Emergent Phenomena of Vector Solitons Induced by the Linear Coupling

Coupling between modes is crucial for generating coherent structures and spatiotemporal chaos in optical systems. In an ultrafast fiber laser with birefringence, the stable pulse is viewed as a vector soliton (VS) with two orthogonal modes nonlinearly coupled through the Kerr effect and gain/loss. However, the dynamics of a VS in the presence of linear coupling is unperceived despite linear coupling playing a significant role in various optical systems. Here, it is shown that a local linear coupling between polarization modes in lasers facilitates brand-new nonlinear states, including stationary, breathing, and chaotic VSs. The observed solitary states can be regarded as emergent phenomena when two particles (polarization modes) in a system have a simple interaction (linear coupling), which are ubiquitous in biology, chemistry, and complex systems. It is found that linear coupling is essential for sustaining the internal balance between two modes within the VS. Chaotic dynamics of VS emerge under weak linear coupling, while the two modes lose trapping due to the birefringence in the absence of linear coupling. This work can offer new insight into the two-mode nonlinear system and inspire research interests in the intelligent manipulation of ultrashort pulse lasers.