Analytic Modeling of Four-wave-mixing with Inter-channel Walk-off in Wavelength-division-multiplexed Optical Links

Fiber nonlinearity can cause interactions and crosstalk between co-propagating dense wavelength division multiplexed channels in high capacity optical fiber communication systems. The crosstalk between channels leads to degradation of the bit error performance of the system. One of the mechanisms of this crosstalk is Four-Wave-Mixing (FWM) caused by the fiber nonlinearity. It is important to have an analytic model for the FWM to estimate and minimize the impact of FWM for a given transmission system design. Conventional analytic models for FWM ignore the inter-channel walk-off effect. In this thesis a model for FWM is developed which rigorously accounts for the walk-off effect. The model is derived for degenerate and non-degenerate FWM. This model is derived for conventional RZ-OOK and the emerging RZ-DPSK modulation formats. A detailed physical understanding of the walk-off contribution to the FWM noise is developed. The first direct comparison, between an analytic model for FWM and split-step Fourier (SSF) simulations for the general case of random modulated channels is presented, for a single span 10-Gb/s link. It is shown that for both RZ-OOK and RZ-DPSK modulation formats the walk-off effect significantly increases the FWM noise variance for all FWM types before any filtering at the end of fiber. When a multiplexer/de-multiplexer is used the walk-off effect is significant and observable for the degenerate FWM case but is no longer significant for the non-degenerate FWM case. In the typical situation when a sub-bit-rate electrical low pass filter is also used, the walk-off effect is effectively removed for all three types of FWM. Comparing the models for the two modulation formats it is found that the FWM noise standard deviation and related BER penalty are much smaller for RZ-DPSK as compared to that for RZ-OOK at the same average launch power.Ph