Distributed Kerr-lens mode locking based on spatiotemporal dissipative solitons in multimode fiber lasers

We introduce a mechanism of stable spatiotemporal soliton formation in a multimode fiber laser. This is based on spatially graded dissipation, leading to distributed Kerr-lens mode locking. Our analysis involves solutions of a generalized dissipative Gross-Pitaevskii equation. This equation has a broad range of applications in nonlinear physics, including nonlinear optics, spatiotemporal pattern formation, plasma dynamics, and Bose-Einstein condensates. We demonstrate that the careful control of dissipative and nondissipative physical mechanisms results in the self-emergence of stable ($2+1$)-dimensional dissipative solitons. Achieving such a regime does not require the presence of any additional dissipative nonlinearities, such as a mode locker in a laser, or inelastic scattering in a Bose-Einstein condensate. Our method allows for stable energy (or ``mass'') harvesting by coherent localized structures, such as ultrashort laser pulses or Bose-Einstein condensates.