Modal decomposition of an incoherent combined laser beam based on the combination of residual networks and a stochastic parallel gradient descent algorithm

Abstract

With the increase of the superimposed eigenmodes number, the traditional numerical modal decomposition (MD) technique will inevitably suffer from ambiguity and local minima problems and thus is typically unsuitable for conducting modal decomposition of an incoherent combined laser beam. In this paper, we propose a novel, to the best of our knowledge, MD algorithm, named ResNet-SPGD, which combines the advantages of residual networks (ResNet) and stochastic parallel gradient descent (SPGD) algorithm. Via setting the modal mode coefficients obtained from the CNN model as the initial value of the SPGD algorithm, such algorithm shows an attractive solution to mitigate the problem of modal ambiguity. The proposed algorithm is preliminarily applied to the modal decomposition of an incoherent combined laser beam, and the feasibility is demonstrated via numerical simulations. Complete MD is performed with high accuracy, and the only cost is the sacrifice of some real-time capacity.

Convolutional Neural Network Combined With Stochastic Parallel Gradient Descent to Decompose Fiber Modes Based on Far-Field Measurements

“…The overfitting issue, which crucially degrades the accuracy of the CNN, can be prevented by letting the training set consist of a sufficiently large amount of data [28]. However, the procedure of training the CNN with such a large amount of data may require an excessive amount of RAM (random access memory) resources and increase the total training time.…”

“…Notwithstanding, in order to maximize the benefit of a CNN method in view of the calculation time, it is important how to set its layers. If the number of the CNN layers is too small, the result may not converge, and conversely, if it is too large, the calculation time may become too long or overfitting of the training data may occur [28].…”

“…Recently, a novel MD method combining the advantage of the SPGD algorithm in terms of accuracy and the advantage of CNN in terms of speed has been proposed based on numerical simulations [28]. It was reported that this method could overcome the typical local-minimum issue of the SPGD algorithm by first obtaining the interim conditions close to the global minimum via the CNN and could greatly reduce the number of SPGD iterations, which is crucially related to the ultimate MD rate.…”

“…It was reported that this method could overcome the typical local-minimum issue of the SPGD algorithm by first obtaining the interim conditions close to the global minimum via the CNN and could greatly reduce the number of SPGD iterations, which is crucially related to the ultimate MD rate. However, the aforementioned method was based on the measurement of a near-field intensity pattern which would inevitably require an additional optical system such as a 4-f system like most other methods [10]- [12], [15]- [20], [28]. Furthermore, it has yet to be confirmed whether or how well such a method can obtain the modal coefficients in real-time and real experimental environments, because no experiment was carried out based on it.…”

“…It is noteworthy that although this method uses the SPGD algorithm to finalize the MD after first obtaining the initial value of each mode's coefficient via the CNN as in Ref. [28], the following novel aspects are distinctively investigated and clarified in this paper:…”