A topological charge selection rule for phase singularities

TL;DR

This paper investigates how discrete rotational symmetry influences the dynamics and decay of phase singularities, establishing a topological charge conservation rule and proposing a method to engineer vortex cluster configurations.

Contribution

It introduces a topological charge selection rule for phase singularities and presents a flexible method to engineer vortex cluster configurations based on symmetry considerations.

Findings

Identified a topological charge conservation rule.

Designed an effective model for vortex cluster dynamics.

Proposed a method to engineer specific vortex configurations.

Abstract

We present an study of the dynamics and decay pattern of phase singularities due to the action of a system with a discrete rotational symmetry of finite order. A topological charge conservation rule is identified. The role played by the underlying symmetry is emphasized. An effective model describing the short range dynamics of the vortex clusters has been designed. A method to engineer any desired configuration of clusters of phase singularities is proposed. Its flexibility to create and control clusters of vortices is discussed.