## 3 Results and Discussion
### Trapping Force of an NP in Enhanced Near-Field
So, trapping ability is sensitively dependent on some critical factors, like the wavelength of the laser, the size and shape of objects, and the distance between probes and objects, which should be investigated further with experiments. The simulations of trapping force with the single AFM probe have proven the feasibility of nano-manipulation using a polarized near-field laser. As a laser-irradiated dual probe can also arouse the effective electric-field, trapping forces of three configurations of the dual probe (ODPs irradiated by the HP laser, ODPs irradiated by the VP laser, and CDPs irradiated by the HP laser) were calculated to explore the excellent methods of enhancement. To make a comparison with the single probe, the distance between tips and NP was set to \(D_{3}=10\) nm, as shown in Figure 1c. Figure 7 gives the component forces along \(x,y,z\) axis applied on the silver NP versus the wavelength of the incident laser and corresponding  
Figure 5: Trapping force of an NP using single probe irradiated by VP laser. (**a**) Distributions of electric field in \(y\)-\(z\) plane; (**b**) Electric intensities at the end of probe tip versus wavelength of incident laser; Total optical force (**c**) and component forces along \(x,y,z\) axis (**d**) applied on the NP versus wavelength of incident laser; (**e**) Distributions of optical forces per unit volume in vector form for wavelength 717 nm. Figure 6: Total trapping force induced by VP laser with wavelength 717 nm as functions of some critical factors. (**a**) Diameter of NP; (**b**) Distance between the tip and the NP. distribution of electric field when the \(z\) component forces are at their maximum. For the ODPs and CDPs irradiated by the HP laser, the max forces along the \(z\) direction are about \(2.6\times 10^{-26}\) N and \(3.0\times 10^{-26}\) N respectively when the wavelengths are 964 nm and 744 nm. These forces are even lower than the single probe irradiated by the VP laser, because the enhancement fields are located between two tips of AFM probes rather than between the tips and the NP, as the bottom diagrams of Figure 7a,c show. So, even the enhancement intensities of these two schemes with or without NP are high enough, but the trapping force also heavily depends on the location of the evanescent field. Figure 7b presents a preferred manipulation scheme with maximum trapping force \(\sim\)11.3 \(\times\) 10\({}^{-26}\) N. Compared to the single probe irradiated by the VP laser (seeing Figure 5d), the dual probe has not only a higher trapping force, but also two suitable ranges of wavelengths around 717 nm and 646 nm. If trapping forces along the \(z\) direction larger than \(7\times 10^{-26}\) N were assumed to be effective for moving the NP, the suitable range wavelength of single probe would only be about 709-757 nm, but 600-767 nm for dual probes. Such a wide wavelength range gives a more stable trap and also enormous potential in the aspect of application. The bottom diagram of Figure 7b gives a deeper insight into the excellent manipulation capacity of the dual probe irradiated by the VP laser. The excellent manipulation ability can be attributed to the two metallic tips which provide a lager effect area of evanescent between the tips and the silver NP than the other two configurations. As the distance \(D_{2}\) between tips and NP also has an effect on the trapping force, Figure S6 presents the trapping force and electric field of a dual probe with a narrow gap \(\sim\)5 nm. The intensities of the optical force of all configurations increased as the distance decreases. No new effective peak of the force emerges, which means that the distance has little influence on the effective wavelength of the laser source for manipulation. Besides, a small gap can induce new evanescent fields between the tips and the NP for the dual probe irradiated by the HP laser, as the electric fields showed in Figure S6a,c.