Kerr beam self-cleaning under different initial modal excitation conditions in the anomalous dispersion regime of a graded-index multimode fiber

We investigated the phenomenon of Kerr beam self-cleaning (KBSC) under a variety of initial modal excitation conditions in the anomalous dispersion region of a graded-index multimode fiber (GRIN-MMF) by solving the generalized multimode nonlinear Schrodinger equation (GMMNLSE). Our results clearly indicate that the phenomenon of beam self-cleaning is highly dependent on the initial modal excitation conditions, and the power threshold (Pth) th ) required for beam self-cleanup varies depending on the initial modal energy distribution conditions considered. We also show that such beam self-cleanup does not occur for any arbitrary initial modal excitation, even at the highest values of input power launched. The temporal and spectral analysis reveals that a spatiotemporal soliton formed initially at a certain power value becomes unstable, thereby shedding dispersive waves and a number of multimode solitons through the fission process, and the nonlinear energy exchanges among the constituent modes lead to a self-cleaned multimode beam. Moreover, we also show that the use of the fiber of longer length permits us to substantially reduce the power threshold (Pth) th ) required to observe beam self-cleaning. Our results realizing the Kerr beam self-cleaning effect with femtosecond pulses in the anomalous dispersion regime of a GRIN-MMF offer innovative and interesting perspectives for the potential extension of the concept of thermalization of classical nonlinear waves to the spatiotemporal domain and may pave the way for a better understanding and control of various novel nonlinear spatiotemporal phenomena in multimode platforms, in developing the next generation of tunable, broadband high-power lasers with nearly single-mode emission.