Effects of polarization mode dispersion on cross-phase modulation in a WDM optical transmission system

The cross-phase modulation (XPM) changes the state-of-polarization (SOP) of various channels and leads to amplitude modulation of the propagating waves in a WDM system. Due to the presence of polarization mode dispersion (PMD), the angles between the SOP of the channels change randomly and cause the modulation amplitude fluctuation random in the perturbed channel. We analytically derive the dynamic equation of the perturbed channel, determine the combined probability density function of the random angle between the SOP of pumps and probe channel and evaluate the effects of PMD on XPM for a 4-channel IM-DD WDM system in terms of BER at bit rate of 10 Gb/s per channel. We also simulate the impact PMD on XPM for a 4-channel WDM system in terms of eye diagram and found that eye opening penalty is 1.85 dB higher when the fiber PMD coefficient increases from 0.5 to 1.5 ps/√km.