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There is an upward trend in using multimode fiber for an increasing number of applications such as optical telecommunication, endoscopic imaging or laser beam shaping, which require knowledge of the fiber characteristics. In this paper, we propose a new method for learning the complex transmission matrix of a multimode fiber from a set of speckled output patterns without interferometric setup. In a first step, our method finds a model to predict the intensity pattern of a coherent beam at the distal end of the multimode fiber. In a second step, this model is improved by using some additional intensity images in the far field, resulting in the prediction of the actual 3D complex field leaving the multimode fiber, without the use of a reference beam. Our two-step method was validated numerically and experimentally with a standard 50 &#x03BC;m-core diameter step-index fiber guiding up to 140 LP modes at 1064 nm. Experimentally, using the validation set, we obtain a similarity between predicted and true speckle images at fiber output of 99.2&#x0025; and 98.5&#x0025; respectively in the near field and far field, proving the accuracy of the retrieved complex transmission matrix. Finally, we successfully demonstrated projection of images simultaneously in two planes as proof of complex field shaping.

Retrieving the Complex Transmission Matrix of a Multimode Fiber by Machine Learning for 3D Beam Shaping