Coupled-mode analysis of stimulated Raman scattering and four-wave mixing in wavelength-division multiplexed systems

We present a coupled mode theory that describes the combined action of stimulated Raman scattering and four-wave mixing in wavelength-division multiplexing systems. Our model takes into account the limited Raman bandwidth of silica fibers and is able to predict the nonlinear penalties that affect arbitrarily large WDM systems. With this model, we show numerically that the so-called Raman-induced power tilt reaches a maximum for a total optical bandwidth slightly larger than the Raman frequency shift and decreases beyond that, in contrast to what is predicted by the usual triangular approximation. A new analytical formulation of the Raman tilt is derived that is valid for an arbitrary number of channels and unlimited optical bandwidth. Our investigations also demonstrate that four-wave mixing leads to phase-sensitive periodic energy exchanges among channels that affect the Raman tilt.