Polarization oscillations and soliton stability in birefringent optical fibres

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Abstract
Propagation of short pulses in linearly birefringent optical fibres is considered analytically with the help of a variational (Lagrangian) approach for two coupled nonlinear Schrödinger equations. For nearly equal amplitudes of the polarization pulses we study the trapping of solitons due to the nonlinear coupling in the case of strong birefringence, and we find also the amplitude threshold for the trapping when the solitons are produced by a symmetric output pulse. In the case of small birefringence we propose an analytical explanation of the soliton instabilities observed earlier in numerical simulations. The analysis demonstrates instability of the fast polarization mode and stability of the slow one, the effect having a threshold which depends on birefringence. Our results may also be applied to an elliptically birefringent fibre when the birefringence is large.