Interplay between Raman self-frequency shift and cross-phase modulation in the vector-soliton of a birefringent fiber

Competition between cross-phase modulation (XPM) interaction and Raman-induced red-frequency shift is observed in the orthogonally polarized components (in the form of optical pulses) of a vector-soliton propagating in the fundamental mode of a birefringent fiber exhibiting negative third-order dispersion and group velocity birefringence. Both pulses experience opposite frequency shifts due to XPM, which reinforces the Raman self-frequency shift of one pulse while it hinders the self-frequency shift of the other. A large redshift in one of the pulses of the vector-soliton suggests transfer of a greater part of its energy to the dispersive radiation, leading to an asymmetry in the longitudinal evolution of the amplitudes as well as the frequencies of both the pulses of the vector-soliton. To support our analysis, an analytical approach is developed in order to understand the interplay between the Raman effect and XPM. The findings of the analytical approach are in good qualitative agreement with the numerical results, which is consistent with the results of Phys. Rev. E70, 016615 (2004)PLEEE81063-651X10.1103/PhysRevE.70.016615. The derived analytical relations accommodate additional nonlinear interactions originating from the XPM, as well as mutual Raman interaction, which makes our approach much superior to that used in Phys. Rev. E70, 016615 (2004)PLEEE81063-651X10.1103/PhysRevE.70.016615. It is also possible to understand the interaction between two frequency-shifted solitons in a true single-mode fiber or other waveguide system exhibiting negative third-order dispersion by a slight modification of our theoretical approach.