NOSTER

Abstract: We introduce a Hamiltonian approach to study the stability of three-dimensional spatiotemporal solitons in graded-index multimode optical fibers. Nonlinear light bullet propagation in these fibers can be described by means of a Gross–Pitaevskii equation with a two-dimensional parabolic potential. We apply a variational approach, based on the Ritz optimization method, and compare its predictions with extensive numerical simulations. We analytically find that, in fibers with a pure Kerr self-focusing nonlinearity, spatiotemporal solitons are stable for low energies, in perfect agreement with numerical simulations. However, above a certain energy threshold, simulations reveal that the spatiotemporal solitons undergo wave collapse, which is not captured by the variational approach. 

Abstract: In this work, we present a detailed study of the dynamics and stability of fundamental spatiotemporal solitons emerging in multimode waveguides with a parabolic transverse profile of the linear refractive index. Pulsed beam propagation in these structures can be described by using a Gross–Pitaevskii equation with a two-dimensional parabolic spatial potential. Our investigations compare variational approaches, based on the Ritz optimization method, with extensive numerical simulations. We found that, with a Kerr self-focusing nonlinearity, spatiotemporal solitons are stable for low pulse energies, where our analytical results find a perfect agreement with the numerical simulations. However, with progressively increasing energies, solitons eventually undergo wave collapse: this occurs below the theoretical limit, which is predicted within the variational approach. In a self-defocusing scenario, a similar trend is found, where the good agreement persists for low energies. For large soliton energies, however, complex spatiotemporal dynamics emerge. 

Abstract: Spatial beam self-cleaning, a manifestation of the Kerr effect in graded-index multimode fibers, involves a nonlinear transfer of power among modes, which leads to robust bell-shaped output beams. The resulting mode power distribution can be described by statistical mechanics arguments. Although the spatial coherence of the output beam was experimentally demonstrated, there is no direct study of modal phase evolutions. Based on a holographic mode decomposition method, we reveal that nonlinear spatial phase-locking occurs between the fundamental and its neighboring low-order modes, in agreement with theoretical predictions. As such, our results dispel the current belief that the spatial beam self-cleaning effect is the mere result of a wave thermalization process. 

Abstract: We develop a spatiotemporal mode decomposition technique to study the spatial and temporal mode power distribution of ultrashort pulses in long spans of graded-index multimode fiber, for different input laser conditions. We find that the beam mode power content in the dispersive pulse propagation regime can be described by the Bose–Einstein law, as a result of the process of power diffusion from linear and nonlinear mode coupling among nondegenerate mode groups. In the soliton regime, the output mode power distribution approaches the Rayleigh–Jeans law.

We analyze the stability and dynamics of dissipative Kerr solitons (DKSs) in the presence of a parabolic potential. This potential stabilizes oscillatory and chaotic regimes, favoring the generation of static DKSs. Furthermore, the potential induces the emergence of new dissipative structures, such as asymmetric breathers and chimera-like states. Based on a mode decomposition of these states, we unveil the underlying modal interactions.