  Deep sub-wavelength localization and displacement sensing of optical
nanoantennas have emerged as extensively pursued objectives in nanometrology,
where focused beams serve as high-precision optical rulers while the scattered
light provides an optical readout. Here, we show that in these schemes using an
optical excitation as a position gauge implies that the sensitivity to
displacements of a nanoantenna depends on the spatial gradients of the
excitation field. Specifically, we explore one of such novel localization
schemes based on appearance of transversely spinning fields in strongly
confined optical beams, resulting in far-field segmentation of left- and
right-hand circular polarizations of the scattered light, an effect known as
the giant spin-Hall effect of light. We construct vector beams with augmented
transverse spin density gradient in the focal plane and experimentally confirm
enhanced sensitivity of the far-field spin-segmentation to lateral
displacements of an electric-dipole nanoantenna. We conclude that sculpturing
of electromagnetic field gradients and intelligent design of scatterers pave
the way towards future improvements in displacement sensitivity.
