  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.
