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. 

The NOSTERDIS project is about unveiling the dynamics, stability and features of three-dimensional spatiotemporal high-order dissipative solitons arising in externally driven multimode Kerr cavities. Based on the results obtained in my Marie Curie project NOSTER, regarding conservative systems, NOSTERDIS introduces dissipation and gain as key elements, to move substantially beyond the paradigm of the NOSTER project. 

Dissipative solitons appear due to a double equilibrium between diffraction, chromatic dispersion, and Kerr nonlinearity (already present in single pass conservative systems) on the one hand, and the counterbalance between energy dissipation and external driving, inherent to the optical cavity, on the other hand. In comparison with conservative spatiotemporal solitons, whose observation as steadily propagating states remains elusive (due to different types of spatiotemporal instabilities), dissipative ones are more robust, and therefore, easier to excite experimentally. 

My approach in this project is to perform a detailed bifurcation analysis of these multidimensional dissipative states, based on dynamical systems theory. Applying advanced analytical and numerical methods, I will first characterize the dynamical properties of these states in different regimes of operation and unveil the bifurcation structure of radially symmetric and asymmetric solitons. Preliminary results show that, despite their robustness, dissipative spatiotemporal solitons may also undergo certain instabilities such as wave collapse. In the second stage of this project, I will seek for new stabilization mechanisms based on high-order dispersion effects and nonlinearities. The understanding of these states is crucial and may enable a tremendous breakthrough in different technological areas such as the generation of new types of multidimensional Kerr frequency combs.