Polarization-engineered displacement sensing of nanoparticles via tracking scattering C-points.

We propose a polarization-engineered displacement sensing scheme that connects the three-dimensional polarization landscape of a tightly focused field with the scattering C-points of an embedded dipolar scatterer. The particle's displacement is encoded as angular shifts of the C-points in the far field. To engineer local polarization states, we first use circularly polarized light to localize the spin-rotating polarization landscape at the focal center, yielding a sensitive, nearly linear evolution of C-points. Furthermore, by employing structured light, we confine the polarization ellipticity variation to the focal center and enable active tuning of displacement sensitivity. Our work demonstrates that engineering of focal-field polarization landscapes via incident light modulation enables tunable high-sensitivity displacement measurement, with potential applications in precision metrology and nanoscale optical sensing.