High-Precision Modal Decomposition of Laser Beams Based on Globally Optimized SPGD Algorithm

We propose a globally optimized stochastic parallel gradient descent (SPGD) algorithm to analyze the modal content of laser beams with high precision. Modal decomposition (MD) based on conventional SPGD algorithms often falls to a local minimum when a laser beam consists of six or more fiber eigenmodes, which results in a false combination of modes. While keeping the simplicity and speed advantages of the SPGD algorithm, we adopted several optimization techniques to discern the global minimum from local minima and achieve better accuracy. The enhanced SPGD algorithm includes the annealing of the learning rates, identifying and escaping of local minima with large perturbations, and comparing of the transient error function with a reference value. We were able to exactly analyze the modal content of beams from six-mode optical fibers with high precision in seconds. Calculation of the modal weight and phase percentage errors, as well as simulations of far-field evolution images, confirmed the importance of finding the global minimum in improving the accuracy and real-time analysis of MD. The simple structure of the enhanced algorithm and its global optimization ability in multimode fibers will accelerate numerical MD in diverse laser applications.