For a long time, interest in multimode (MM) optical fibers has remained limited, owing to the poor quality of laser beams emerging at their output. A typical indicator of beam quality is inversely proportional to the number of excited modes. However, recent intensive research of nonlinear propagation effects, involving high-power laser beams in MM graded-index (GRIN) fibers, has led to the discovery of previously unexpected phenomena, such as the Kerr-activated self-cleaning of a beam . The manifestation of self-cleaning is that most of the beam energy flows into the fundamental mode of the fiber. This process is accompanied by a redistribution of energy towards higher-order modes . Increasing the fundamental mode energy leads to improving the output beam quality. The standard method to determine the beam quality is to measure the M2-parameter (m-squared). This parameter measures the divergence of the beam with respect to the Gaussian beam. However, since self-cleaning involves a nonlinear redistribution of energy carried by a large number of fiber modes, this approach is not entirely correct, and a full mode decomposition (MD) of the output beam appears to be a much more informative method.