## 2 Principle and Simulation Results
It can be easily seen that under \(\gamma\
eq 0\), the equiphase lines of the SPP beams excited by the upper and lower nano-rectangular slot arrays (OP\({}^{\prime}\) and OQ\({}^{\prime}\)) are rotated counterclockwise with respect to the equiphase lines under \(\gamma=0\) by \(\beta\), which is given by:  
\[\beta=\arcsin\biggl{(}\frac{k_{o}\sin(\gamma)\cdot\cos(\theta)}{k_{spp}} \biggr{)}. \tag{1}\]  
Figure 1: (**a**) The schematic diagram of tunable and spin-controlled nondiffracting SPP-beam directional launching device, in which a nano-rectangular slot array structure is etched on a gold film. (**b**) The schematic diagram of the rectangle slot array and its parameters. The width and length of the nano-rectangular slot are \(W\) and \(L\). Figure 2: (**a,b**) The nondiffracting SPP-beam intensity distribution of a single-aperture array and two-aperture array when the incident light is LCP. (**c**) The transversal electric field intensity distributions at \(x=\pm 13\) μm for the incident polarization are LCP and RCP. (**d**) The intensity distribution of the nondiffracting SPP beam in the case that there exists a cylinder obstacle. In this case, the main lobe of the nondiffracting SPP beam will be located on the red dashed line of Figure 3, which has an angle \(\beta\) with the x-axis. Figure 4a-d shows the results of modulating the SPP-beam launching direction by changing \(\gamma\). We can observe that when the inclined angle is \(5^{\circ}\) and \(-5^{\circ}\), the main lobe of the nondiffracting SPP beam is inclined without destroying its nondiffracting property, and the inclined angle of the nondiffracting SPP beam is approximately \(5^{\circ}\), which shows good agreement with the calculation result of the equation. We then further extracted the transversal electric field intensity distributions at \(x=\pm 13\)\(\upmu\)m when the incident light is LCP and RCP, respectively. The results are shown in Figure 5a. The figure shows that, despite the change in the inclined angle of the incident light, the intensity distribution curves still approximate the cosine-Gauss distribution and have good consistency for the incident light with different polarization states. However, because the aperture array is not symmetrical with the x-axis, both the intensity and transverse displacement of the main lobe maximum strength point under \(\gamma=5^{\circ}\) are slightly  
Figure 4: **(a,b)** The nondiffracting SPP-beam intensity distribution under inclined angle \(\gamma=5^{\circ}\) when the incident light is LCP and RCP, respectively. **(c,d)** The nondiffracting SPP-beam intensity distribution under inclined angle \(\gamma=-5^{\circ}\) when the incident light is LCP and RCP, respectively. Figure 3: The vector relationship of the \(k_{int}\) and the nondiffracting SPP-beam launching direction (the inset shows the incident light direction). The line segments OP and OQ, respectively, are the equiphase lines of the SPP beams excited by the upper and lower nano-rectangular slot arrays when \(\gamma=0\); the line segments OP\({}^{\prime}\) and OQ\({}^{\prime}\), respectively, are the equiphase lines of the SPP beams excited by the upper and lower nano-rectangular slot arrays when \(\gamma\
eq 0\); OF is the nondiffracting SPPs beam launching direction when \(\gamma=0\); and OF\({}^{\prime}\) is the nondiffracting SPP-beam launching direction when \(\gamma\
eq 0\). larger than those under \(\gamma=-5^{\circ}\). The self-healing ability of the main lobe of the SPP beam is also demonstrated by setting a gold cylinder with a radius of 150 nm at the point of coordinate (13 \(\upmu\)m, 0.94 \(\upmu\)m) under RCP incidence and inclined angle \(\gamma=5^{\circ}\) (see Figure 5b). Hence, it is demonstrated that, in practical applications, the SPP launching directions can be effectively regulated by controlling \(\gamma\) without destroying its nondiffracting property.