SOLITARY-WAVE STABILITY IN BIREFRINGENT OPTICAL FIBERS

Soliton stability in birefringent optical fibers that is due to cross-phase modulation has been studied. The relationship between the threshold amplitude of stable solitons and the strength of the linear birefringence is obtained by using a virial theorem. It is found that the threshold amplitude depends on the birefringence nonlinearly. Above threshold each partial pulse will bind to the other, and a solitonlike state is formed; otherwise the partial pulses will split, which is undesirable for communication applications. Several conservation laws are found for the coupled nonlinear Schrodinger equations (NSE's), and it is shown that the conservation of momentum results in symmetric frequency shifts of both partial pulses, which is crucial for the understanding of soliton collisions involving the walk-off effect. Based on momentum conservation and the linear dispersion of the coupled NSE's, a solitary-wave solution is found, and the physical meaning of the solution is explained. It is also found that the interaction of the partial pulses can be treated as a nonlinear oscillator, with gain or loss depending on pulse shape and pulse amplitude, when birefringence is small and the pulse shape does not change much. Some other trapping behavior is analyzed also.