Abstract:
In recent years, optical vortex knots have been the subject of active research. The knots
appear in various areas of physics and understanding the mechanism that is responsible
for their formation is a problem that extends beyond optics. However, due to their
spontaneous nature, it is impossible to predict their location. To unravel such a complex
problem, it is important to understand simpler systems that may allow for the generation
of vortex knots. In this thesis, I investigate the interference between the elliptical Gaussian
beam and the plane wave, as a result of which vortex rings appear. The rings are basically
the unknots, and the ellipticity allows for ring deformations. Consequently, at certain
parameters, the rings are able to reconnect. I identify two types of ring reconnections:
the reconnection that merges the rings together, and the self-crossing, where a loop-like
structure is formed from a single ring crossing itself. This study has the potential to
pinpoint specifics of the underlying mechanism that causes spontaneous knottings.