant and redundant parameters in complex nonlinear systems. Furthermore, using an autoencoder to study the interaction processes of dissipative solitons in a passively mode-locked fiber laser can not only extract the main characteristic parameters of the soliton structure but also enhance the physical analysis ability of the network by mining the relationship between the full connection layer parameters and the soliton characteristic parameters.
This study proposes a passively mode-locked fiber laser that operates in the 1550 nm wavelength band based on nonlinear polarization rotation technology. The total cavity length, dispersion, and repetition frequency of the laser were 7.9 m, -0.133 ps2, and 26.8 MHz, respectively. When the output power of the fixed pump source was 127 mW, three soliton bound states were obtained by adjusting the polarization controller. Additionally, multiple sets of real-time spectral information was obtained using TS-DFT technology. The solitons exhibited obvious interference fringes owing to spectral coherence superposition. We observed and collected data on the dynamics of different soliton bound states, thereby introducing a large amount of analyzable data into the network model. Furthermore, we designed an evolutionary convolutional autoencoder model based on the operational methods of convolution and pooling in neural networks. The model was comprised of two parts: a dynamic encoder, which compresses the input multidimensional data through a convolutional transformation for feature compression, and a propagation decoder, which generates convolutional kernels and bias matrices using the feature parameters. The initial spectrum was then convolved layer-by-layer and finally reconstructed into multidimensional data. By minimizing the deviation between the input and output spectral matrices for network learning, data dimensionality reduction and system evolution feature extraction can be achieved.
An evolutionary convolutional autoencoder model was used to extract characteristic parameters from the dynamics of different soliton bound states, and they were predicted and reconstructed them. After 200 iterations, the training and testing losses were approximately 0.0952 and 0.1017, respectively. Through continuous parameter debugging, we found that the network was most effective when the number of latent parameters was 35. We believe that there is a correspondence between this and the dimensions of the parameter space in dissipative systems. The reconstructed spectrum showed an interference stripe distribution and changes similar to the actual spectrum, with an average Pearson correlation coefficient of 98.52%. To further characterize the effectiveness of the network structure reconstruction, Fourier transforms were applied to the original and reconstructed spectra to obtain their autocorrelation traces and phase difference evolution curves. The phase evolution information of the original and reconstructed spectra was consistent, and the network model reproduced the high-frequency oscillation dynamics of the soliton pairs.
In this study, a 1550 nm band passively mode-locked fiber laser was developed based on nonlinear polarization rotation technology. The dynamics of the soliton bound states in the laser were measured using TS-DFT real-time detection technology, and the evolution of the soliton spacing and phase difference was analyzed based on the autocorrelation algorithm. Simultaneously, a design for an evolutionary convolution self-coding model was presented for feature extraction and the prediction of soliton bound state dynamics. This study provides new insights into soliton dynamics and helps to explore the physical mechanisms of soliton interactions.
