# Simulation Study of Dynamic Rotation and Deformation for Plasmonic Electric Field-Skyrmions
## 3 Results and Discussions  
### Dynamic Rotation for Skyrmions  
Stable topological optical skyrmions can be constructed by plasmonic standing wave interference. Considering the sub-wavelength characteristics of electric field skyrmions, implementing their rotational properties leads to more interesting discoveries and broader prospects for applications in nano-photonics. We control the phase difference of the light sources as a variable, and by adjusting the phase difference in different directions, we have achieved a gradual counterclockwise rotation of the skyrmion from horizontal to small-acute-angle tilted, further increasing the inclination, and finally fully rotating it to a right-angled tilted position. Throughout the entire process, the skyrmion rotates precisely within the subwavelength local range, maintaining its original topological shape (with the same deformation). Figure 2: Multi-arc symmetric slit array excited by 12 incident beams with varying phases, as shown in the three-dimensional view in (**a**). The slit array is indicated by red shading distributed on the Ag surface, the distance from the outer side to the center of the structure \(D\) by yellow dashed arrows, and the distance from the inner side of each arc-shaped slit to the center of the structure \(D\) by green dashed arrows, as shown in the top view in (**b**). The distributed phase of the SPP waves is indicated by yellow, standard Néel-type optical skyrmions before phase modulation in (**c**). The polarization direction of sources is indicated by blue arrows in (**a**,**c**), and the incident direction of sources is indicated by purple. Figure 3 shows the process of dynamic rotation of the skyrmion. From the perspective of the squared electric field strength, the middle bright spot has a higher electric field strength, while the surrounding bright spot has a lower electric field strength. The complete morphology of the skyrmion and topological domain walls is inside the blue dashed lines. The direction of the yellow dashed arrow indicates that the rotation characteristics are sensitive to the positions of the adjusted slits. We did not consider magnetic field vectors here because they do not meet the conditions for SPP to form skyrmions. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Rotation State** & **Adjusted Values of Phase** & **Positions of Slits** \\ \hline Horizontal state & \(\varphi_{4}=0.5\pi,\varphi_{\pi}=0\), & 4 \\ \((\theta_{r}=0 rad)\) & \((n=1,\ldots,12,n\
eq 4)\) & \\ Small-acute-angle tilted state & \(\varphi_{3}=0.5\pi,\varphi_{\pi}=0\), & 3 \\ \((\theta_{r}=\
icefrac{{\pi}}{{rad}})\) & \((n=1,\ldots,12,n\
eq 3)\) & \\ large-acute-angle tilted state & \(\varphi_{2}=0.5\pi,\varphi_{\pi}=0\), & 2 \\ \((\theta_{r}=\
icefrac{{\pi}}{{rad}})\) & \((n=1,\ldots,12,n\
eq 2)\) & \\ Right-angled tilted state & \(\varphi_{1}=0.5\pi,\varphi_{\pi}=0\), & 1 \\ \((\theta_{r}=\
icefrac{{\pi}}{{rad}})\) & \((n=1,\ldots,12,n\
eq 1)\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The incident light phase value and slit position correspond to different skyrmion rotation states. Figure 3: _Cont._  
The detailed parameters corresponding to skyrmion rotation states are presented in Table 1. It is worth noting that the parameter \(\mathbf{\theta_{r}}\) of rotation states indicates the angle between the yellow dashed arrow and the green dashed arrow in Figure 3a-d. The angle between the blue dashed arrow in Figure 3e-h and the direction of the positive X-axis is \(\mathbf{\theta_{p}}\), which is the parameter of the direction of the position vector of the regulated slits. We selected slits in different orientations to control the phase difference, which will be crucial. In addition, according to our simulation results, rotations occur in all 12 directions in the two-dimensional plane.