Measurement of a wavelength sized optical vortex knot

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.