# Deep Learning for Computational Mode Decomposition in Optical Fibers
## 1 Introduction  
Optical fibers are used in a variety of applications. On the one hand, they are used in biophotonics as an image transmitting device [1, 2]. On the other hand, multimode optical fibers (MMF) are also used in information technology, where the high number of modes permits spatial multiplexing. The basic idea is to transmit the eigenmodes of the optical fiber in order to obtain a Multiple-Input Multiple-Output (MIMO) transmission system with only one single fiber. Mode division multiplexing is said to be the next key development for increasing possible transmission rates [3]. However, light propagation through an MMF is nontrivial: a coherent light signal launched into an MMF exits as a speckle pattern due to mode-mixing effects [4]. These arise from two major sources. First, angle deviations occur during light injection; second, external parameters such as temperature fluctuations, mechanical stress (bending or twisting), and manufacturing tolerances have a considerable influence on the light transmission. For a long time, this made MMFs unsuitable for laser-based applications. However, due to the technological and methodological development, methods have been demonstrated that allow compensating and controlling the light distortions from the MMFs. While the first works were based on analogue holography approaches [5], in recent years, digital holography and wavefront shaping have shown a tremendous potential [6]. Iterative optimization [7, 8], digital optical phase conjugation [9, 10, 11], or the transmission matrix (**T**) method [12] were developed to control the light transmission of an MMF even in \"real time\". For the transmission of complex patterns in the fields of biophotonics and communications engineering, the **T** method has proven its worth [13, 14, 15, 16]. The complex-valued weights of **T** link the modes, excited at the MMF input, with those that exit the MMF. With complete knowledge of the **T** method, it is thus possible to generate arbitrary structures atthe output of the MMF, limited by the degrees of freedom of the MMF's mode domain. Measurement of the **T** requires a complex analysis of the light field at the MMF. The light field leaving the MMF is a superposition consisting of the light-field distributions of the modes, which are contained in the finite mode domain of the MMF. An extremely reliable measurement technique that performs mode analysis in an MMF is \(S^{2}\) imaging [17]. However, since \(S^{2}\) imaging is a scanning method, it is not suitable for the intended application in the field of MIMO communication technology [18], as this requires a single-shot mode decomposition (MD). In previous work, the author has shown a technique based on Digital Holography (DH) with which complex-valued MMF speckle patterns can be reconstructed and decomposed into the individual mode components by means of an orthogonal series expansion [19]. However, digital holographic techniques have the drawbacks that they are prone to environmental perturbations and phase instabilities [20; 21] and that a reference beam is required. In optical data transmission, this would mean that an additional single-mode fiber has to be used carrying the coherent reference beam, which is impractical. A possible solution to this problem could be to tailor a reference beam using self-referencing. Here, the object beam is duplicated and optically processed to generate the reference beam [22]. However, it is not straightforward to apply this approach to the introduced MD problem, as an adaptive pinhole would be required. For this reason, it is preferable to find an alternative to DH-based analysis methods for the MD. The most favorable solution would be to perform the mode decomposition with simple intensity-based camera images, removing the need for phase measurements. This could replace the entire holographic setup with one single camera and thus, would realize a less complex measurement system, which is significantly more robust and cheap.