We introduce a microscopy technique that facilitates the prediction of spatial features of chirality of nanoscale samples by exploiting the photo-induced optical force exerted on an achiral tip in the vicinity of the test specimen. The tip-sample interactive system is illuminated by structured light to probe both the transverse and longitudinal (with respect to the beam propagation direction) components of the sample's magnetoelectric polarizability as the manifestation of its sense of handedness, i.e., chirality. We specifically prove that although circularly polarized waves are adequate to detect the transverse polarizability components of the sample, they are unable to probe the longitudinal component. To overcome this inadequacy and probe the longitudinal chirality, we propose a judiciously engineered combination of radially and azimuthally polarized beams, as optical vortices possessing pure longitudinal electric and magnetic field components along their vortex axis, respectively. The proposed technique may benefit branches of science like stereochemistry, biomedicine, physical and material science, and pharmaceutics.
1) LOCAL FIELDS AT THE TIP-APEX AND SAMPLE LOCATION, EXCITED BY AN ARPBWe prove that under ARPB excitation (a superposition of two coaxial beams: an APB and an RPB with proper phase shift ) the local fields at the tip-apex and sample locations (both on the ARPB axis, see Fig. 1 of the paper) lack transverse components and we determine the longitudinal field components that include the near-field interaction. We consider the schematic of the problem in Fig. 1 of the manuscript and assume that the tip-apex and chiral sample are located at t z and s z , respectively, at a distance d from each other.