Polarization dynamics of ultrafast solitons

We study the polarization dynamics of ultrafast solitons in mode-locked fiber lasers. We find that when a stable soliton is generated, its state of polarization shifts toward a stable state, and when the soliton is generated with excess power levels it experiences relaxation oscillations in its intensity and timing. On the other hand, when a soliton is generated in an unstable state of polarization, it either decays in intensity until it disappears, or its temporal width decreases until it explodes into several solitons, and then it disappears. We also found that when two solitons are simultaneously generated close to each other, they attract each other until they collide and merge into a single soliton. Although these two solitons are generated with different states-of-polarization, they shift their state of polarization closer to each other until the polarization coincides when they collide. We support our findings by numerical calculations of a non-Lagrangian approach by simulating the Ginzburg-Landau equation governing the dynamics of solitons in a laser cavity. Our model also predicts the relaxation oscillations of stable solitons and the two types of unstable solitons observed in the experimental measurements.