Measurement of a wavelength sized optical vortex knot

TL;DR

This paper reports the first measurement of an optical vortex knot with a size close to the wavelength, demonstrating potential for miniaturized optical structures and observing vortex reconnection phenomena.

Contribution

It presents the first experimental measurement of a wavelength-sized optical vortex knot, specifically a trefoil, and explores vortex line reconnection at this scale.

Findings

Measured a 1.99 λ long optical vortex knot in a sub-2 λ volume.

Observed vortex reconnection and transition to vortex loops.

Demonstrated control of vortex topology at wavelength scale.

Abstract

In the past decade, optical vortex knots with axial dimensions on the order of $10^2-10^5$ wavelengths ($\lambda$) have been implemented in the laboratory. However, many potential applications require a drastic reduction on the the size of these knots to the order of $\lambda$. In this work, we show the first measurement of an optical vortex knot (trefoil) with an axial length of $1.99\, \lambda$ contained within a volume ($x\times y\times z$) of $1.90\times 2.19\times 1.99 \, \lambda^3$. Prior to focusing, the laser light is linearly polarized ($x$, horizontal) and we observe the knot in the dominant $x$ polarization component of the tightly focused field. We also observe the transition of the trefoil knot to a couple of vortex loops via reconnection of the vortex lines as we change the spatial scale of the angular spectrum representation of the field.