Dynamics of three-dimensional spatiotemporal solitons in multimode waveguides

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.

Automated summary

In this study, we investigated the dynamics and stability of fundamental spatiotemporal solitons in multimode waveguides. Through a comparison of variational methods and numerical simulations, we found that solitons are stable at low energies but undergo wave collapse as the energy increases.