Phase locking and periodic evolution of solitons in passively mode-locked fiber lasers with a semiconductor saturable absorber

Passively mode-locked lasers with intracavity weakly birefringent fiber are theoretically analyzed based on two coupled complex one-dimensional Ginzburg-Landau equations. The model includes fiber birefringence, spectral filtering, saturable gain, and saturable loss. Phase-locked soliton solutions are found for small amounts of birefringence and several types of soliton with periodic polarization evolution for higher amounts of birefringence. Numerical simulations show qualitative agreement with experimental results.