## 3 Results and Discussion
### Trapping Force of an NP in Enhanced Near-Field  
To reveal the manipulation ability of near-field induced by the combination of the SNOM probe and AFM probe, the electric field and trapping force exerted on an NP were calculated further. According to the above results, simulations of the single AFM probe irradiated by the VP laser from an SNOM probe were performed first. Figure 5a shows the distribution of the electric field when a silver NP with diameter \(d\) = 70 nm was added into the near-field (the distance between the probe tip and the NP was \(D_{1}\) = 10 nm). Similar to the electric distribution of AFM probe without the NP, there is still an evanescent field between the AFM tip and the NP. However, the maximum intensity increases to 19.1 V/m, which is higher than the intensity without an NP. This strong enhancement with nanoscale size will apply an effective force on the silver NP. The intensity of the near-field at the end of the tip, as shown in Figure 1b, demonstrates that the suitable wavelength is still about 717 nm due to the strongest enhancement. Sequentially, based on the Maxwell stress tensor, total trapping force exerted by the near-field was calculated. Figure 5c presents the total force induced by VP laser with wavelength in the range 300 nm-1200 nm. The variations of optical force and electric intensity are highly correlated. So, it can be concluded again that evanescent fields with strong enhancement are the essential conditions for optical manipulation. The maximum force is about 8.2 \(\times\) 10\({}^{-26}\) N (the value does not present the real value, due to the amplitude of the source laser being set to 1). To gain deeper insight into the orientation of the optical force, component forces along the \(x\), \(y\), \(z\) axes were plotted in Figure 5d. For the laser wavelength from 600 to 1200 nm, the component force along the \(z\) axis is dominant, so that the evanescent field at the tip can trap the NP and move it toward the AFM probe. Optical force per unit volume also confirms this conclusion, as shown in Figure 5e. The red vectors, only at the top of the silver NP, mean that a large force along the \(z\) direction is applied. However, in other directions, the disorder and the weak force are incapable of nano-manipulation, as the blue vectors show. So, the forces aroused by the near-field provide a possibility for the expected manipulation of an NP, while controlling the movement of the AFM and SNOM probes or the substrate. However, component force along the \(x\) axis is significant in the wavelength range 300-600 nm. This result can be attributed to forming the near-field around the aperture of the SNOM probe; see the distribution of the electric field for the 515 nm laser in Figure S3. These undesirable fields lead to disordered forces along the \(x\) and \(z\) directions, which will result in ineffective manipulation. So, avoiding the useless effect of the SNOM probe is also critical during manipulation. Then, the capacity of manipulation was evaluated further, varying particle size and the distance between the tip and NP. Figure S4 shows the total force versus wavelength. Here, Figure 6a,b gives the total force as functions of diameter \(d\) of an NP and the distance \(D_{1}\), when the wavelength is 717 nm. The optical force is linearly correlated with the diameter, which is similar to other optical trappings [29]. Since the effective area of the near-field is so small, the effect of diameter also reflects the edge shape of the nano-objects on manipulation. Apparently, the smaller curvature of the edge in the effective area causes higher enhancement and corresponding optical force, but the shape out of the effective area has limited influence. Figure S5 shows the larger trapping force of a nano-cube with a size of 70 nm greater than NPs, which confirms the conclusion. However, optical force decays exponentially as the distance increases. It is reasonable because the intensity of electric field also drops exponentially, as shown in Figure 2f.