Impulse Response of Cross-Phase Modulation Filters in Multi-Span Transmission Systems with Dispersion Compensation

As shown by Chiang et al. 1996., cross-phase modulation on each channel of a wavelength-division-multiplexed transmission system can be viewed as a phase modulation, where the modulating signal is the sum of the input intensities of all the other copropagating channels, each filtered by a low-pass filter, whose bandwidth decreases with the walk-off parameter. We give an explicit expression of the impulse response of such filter in the general case of dispersion mapped transmission systems. We show by simulation that this filter, in intensity-modulated transmission systems, gives an optimal prediction of the signal phase even when the underlying assumption of negligible envelope distortion upon which its derivation is based is strongly violated. As an application, we show an analytical evaluation of the spectral broadening induced by XPM in multi-span compensated systems.