Topological Vortex and Knotted Dissipative Optical 3D Solitons Generated by 2D Vortex Solitons

Area of Science:

• Nonlinear Optics
• Topological Photonics
• Laser Physics

Background:

• Dissipative optical solitons are crucial for understanding light-matter interactions in lasers.
• Topological concepts offer new paradigms for robust optical phenomena.
• Previous research focused primarily on lower-dimensional or non-dissipative systems.

Purpose of the Study:

• To predict a new class of three-dimensional (3D) topological dissipative optical one-component solitons.
• To investigate the complex vortex line structures and topological properties of these solitons.
• To explore their generation mechanism and stability in homogeneous laser media.

Main Methods:

• Theoretical prediction of 3D topological dissipative optical solitons.
• Numerical simulations to confirm the stability of the predicted soliton structures.
• Analysis of vortex line skeletons, including knotting, linking, and topological charge.

Main Results:

• A new class of 3D topological dissipative optical solitons in homogeneous laser media with fast saturable absorption is predicted.
• Soliton skeletons consist of tangles of closed and unclosed vortex lines, exhibiting complex topological configurations (knotted, linked, unknotted, unlinked).
• Stable "hula-hoop" soliton propagation is confirmed numerically, with vortex lines possessing unit topological charge.

Conclusions:

• The study predicts novel 3D topological dissipative optical solitons with intricate vortex line tangles.
• These solitons demonstrate topological robustness and stability, offering new possibilities for optical control.
• The findings open avenues for exploring complex topological structures in dissipative optical systems.