Statistics of Higher-Order Modal Dispersion in Multi-Mode Fiber With Strong Mode Coupling

The effects of mode coupling and first-order modal dispersion in mode-division multiplexed multi-mode fiber systems are well studied. However, when modal delays become frequency-dependent, higher-order modal dispersion effects, such as mode-dependent chromatic dispersion, must be incorporated into propagation models. This work investigates the statistical properties of first- and second-order group-delay operators under strong coupling conditions using a multi-section random matrix model, accounting for both intrinsic (uncoupled) group delays and mode-dependent chromatic dispersion. We show that the asymptotic distributions of these operators are determined by the number of sections, the delay spreads of the uncoupled delays, and mode-dependent chromatic dispersion. For typical graded-index multimode fibers, the uncoupled group delays have a significantly greater impact than the mode-dependent chromatic dispersion. As a result, the complexity of digital signal processing is ultimately dictated by the statistics of the first-order group-delay operator. Additionally, we derive analytical expressions for the expected intensity pulse response to provide a time-domain perspective on the higher-order effects.