Modeling and Analysis of the Contribution of Channel Walk-Off to Nondegenerate and Degenerate Four-Wave-Mixing Noise in RZ-OOK Optical Transmission Systems

A finite-band noise model for degenerate four-wave mixing (FWM) including channel walk-off in return-to-zero ON—OFF-keying (RZ-OOK) transmission is extended to include nondegenerate FWM (ND-FWM). The model is verified by comparing the results for the noise variance for each type of FWM to split-step-Fourier (SSF) simulations for a 10-Gb/s single span link, and excellent agreement is obtained. A physical interpretation of the walk-off effect on the FWM noise is formulated in terms of intracollision and intercollision interference of the corresponding generated FWM waves. The author shows that the walk-off effect modifies the FWM noise power spectral density only at high frequencies by producing distinct peaks at locations determined by the channel spacing. In principle, the walk-off effect significantly increases the noise variance for both types of FWM before any filtering at the end of fiber. Upon demultiplexing, it is found that the walk-off effect is significant and observable for the degenerate FWM case but is no longer significant for the ND-FWM case. When a sub-bit-rate electrical filter is used in the receiver, the walk-off effect becomes insignificant for all types of FWM. They systematically conclude that the walk-off effect is unimportant for FWM in typical RZ-OOK systems when tight electrical filtering is used. They also illustrate the accuracy of the model for the more general case where more than one FWM tone is coincident on a probe channel by comparing the analytic model to SSF simulations for a five-channel example.