Modal Statistics in Mode-Division-Multiplexed Systems Using Mode Scramblers

Typical multi-mode fibers exhibit strong intra-group mode coupling and weak inter-group mode coupling. Mode scramblers can be inserted at periodic intervals to enhance inter-group coupling. The deterministic mode coupling of the mode scramblers, in concert with the random mode coupling of the fiber spans, can effect strong random mode coupling between all modes. This reduces both modal dispersion and mode-dependent loss, thereby decreasing receiver complexity and increasing link capacity. In this paper, we analyze the effect of mode scramblers on end-to-end group-delay and mode-dependent loss standard deviations in long-haul multi-mode fiber links. We develop analytical tools in the generalized Jones and Stokes representations. We propose design criteria for mode scramblers that ensure strong end-to-end coupling: the mode-group-averaged power coupling matrix should be primitive and its non-dominant eigenvalues should be near zero. We argue that when the mode scramblers satisfy these criteria, the probability distribution of the system transfer matrix asymptotically approaches that of a system with strong random mode coupling between all modes. Consequently, group-delay and mode-dependent loss standard deviations become sufficient statistics of the eigenvalues of the group-delay operator and the modal gains operator, respectively. We also show that under certain conditions on the uncoupled group delays, it is possible to design self-compensating mode scramblers to reduce group delay accumulation below that of standard strong random coupling.