Singular knot bundle in light

Abstract

As the size of an optical vortex knot, imprinted in a coherent light beam, is decreased, nonparaxial effects alter the structure of the knotted optical singularity. For knot structures approaching the scale of wavelength, longitudinal polarization effects become non-negligible and the electric and magnetic fields differ, leading to intertwined knotted nodal structures in the transverse and longitudinal polarization components which we call a knot bundle of polarization singularities. We analyze their structure using polynomial beam approximations, and numerical diffraction theory. The analysis reveals features of spin-orbit effects and polarization topology in tightly-focused geometry, and we propose an experiment to measure this phenomenon.