Dynamics of breathing dissipative soliton pairs in a bidirectional ultrafast fiber laser

The breathing dissipative soliton as a dynamic solution to many nonlinear systems has induced substantial interest in nonlinear photonics and ultrafast laser science. However, the exotic breathing multi-soliton dynamics are still largely unexplored in the bidirectional fiber laser compared to the unidirectional laser. Here, we reveal nonequilibrium dynamics of a breathing soliton pair (BSP) with energy transfer in a bidirectional laser; in particular, the dissociation and annihilation of the BSP was triggered by control over intra-cavity polarization. Optical rogue waves were detected simultaneously, and the collision of breathers significantly increased the intensity of rogue waves, which is characteristic of the bidirectional laser. Further, the buildup dynamics of the BSP with nanosecond pulse separation and a breathing soliton molecule were observed. Multiple single soliton explosions and transient pulse splitting are distinct features of soliton molecule buildup compared to the soliton pair. These findings shed new insights into the multiple breather dynamics of nonlinear systems.