Real-time observation of spatial-spectral oscillatory dynamics in spatiotemporal soliton molecules

We observe the spatial-spectral oscillations dynamics of spatiotemporal soliton molecules (STSMs) in real time, based on the acquisition of two distinct fixed spatial points on the output speckle grains (SGs) of a spatiotemporal mode-locked (STML) fiber laser. The spatial energies and the mapped spectral center of mass by dispersive Fourier transform of STSMs at two SGs show complementary dual-periodic oscillations. The observed phenomena originate from the gain competition and the gain saturation effects between distinct transverse modes, as well as the linear and nonlinear phase shift variations between distinct dominant modes. Numerical simulations validate the experimental results. This study extends our understanding of the complex STSMs dynamics in STML fiber lasers and provides what we believe to be new insights to explore the underlying spatiotemporal nonlinear interactions.