Abstract
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.
Highlights
As laser performance and applications evolve, analyzing and assessing beam quality is becoming correspondingly important
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
Summary
As laser performance and applications evolve, analyzing and assessing beam quality is becoming correspondingly important. S2 [8] imaging requires broadband light source and optical spectrum analyzer to measure the wavelength modulation induced by modal interference These techniques are often not integrated with the main laser system and require additional time for experimentation and analysis. The Gerchberg-Saxton [13], [14], stochastic parallel gradient descent (SPGD) [5], [15], and genetic algorithm [16] have been widely studied In these numerical methods, the reconstructed beam profile—which is a linear combination of each eigenmode—is iteratively compared with the input beam to find the most probable MD solution or to minimize the error function between the two. With rigorous analysis and the globally optimized SPGD algorithm, any random initial conditions can converge on the global minimum for up to six modes based on the near-field beam profile. The enhanced SPGD algorithm can be applied to beams in which a higher number of eigenmodes are superposed
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