KNOTTED OPTICAL VORTEX LINES IN NONLINEAR SATURABLE MEDIUM

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