Dimensional Insights into Dissipative Kerr Solitons

The ENLIGHTENS project focuses on investigating how dimensions influence the dynamics, stability, and characteristics of dissipative solitons (DS) within externally driven multimode Kerr cavities.

DS are fascinating localized structures that maintain their inherent shapes during propagation, owing to a delicate balance between the nonlinear Kerr effect, linear dispersion/diffraction, gain, and dissipative processes.

These states retain their temporal profiles along the propagation direction, forming temporal solitons, or preserve spatial profiles orthogonal to the propagation direction, leading to the emergence of spatial solitons.

Spatiotemporal solitons (STDS) represent a class of states that not only maintain spatial but also temporal profiles, exhibiting complex dynamics. However, such states tend to be vulnerable to wave collapse.

In this context, the ENLIGHTENS project seeks to explore the dimensional aspects affecting the stability of DS as dimensions increase and develop strategies to enhance their stability.

My preliminary findings suggest that phase modulation has the potential to expand the stability range within 1D temporal DS and could potentially stabilize 3D STDS.

Within this framework, I will further conduct a comprehensive bifurcation analysis of these 1D temporal dissipative states under various influences, laying the groundwork for further investigation.

Subsequently, I will focus on the transition of these 1D states by introducing spatial effects as a weak perturbation that later becomes a dominant factor in the system.

This methodology enables me to progressively tackle increasing complexity, facilitating the study of high-dimensional problems in a step-by-step fashion.

Understanding these states holds paramount significance and carries the potential for groundbreaking advancements across diverse technological domains, including the development of innovative multidimensional Kerr frequency combs.