100 laser beam array phase-locked in a neural network loop

Recently, neural networks (NN) were investigated to recover and control the phase of laser arrays in view of performing coherent beam combining (CBC) [1] , [2] . These pioneering demonstrations, based on phase recovery, face limitations in terms of accuracy and scalability. In this communication, we report numerical and experimental results obtained with a new NN phase correction approach designed to overcome these limitations and well suited to continuous control of a physical parameter. It consists in including in a phase error reduction loop a simple NN trained by a specific reinforcement learning (RL) scheme [3] . As done in [4] , m sparse intensity measurements, carried out over a speckle field resulting from the interferences of n laser beams with unknown phases (Φ) through a scattering medium, feed an optimised trained NN. Then, from these measurements, the NN delivers phase correction values to apply to the laser beams, by means of phase modulators, in order to reach and maintain a user-defined phase pattern (Φ t ). For that purpose, a modified and innovative T-iterations RL scheme, that we called quasi-RL, was applied. Like any RL process, quasi-RL is based on a reward (R) and a training set of data (TS). Here, R is the phasing quality at each correction and TS consists in a set of vectors pairs (random phase pattern, measured intensity) that are generated as a random initial state at each learning step (before applying phase reduction loop). Thus, learning the NN to converge to Φt in a fixed number of iterations T is equivalent to maximising R at each step of error reduction loop for different initial states. In our training process, the phase corrections to apply at each iteration are known, so that R can be calculated as a loss function for supervised learning. This specific scheme allows fast learning process.