Sub-sampled modal decomposition in few-mode fibers

General error analysis of matrix-operation-mode decomposition technique in few-mode fiber laser

The mode decomposition based on matrix operation (MDMO) is one of the fastest mode decomposition (MD) techniques, which is important to the few-mode fiber laser characterization and its applications. In this paper, the general error of the MDMO technique was analyzed, where different influencing factors, such as position deviation of the optical imaging system, coordinate deviation of the image acquisition system, aberrations, and mode distortion were considered. It is found that the MDMO technique based on far-field intensity distribution is less affected by optical imaging system position deviation, coordinate deviation of the image acquisition system, and mode distortion than those based on direct near-field decomposition. But far-field decomposition is more affected by aberration than those based on near-field decomposition. In particular, the numerical results show that the deviation of the coordinate axis direction is an important factor limiting the accuracy of MD. In addition, replacing the ideal eigenmode basis with a distorted eigenmode basis can effectively suppress the decrease in mode decomposition accuracy caused by fiber bending. Moreover, based on detailed numerical analysis results, fitting formulas for estimating the accuracy of the MDMO technique with imperfections are also provided, which provides a comprehensive method for evaluating the accuracy of the MDMO technique in practical engineering operations.

Analysis of an image noise sensitivity mechanism for matrix-operation-mode-decomposition and a strong anti-noise method

Mode decomposition (MD) based on the matrix operation (MDMO) is one of the fastest mode decomposition methods in fiber laser which has great potential for optical communications, nonlinear optics and spatial characterization applications. However, we found that the image noise sensitivity is the main limit to the accuracy of the original MDMO method, but improving the decomposition accuracy by using conventional image filtering methods is almost ineffective. By using the norm theory of matrices, the analysis result shows that both the image noise and the coefficient matrix condition number determine the total upper-bound error of the original MDMO method. Besides, the greater the condition number, the more sensitive of MDMO method is to noise. In addition, it is found that the local error of each mode information solution in the original MDMO method is different, which depends on the L2-norm of each row vector of the inverse coefficient matrix. Moreover, a more noise-insensitive MD method is achieved by screening out the information corresponding to large L2-norm. In particular, selecting the higher accuracy among the original MDMO method and such noise-insensitive method as the result in a single MD process, a strong anti-noise MD method was proposed in this paper, which displays high MD accuracy in strong noise for both near-filed and far-filed MD cases.

Theoretical and experimental studies on intermodal nonlinear effects of a high-power near-single-mode CW Yb-doped fiber laser

An intermodal-nonlinearity-induced time-frequency evolution model of high-power near-single-mode continuous-wave fiber lasers (NSM-CWHPFLs) was proposed to simulate the evolution of spectral characteristics and beam quality under the combined action of intermodal and intramodal nonlinear effects. The influence of fiber laser parameters on intermodal nonlinearities was analyzed, and a suppression method involving fiber coiling and seed mode characteristic optimization was proposed. Verification experiments were conducted with 20/400, 25/400, and 30/600 fiber-based NSM-CWHPFLs. The results demonstrate the accuracy of the theoretical model, clarify the physical mechanisms of nonlinear spectral sidebands, and demonstrate the comprehensive optimization of intermodal-nonlinearity-induced spectral distortion and mode degradation.

High-performance mode decomposition using physics- and data-driven deep learning

A novel physics- and data-driven deep-learning (PDDL) method is proposed to execute complete mode decomposition (MD) for few-mode fibers (FMFs). The PDDL scheme underlies using the embedded beam propagation model of FMF to guide the neural network (NN) to learn the essential physical features and eliminate unexpected features that conflict with the physical laws. It can greatly enhance the NN's robustness, adaptability, and generalization ability in MD. In the case of obtaining the real modal weights (ρ2) and relative phases (θ), the PDDL method is investigated both in theory and experiment. Numerical results show that the PDDL scheme eliminates the generalization defect of traditional DL-based MD and the error fluctuation is alleviated. Compared with the DL-based MD, in the 8-mode case, the errors of ρ2 and θ can be reduced by 12 times and 100 times for beam patterns that differ greatly from the training dataset. Moreover, the PDDL maintains high accuracy even in the 8-mode MD case with a practical maximum noise factor of 0.12. In terms of adaptation, with a large variation of the core radius and NA of the FMF, the error keeps lower than 0.43% and 2.08% for ρ2 and θ, respectively without regenerating new dataset and retraining NN. The experimental configuration is set up and verifies the accuracy of the PDDL-based MD. Results show that the correlation factor of the real and reconstructed beam patterns is higher than 98%. The proposed MD-scheme shows much potential in the application of practical modal coupling characterization and laser beam quality analysis.

M2 factor estimation in few-mode fibers based on a shallow neural network

A high-accuracy, high-speed, and low-cost M² factor estimation method for few-mode fibers based on a shallow neural network is presented in this work. Benefiting from the dimensionality reduction technique, which transforms the two-dimension near-field image into a one-dimension vector, a neural network with only two hidden layers can estimate the M² factor directly. In the simulation, the mean estimation error is smaller than 3% even when the mode number increases to 10. The estimation time of 10000 simulation test samples is around 0.16s, which indicates a high potential for real-time applications. The experiment results of 50 samples from the 3-mode fiber have a mean estimation error of 0.86%. The strategies involved in this method can be easily extended to other applications related to laser characterization.