Oral presentation

Session Information

Location: Science and Cultural Center - FORTH
Day: 2. Thursday 17th
Time: 09:30-09:50
Chairperson: to be announced…

Presentation Details

Presentation Type: Oral presentation
Title: Catastrophes in topological transformations of optical vortex rings
Abstract: Optical vortex rings – loops of darkness with singular phase at the core – are fascinating topological objects that are fundamental to turbulent systems. In our recent studies, we have proposed a theoretical model consisting of a Gaussian beam and a plane wave, which can generate stable vortex rings. Continuously varying one of the control parameters (for example, the relative phase) changes the number of rings through a series of topological transformations – events that affect the system's global topology [1]. We have also shown that breaking the symmetry does not hinder the formation of vortex rings; instead, it leads to more complex ring configurations and unlocks new types of topological events which were not possible before [2]. We found that, beyond a certain degree of asymmetry, even a small additional variation can cause unexpected and dramatic changes in the types of topological transformations observed in the system. Such abrupt changes are a fundamental focus of catastrophe theory, a branch of bifurcation theory introduced by R. Thom and pioneered by C. Zeeman. Catastrophe theory studies the degenerate critical points of a potential function that can appear or disappear as the parameters are varied. If the first and subsequent derivatives of a critical point are zero, they are referred to as singularities of a potential function. Mapping these singularities onto the parameter space reveals one of the well-defined patterns called the seven elementary catastrophes. Catastrophes are well established in optics; in fact, the bright caustic patterns generated by curved surfaces assume the form of one of the seven elementary catastrophes, regardless of the precise geometry of the surface. The connection between catastrophes and optical vortices is also well established: near these bright caustics, arrangements of optical vortices can be found, forming a skeleton that supports points of diverging intensity. In this work, we demonstrate that catastrophes may arise in the space of control parameters through foldings of bifurcation lines corresponding to topological events. This approach offers a useful framework for describing the dynamics of complex topological transformations of vortex structures, with vortex rings serving as a representative example in our case. [1] A. Desyatnikov. Optics Express 31 (2023), 31955–31968 [2] Z. Kulchukova. Optics Letters 49 (2024) 915–918

Presenter

Ms Zhamila Kulchukova
Physikalisch-Technische Bundesanstalt | Germany

Authors

1. Kulchukova, Zhamila | Fundamentale Physik für Metrologie, Physikalisch-Technische Bundesanstalt, Braunschweig, Germany
2. Desyatnikov, Anton | Department of Physics, Nazarbayev University, Astana, Kazakhstan
3. Ferrando, Albert | {Affiliation3:value}