Аннотация:
In last 50 years, a significant progress was noticed in medicine, communications
and entertainment. Such advanced development of these fields was directly related to
ability of controlling light. Photonics is exactly about this ability. At the present time,
photonics is walking together with a fundamental physical concept, optical soliton.
Optical solitons are shape-preserving laser beams. They are found potentially useful
in data transmission, which is very significant nowadays. Hence, research in the field
of optical solitons is still a vital issue.
When optical soliton is perturbed in a specific manner, there appear zeros of
optical field around the soliton, which are called optical vortices. In general optical
vortices are lines in space. Hence, we might expect them to become knotted.
Knotting optical vortices around perturbed seems spontaneous and cannot be directly
predicted. To explain this phenomenon, a similar system is constructed based on perturbation
theory. In this system, however, we have a mathematical problem which
yet lacks a full understanding. We address this problem by introducing concepts from
three disciplines: laser physics, knot theory and singular optics.
We believe that understanding the mechanism underlying spontaneous knotting
of optical vortices will be a step forward in other systems too, such as quantum
turbulence in superfluids and formation of optical vortices around other types of
optical solitons.