Digital analysis of a speckle pattern of chaotic mode composition and restoration of a regular intensity pattern after a multimode fiber

A process of mode matching in a chaotic speckle pattern without reference beam responsible for the formation holographic grating was studied experimentally and theoretically. Our approach based on measuring amplitudes phases Hermite-Gauss (HG) Laguerre-Gauss (LG) modes formed by radiation multimode gradient fiber. The hologram spatial light modulator using fiber model while taking into account polarization dispersion, as well random phase jumps each eigenmode. We managed to match 210 restore not only original pattern, but also structured LG entire chain HG eigenmodes.