## 3 Results and Discussion
### Distribution of Electric Field around Tip without NP
Besides metallic tips, laser-irradiated structures with nano-gaps, like nano-antennas, nano-holes, and nano-bowties, are also advance methods to aro  
Figure 2: Single probe irradiated by polarized near-field laser coming from an SNOM probe. (**a**) Distributions of electric field around two probes induced by VP laser; (**b**) Electric intensities at the end of probe tip versus wavelengths of incident VP and HP laser. Distributions of electric fields in \(y\)-\(z\) plane induced by VP laser (**c**) and HP laser (**d**) with wavelength of 717 nm; Corresponding distributions of electric field along \(y\)-axis (**e**) and \(z\)-axis (**f**). field by adjusting the distance of the gap [22; 23; 25]. Considering that the probes of AFM-based or SEM-based manipulation systems can be located and moved with nanoscale or even sub-nanoscale resolution, nano-gaps can also be acquired by two metallic tips. So, in this paper, optical manipulating based on two configurations of ODPs and CDPs (see Figure 1c,d) was further simulated. Similar to single probe, the calculation results of the dual probe show that the wavelength of the laser mainly influences the maximum intensity of enhancement fields instead of the distribution. So, VP and HP lasers with a wavelength of 717 nm were taken as examples to explore the electric field around ODPs and CDPs. Likewise, the distances between two tips of all configurations were set to \(D_{3}\) = 10 nm. The distributions are shown in Figure 3. For ODPs irradiated by the HP laser, the maximum intensity is \(\sim\)11.6 V/m, which is approximately equal to the single probe irradiated by the VP laser. According to the simulation results of the single probe irradiated by the VP and HP lasers in this paper and other previous works [26], the increase of the angle between the axis of the AFM probe and the polarized direction of the laser can lead to a decrease in enhancement intensity. Hence, if there was only one probe in the configuration of ODPs, the maximum intensity would be lower than the single probe irradiated by the parallel polarized laser (see Figure S2), because the probe has an angle with the polarized direction of the incident laser. However as the nano-gap between two nano-structures can improve the enhancement of the near-field [25], the small gap of the ODP helps to enhance the intensity of the optical field further. So, these negative and positive effects both result in the similar maximum intensity of the ODPs irradiated by HP laser comparing to the single probe irradiated VP laser, which also proves the capacity of dual probes to enhance the near-field. Moreover, the enhanced field, which is aroused between two metallic tips, has a larger high intensity area than the single probe. When the source changes to the VP laser, the enhanced field is divided into two parts located at the bottom of every probe, which is more like that of a single probe, as shown in Figure 3b. However, the intensity is lower (the maximum is \(\sim\)5.4 V/m). The decrease in intensity can also be attributed to the existing angles between the polarization direction of the laser and axial direction of AFM probes. If using CDPs, the HP laser induces an effective electric field for trapping a NP, since the axes of both probes are parallel to the laser polarization direction. The distribution of the electric field in Figure 3c also demonstrates that this configuration can provide the strongest enhancement and corresponding largest area with higher intensity (maximum: \(\sim\)18.4 V/m) than the others. However, the VP laser cannot produce a trap for manipulation, due to the dispersive electric field presented in Figure 3d. So, according to the electric distribution, three configurations, including ODPs irradiated by HP and VP lasers and CDPs by the HP laser, are suitable candidates for stable manipulation. Since the size of the nano-gap has a significant effect on the enhancement, the electric fields of three desirable configurations with different probe distances \(D_{3}\) were calculated.