Model for polarization-dependent gain due to pump depletion in a WDM system with forward-pumped Raman amplification

We study polarization-dependent gain (PDG) due to signal-induced pump depletion (SIPD) in a wavelength-division-multiplexing (WDM) system with forward-pumped Raman amplification. It is found that SIPD can polarize the pump significantly in fiber with very low polarization-mode dispersion (PMD). To quantify the impact of fiber PMD on SIPD-induced PDG for a practical WDM system with many signal channels and multiple Raman pumps, an approximate vector model has been developed. The developed model allows us to directly calculate PDG from both SIPD and signal-signal Raman interaction (SSRI) with greatly reduced computation time. Based on the developed model, detailed numerical investigations for two typical C-band WDM systems are presented. It is shown that significant PDG can be introduced by SIPD when the fiber PMD coefficient is lower than 0.01 ps/km¹2/ even if the pumps are fully depolarized. It is also shown that PDG due to SIPD and PDG due to SSRI are in phase at shorter wavelength channels but out of phase at longer wavelength channels.