Veretenov N A, Fedorov S V, Rosanov N N
Vavilov State Optical Institute, 199034 St. Petersburg, Russia.
ITMO University, 197101 St. Petersburg, Russia.
Phys Rev Lett. 2017 Dec 29;119(26):263901. doi: 10.1103/PhysRevLett.119.263901. Epub 2017 Dec 28.
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.
我们预测在具有快速饱和吸收的均匀激光介质中存在一类新型的三维（3D）拓扑耗散光单组分孤子。它们由场消失的涡旋线形成的骨架是缠结，即(N_{c})个打结或未打结、相连或不相连的闭合线以及(M)条未闭合线，这些未闭合线穿过所有闭合线并终止于无限远的孤子边缘。它们是通过将二维激光孤子或其复合体绕具有拓扑电荷(M_{0})的未闭合无限涡旋线旋转后嵌入三维空间而产生的（(N_{c})、(M)和(M_{0})为整数）。通过这种结构传播，形成了“呼拉圈”孤子；其稳定性通过数值计算得到证实。对于所发现的孤子，所有涡旋线都具有单位拓扑电荷：闭合线的数量(N_{c}=1)和(2)（未打结、三叶结和所罗门结链接）；未闭合的涡旋线未打结且不相连，其数量(M = 1)、(2)和(3)。
