The aim of NOSTER has been to study the emergence of spatiotemporal localized structures, such as solitons, in multimode optical fibers (hereafter MMFs). The emergence and dynamics of solitary waves, or simply solitons, continuously attract tremendous attention. Solitons propagate without suffering any shape modification and emerge from the interplay between linear and nonlinear processes, which separately would cause the wave to decay. These solitary waves arise in a plethora of different natural contexts, including hydrodynamics, plasma and condensed matter physics, biology, and nonlinear optics, to cite a few. In nonlinear optics, these particle-like objects may emerge in nonlinear media due to the light confinement in either time or space, leading to temporal or spatial solitons respectively. In this context, light confinement may be related with the nonlinear dependence of the refractive index with the light intensity (optical Kerr effect), which yields to spatial self-(de)focusing and temporal self-phase modulation (SPM).
Spatial solitons form through a balance between natural diffraction-induced spreading on the one hand, and spatial self-focusing on the other hand. In nonlinear dispersive media, such as single-mode optical fibers (SMFs), SPM counteracts temporal broadening due to chromatic dispersion, leading to the formation of temporal solitons, which are essential for the understanding of mode-locking in fiber lasers.
The previous spatial and temporal effects can be coupled and occur simultaneously, such that dispersion and diffraction counteract Kerr nonlinearity at once, leading to light confinement in space-time, and therefore to the formation of a large variety of coherent spatiotemporal localized states. However, in bulk media these states normally undergo a wave collapse and therefore are unstable. A particular type of system which undergoes this type of emergent behavior are MMFs. In these wave-guided systems, the linear refractive index structure acts as spatial guiding potential and arrests the wave collapse, leading to a vast variety of new spatiotemporal phenomena, such as spatiotemporal solitons or light bullets (LBs), breathing behavior, and the formation of optical vortices, among many others.
In this regard, the main objectives (Ob) of NOSTER are the understanding of the formation and behavior of fundamental (Ob1) and vortex spatiotemporal solitons (Ob2). To do so, NOSTER was conceived to fulfill questions arising from the study of such states related to their origin, bifurcation structure, stability and how they interact. Regarding fundamental LBs, I have unveiled and characterize the dynamical regimes, study different mechanisms for arresting wave collapse instabilities and analyzed their collective behavior. In the case of vortex LBs I have found they exist for larger energy regimes than their fundamental counterparts.
