Controllable split polarization singularities for ultra-precise displacement sensing

The topic of optical precise displacement measurement has garnered significant attention and generated widespread interest recently. The use of optical singularity offers a potential solution for this purpose, although effectively manipulating the singularity in an ideal manner remains challenging. In this work, we propose a theoretical approach to achieve controllable position modulation of the C-point in the focal plane, whose spatial position can be easily modulated by adjusting the relative offset factor β and the offset angle α of an azimuthal polarization beam(APB), while the interval and orientation of the C-points can be flexibly regulated. Notably, the chiral polarization state undergoes a distinct reversal along the link-line connecting the two C-points, thereby providing a promising approach for accurate displacement sensing. To evaluate its sensing characteristics, the varying pattern of the scattered field intensity is monitored when sweeping a gold helix and nanoparticle along the link-line. The results of simulation quality index Q verify that the equilibrium factor of the scattering field possesses an obvious linear relationship with the displacement, signifying a precise sub-nanometric sensitivity.This research introduces new methods for the flexible control of polarization singularities in tightly focused fields,thereby enhancing the utilization of circular polarization properties near C-points for displacement sensing.These findings not only enrich the field of nanometer measurement technology but also pave the way for new avenues of research in this domain.