Knotted spacetime electromagnetic vortex unlinking and unknotting with vector and scalar reconnections and field twist compensation

TL;DR

This paper demonstrates that knotted spatiotemporal electromagnetic vortices can undergo topology-changing reconnections during free space propagation, with field twist compensation maintaining topological invariants.

Contribution

It introduces the concept of topology-changing reconnections in knotted electromagnetic vortices and explains how field twist compensates for linking number changes.

Findings

Reconnection events alter the topology of knotted vortices in spacetime.

Field twist compensates for changes in linking number, preserving certain invariants.

Total argument principle remains zero throughout reconnections.

Abstract

Optical vortex knots have been realized in monochromatic laser beams, but monochromatic fields are stationary and their topology is frozen. Here we show that knotted spatiotemporal vortices, whose phase singularities form closed loops in spacetime, undergo topology changing reconnections with free space propagation. When null lines of different vector components unlink, the electric spin, magnetic spin, linear momentum, and electromagnetic helicity densities, each built from a specific pair of field components, twist to exactly compensate the change in linking number. This compensation is enforced by the argument principle where the total for each component pair, combining mutual phase twist, geometric linking, and open-line threading, vanishes identically and remains exactly zero through all reconnection events.