XPM Efficiency Versus Symbol Rate

Cross-Phase Modulation (XPM) limits the information capacity of optical fibers, due to the power fluctuations in one channel affecting the phases of the other channels. A decade ago, we showed that splitting a channel into multiple subcarriers could reduce the effect of XPM on multi-channel systems, due to a reduction in the intensity fluctuations at frequencies where walk-off is low. As commercial systems now take advantage of this effect, it is appropriate to give a more detailed and quantitative explanation of it; in particular to show that the optimal subcarrier rate scales with the square-root of the chirp rate of the symbols, which depends only on the accumulated dispersion in the fiber. Simulations show that the optimal symbol rate is when the time-spread of the symbols due to dispersion is between 2.5× to 6.5× of their transmitted (central pulse) widths. This paper presents simple arguments backed by simulations to identify the key parameters that determine the optimal subcarrier rate. In particular, we show that there is an optimal balance between the intrinsic intensity fluctuations of transmitted symbols (which are lower-frequency for lower symbol rates) and the intensity fluctuations due to chirp (which are lower-frequency for higher symbol rates). We also discuss why the traditional XPM-efficiency equation is not appropriate when data is transmitted, because it assumes the XPM contributions of all spans in an amplified link are equal, rather than increasing with distance.