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

• Published in: Physical review letters 2017-12, Vol.119 (26), p.263901-263901, Article 263901
• Main Authors: Veretenov, N A, Fedorov, S V, Rosanov, N N
• Format: Article
• Language: English
• ISSN: 0031-9007; 1079-7114
• DOI: 10.1103/PhysRevLett.119.263901

We predict a new class of three-dimensional (3D) topological dissipative optical one-component solitons in homogeneous laser media with fast saturable absorption. Their skeletons formed by vortex lines where the field vanishes are tangles, i.e., N_{c} knotted or unknotted, linked or unlinked closed lines and M unclosed lines that thread all the closed lines and end at the infinitely far soliton periphery. They are generated by embedding two-dimensional laser solitons or their complexes in 3D space after their rotation around an unclosed, infinite vortex line with topological charge M_{0} (N_{c}, M, and M_{0} are integers). With such structure propagation, the "hula-hoop" solitons form; their stability is confirmed numerically. For the solitons found, all vortex lines have unit topological charge: the number of closed lines N_{c}=1 and 2 (unknots, trefoils, and Solomon knots links); unclosed vortex lines are unknotted and unlinked, their number M=1, 2, and 3.