Light Propagation and Mode Mixing in Concatenated Multi-mode Fibers

We analyze light propagation in concatenated multi-mode fibers (MMF) using an Random Matrix Theory (RMT) modeling that takes into consideration the polarization mixing and spatial modal mixing between different modes. The latter is a result of fiber imperfections (twisting, defects etc.) and typically is characterized by the strength δ of the coupling between modes and the range of coupling b of different modes. Our analysis lead us to a generalized fluctuation-dissipation relation which describes the decay of an initial excited mode to the other modes of the system. We found that this decay is characterized by three regimes: an initial exponential decay, with a rate which is proportional to δ²b; a slower, power law decay which reflects a diffusion process with a step b; and finally a saturation to an ergodic value which is inverse proportional to the number of available modes.