Nonlinear spatiotemporal light bullets: origin and stability

Project Information

NOSTER

Grant agreement ID: 101023717

DOI

10.3030/101023717

Project closed

EC signature date 5 March 2021

Start date 1 November 2021

End date 31 October 2023

Funded under

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Total cost

€ 171 473,28

EU contribution

€ 171 473,28

Coordinated by

UNIVERSITA DEGLI STUDI DI ROMA LA SAPIENZA
Italy

Periodic Reporting for period 1 - NOSTER (Nonlinear spatiotemporal light bullets: origin and stability)

Reporting period: 2021-11-01 to 2023-10-31

Summary of the context and overall objectives of the project

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.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

The work performed during the whole duration of NOSTER has covered the main objectives of the project. These include:

- The formation of spatiotemporal solitons in waveguides with parabolic potentials in different regimes of operation.
- The characterization of their stability regimes and destructive instabilities such as wave collapse.
- The exploration of different mechanisms for arresting such instabilities and guaranteeing the robustness of such solitons. This mechanism is related to different physical processes such as high-order dispersion effects, competing nonlinearities and dissipative effects.
- Characterization of spatiotemporal solitons in dissipative systems where the continuous inflow/outflow of energy is inherently present.
- The formation of vortex solitons and how they relate to the fundamental ones.
- Unveiling the collective behavior of fundamental and vortex states, their interaction of formation ordered arrangements.

To do so, I have considered an approach based on dynamical systems and bifurcation theory which combines synergically advanced analytical and numerical techniques used for solving nonlinear problems.

The main results I obtained shows that:

- Spatiotemporal solitons undergo wave collapse below the theoretical limit predicted through variational approaches.
- This instability can be partially suppressed through different high-dispersion effects. As a result, solitons can be stabilized within larger energy intervals. Moreover, these effects provide extra degrees of freedom for controlling and manipulating such states.
- High-order nonlinearities, such as quintic self-defocusing ones, are another way of stabilizing fundamental solitons. In this regard, I have found that this new term leads to spatiotemporal solitons bistability where two different states coexist for the same energy.
- Regarding the effects of dissipation, I have discovered that spatiotemporal parabolic potential leads to the suppression of wave collapse, and thus to the stabilization of high-order spatiotemporal dissipative solitons in optical cavities.
- Vortex spatiotemporal 3D solitons are also stabilized when considering spatial parabolic potentials, and they exist at higher energy regimes than the fundamental ones. Indeed, by increasing their vorticity, so does the existence regime where it can be generated. Here, high-order effects have a positive impact on their stability and robustness.
- Regarding their collective behavior, spatiotemporal solitons may interact in different dynamical fashions and eventually lead to ordered arrays that I am currently investigating.

All these results have been disseminated in 9 international conferences and workshops as contributed, main author and invited speaker. Moreover, I have participated in University Open Days of my host department, and I have popularized my field of research giving a talk at high school level in the Spanish School of Rome. Besides, all my results and publications are presented on my webpage.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

By understanding the formation and stabilization of fundamental and vortex spatiotemporal solitons, their connection, and the procedures for their control, I have advanced the discipline of nonlinear waves and optics beyond the former state of the art, where dynamics of such states were highly unexplored.

Potentially, the results of NOSTER will provide a better understanding of the physics behind multimode waveguides and prompt the control and manipulation of high-dimensional solitons for structured light applications, with ramifications in different technological areas such as laser physics telecommunications. Furthermore, these results may find matter analogues in the context of quasi one-dimensional Bose-Einstein condensates.

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