Generation and Research of n+m-type Group Velocity-unlocked Soliton Molecules within a Vector Fiber Cavity

In this paper, we report on the generation of $\mathrm{n}+\mathrm{m}$ type group velocity-unlocked vector soliton molecules in a passively mode-locked fiber laser based on carbon nanotubes (CNTs) with a 2+2-type vector soliton molecule as the initial condition. We adjust the parameters of gain saturation energy, small signal gain, intracavity birefringence, and cross-phase modulation through numerical simulation, and obtain different output results successively. Our investigations demonstrate that 2+1, 3+1, 4+1, 3+2-type group velocity-unlocked vector soliton molecules can be flexibly excited. These results will significantly enhance our understanding of soliton dynamics. They will also aid in elucidating the factors influencing the soliton distribution of vector solitons in the two orthogonal polarization directions, as well as the interactions between solitons.