On Symmetry Properties of Transmission Matrices for Concatenations of Multi Mode Fiber Sections with Linear Coupling

Abstract:
Linear coupling between modes introduces crosstalk in mode division multiplexed transmission systems. We aim to clarify the strength of the contributions of different coupling mechanisms such as fiber axis offset, bending, rotation, etc. to the overall coupling matrix in manufactured fibers. Although the coupling matrices of the individual mechanisms exhibit certain symmetry properties, we find that the overall matrix for a concatenation of multiple fiber sections calculated by the propagation of coherent signals lacks these symmetries. This introduces difficulties for the interpretation of the coupling strength. Effects such as temperature variations and mechanical vibrations introduce fluctuations of phase differences between propagating modes. These effects result in stochastic interference patterns, which complicates the interpretation of the transmission matrix of a concatenation of elements and potentially break the symmetry. In the incoherent case, the coupling matrix of concatenated elements is more symmetrical due to averaging and changes less over time. We argue that averaged versions of the overall coupling matrices corresponding to the ones for the incoherent case should be used for the evaluation of the coupling strength in a concatenation of multiple fiber sections with discrete coupling points. This facilitates the interpretation of the impact of coupling on system performance.