A technique for computing the effect of cross-phase modulation (XPM) on two copropagating analog channels in an optical fiber link is presented. In this approach, the interaction between the two channels is linearized by keeping the self-phase modulation (SPM) and XPM interactions in the strong optical carrier components only at lowest order and then at the next order, deriving the effect on the modulation components of both channels when the optical carrier is strong relative to the other components of the channel. In contrast to some previously suggested approaches, it is not assumed that the pump is undistorted, and therefore, this method accurately describes distortions due to SPM, XPM, and dispersion management in both channels. This method is easily applied to systems with multiple spans employing dispersion management with loss and gain. The expressions for the received radio frequency power and crosstalk between the two channels when direct detection is used are then provided. Using this approach, new expressions for the amplitude modulation and phase modulation modes of the two channels are derived, and the way they exchange energy when SPM, XPM, and dispersion are all considered is explained. This method yields excellent agreement between theory and experimental data.
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