The NOSTER project is about unveiling the dynamics and features of spatiotemporal coherent structures emerging in multimode optical fibers, such as spatiotemporal solitons, also known as light bullets. Solitons are particle-like states, emerging due to a double balance between linear and nonlinear processes, that maintain their shape while propagating in a medium. Solitons arise in a large variety of different natural media, ranging from hydrodynamics and plasma physics, to nonlinear optics and biology. In nonlinear optics, the emergence of solitons is related to the light confinement in time or space. One basic example of a system yielding to this type of state are single mode optical fibers, where the Kerr nonlinearity counteracts the spreading of the light produced by the chromatic dispersion. In multimode optical fibers, temporal and spatial effects, such as chromatic dispersion and diffraction, can occur simultaneously and counteract the Kerr nonlinearity, leading to the space-time confinement of light, and therefore, to the formation of much more complex coherent structures. My approach in this project is to predict and analyze the generation of localized spatiotemporal states, in particular light bullets and vortices, from a pattern forming and bifurcation theory perspective.
Applying advanced analytical and numerical methods, I will first elucidate the origin of light bullets, characterizing their dynamics and bifurcation structure. In a second step, I will study the dynamical properties of optical vortices and the potential transition to optical turbulence. In both cases, their interaction dynamics, and the influence of high-order effects and losses will be analyzed. The understanding of such complex dynamics is crucial, and it will enable a tremendous breakthrough in many technological areas such as high-power multimode fiber lasers, optical communication systems, and a large variety of other industrial and biomedical applications.
This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 101023717
Publications related with the project
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.
F. Mangini, M. Ferraro, Y. Sun, M. Gervaziev, P. Parra-Rivas, D. S Kharenko, V. Couderc, S. Wabnitz, Modal phase-locking in multimode nonlinear optical fibers, Optics Letter, 48, 3677-3680 (2023). Link
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.
M. Zitelli, V. Couderc, M. Ferraro, F. Mangini, P. Parra-Rivas, Y. Sun, and S. Wabnitz, Spatiotemporal mode decomposition of ultrashort pulses in linear and nonlinear graded-index multimode fibers, Photonics Research 11 (5), 750-756 (2023). Link
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.
Y. Sun, P. Parra-Rivas, M. Ferraro, F. Mangini, M. Zitelli, R. Jauberteau, F. R. Talenti, S. Wabnitz, Dissipative Kerr solitons, breathers, and chimera states in coherently driven passive cavities with parabolic potential, Optics Letters, 47, 6353-6356 (2022). Link
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.