## 3 Results and Discussion  
### Distribution of Electric Field around Tip without NP  
According to the expression of the Maxwell stress tensor, before calculating the trapping force applied on an NP, the distribution of the electric field induced by polarized near-field laser around the AFM probe tips should be lucubrated. Figure 2a shows the distributions of electric field in the \(x\)-\(z\) plane, which was produced by the VP laser coming from a SNOM probe. The incident laser propagated in the SiO\({}_{2}\) core and was reflected inward by the Al shell of the SNOM probe, so that the light formed an evanescent field along \(x\) direction and then irradiated the tip of AFM probe through the output aperture. Hence, an enhancement field with size down to subwavelength was excited due to the localized-mode surface plasma at the surface of metallic tip. This small, enhanced field evanescent field is essential for manipulating NP. Although there are some enhancement fields at the edge of the output aperture and the cover shell of SNOM probes, the intensities of these are relatively lower and far from NPs. So, the effects of these enhancement fields on the NP can be ignored. To gain deep insight into the influence of the wavelength and polarization direction of laser on field enhancement, the electric intensities of the point under the probe tip are calculated, as in Figure 2b. According to the results, the VP laser induces particularly stronger enhancement at the end of the probe tip compared to the HP laser. The highest intensity is \(\sim\)8.7 V/m for a wavelength around 717 nm. Although there is a peak at 511 nm for the HP laser, the intensity is just \(\sim\)0.5 V/m. Figure 2c,d  
Figure 1: Configurations of single probe and dual probe irradiated by polarized near-field laser coming from a SNOM probe. Front view (**a**) and slide view (**b**) of single probe; Dual probes with axis angles 90\({}^{\circ}\) (**c**) and 180\({}^{\circ}\) (**d**); (**e**) Time signal of normalized laser. presents the distribution of electric field in \(y\)-\(z\) plane excited by the VP and HP laser with a wavelength of 717 nm. Figure 2e,f also gives the corresponding line distributions of the electric field along the \(y\)-axis and \(x\)-axis, respectively. The white dash lines in Figure 2c,d show the line paths. Illumined by the VP near-field laser, the AFM probe has a symmetrical evanescent field at the extremity, with the highest intensity of \(\sim\)11 V/m. Moreover, the intensity of this enhanced field decays exponentially along all directions, so that it has an effective area with a diameter lower than 80 nm. Hence, this evanescent field provides a strong 3D gradient field to manipulate small NPs. If an NP is placed beneath the AFM probe, it could be trapped and moved towards the extreme intensity points of the gradient field. However, for the HP light, the enhancement exists at the two sides of the probe instead of at the end, as Figure 2d showed. The maximum intensity is only \(\sim\)1.8 V/m. So, this weak and dispersive electric field cannot form a stable trap for NPs. Besides, there is also a small area with lower intensity at the end of the tip, see Figure 2e. The electric field induced by the laser with different wavelengths also has similar distributions (see Figure S1 in Supplementary Materials). So, comparing the two schemes, it is found that the intensity and location of near-field around the AFM probe tip heavily depend on the polarization direction of the incident laser rather than wavelength. If the polarization direction is parallel to the axial direction of the AFM probe, the near-field laser will induce an intensive nanoscale evanescent field, which is suitable for the stable trapping of NPs. However, when the polarization direction is perpendicular to the axial direction of the AFM probe, the evanescent exerted is incapable of desirable manipulation.