The BEAMLOCKER project consisted of two main parts. The first part focused on soliton dynamics in multimode fibers. This included reviewing recent theoretical models and studying spatiotemporal multimode solitons. We examined popular theoretical models and experiments, compared the properties of step-index and graded-index multimode fibers, and reviewed several analytical approaches to understanding multimode soliton formation using generalized multimode nonlinear Schrödinger equation, the 3D+1 spatiotemporal nonlinear Schrödinger equation and 1D+1 representation. These efforts culminated in a book chapter:
• Y. Sun et al., Advances in Nonlinear Photonics, p. 27–55, Elsevier (2023).
Additionally, we introduced the Gaussian quadrature approach, the impact of linear mode coupling, and recent experimental results. This was expanded into a comprehensive review article currently under review. Next, we studied spatiotemporal solitons in graded-index fibers using the 3D spatiotemporal nonlinear Schrödinger equation. By employing a variational approach and various numerical simulations, we considered soliton scenarios under anomalous/self-focusing, normal/self-defocusing, and pure fourth-order dispersion regimes. It was found that high-order dispersion influences the existence of spatiotemporal solitons, leading to three journal publications.
The second part of the project concentrated on single-mode and multimode fiber ring resonators using the continuation method and linear stability analysis. We first examined spatiotemporal soliton formation in multimode fiber cavities, finding that these states are typically unstable but can be stabilized with a spatiotemporal potential. Linear stability analysis and numerical simulations confirmed the stability of these high-order states and 3D breathers, with results published in Physical Review Letters:
• Y. Sun et al., Phys. Rev. Lett. 131, 137201 (2023).
By considering symmetry considerations, we reduced higher-dimensional models into a single 1D model with a dimension parameter, facilitating the continuation analysis of system dynamics in 1D, 2D, and 3D systems. The findings were published in Chaos, Solitons & Fractals:
• Y. Sun et al., Chaos Solit. Fractals 183, 114870 (2024).
Recognizing that a parabolic potential can stabilize 3D solitons, we also investigated 1D temporal solitons with a parabolic potential generated by internal phase modulation in ring resonators. This led to three productive research articles:
• Y. Sun et al., Chaos Solit. Fractals 176, 114064 (2023).
• Y. Sun et al., Opt. Lett. 48, 5403 (2023).
• Y. Sun et al., Opt. Lett. 47, 6353 (2022).
