Theory of Intermodal Four-Wave Mixing with Random Linear Mode Coupling in Few-Mode Fibers

We study theoretically and numerically intermodal four-wave mixing (FWM) in few-mode fibers in the presence of birefringence fluctuations and random linear mode coupling. Two different intermodal FWM processes are investigated. We find that one of them has a much larger FWM bandwidth than the other. The nonlinear contributions of the pumps and probe on the phase-matching conditions and FWM bandwidth are also studied. We include random linear mode coupling between fiber modes using three different models. These three models are derived from an analysis of the impact of random coupling in the presence of differences of propagation constants between modes. We find that random coupling always reduces the FWM efficiency relative to the absence of linear coupling. The reduction factor is relatively small (about 3 dB) when only a few modes linearly couple but can become very large (> 40 dB) when all modes couple. In the limit of a coupling length much shorter than the nonlinear length, FWM efficiency becomes vanishingly small. These results should prove useful in the context of space-division multiplexing with few-mode and multimode fibers.