## 2 Principle and Simulation Results
The mesh precision of the FDTD model is 10 nm, the boundary condition is a perfect match layer (PML), and the simulation parameters are \(h=120\) nm, \(W=40\) nm, \(L=200\) nm, \(S=150\) nm and \(D=300\) nm. The value of the slant angle \(\theta\) is \(10^{\circ}\) and every column has 13 nano-rectangular slots. Obviously, in this aperture structure (the inset of Figure 2a), when the incident light is RCP, the SPP beams excited on the upper and lower subarray will launch toward the right side and cannot converge, and hence cannot generate a nondiffracting SPP beam in this case. Therefore, in order to launch a nondiffracting SPP beam in different directions under different circular polarization incidences, a symmetric pair of subarrays should be etched on the gold film, shown as the inset of Figure 2b. Figure 2b shows the simulated SPP intensity distribution result of this structure under LCP incidence. The result shows that, although the participation of the symmetric pair results in some side lobes, it will not affect the non-diffraction characteristic of the main lobe of the SPP beam. As this structure (the inset of Figure 2b) is mirror symmetric, it is easy to know that it will launch a nondiffracting SPP beam along the positive x-axis under RCP incidence. Hence, we can realize a nondiffracting SPP-beam launching-based spin router. In the simulation of Figure 2b, the distance (\(\delta\), see the inset of Figure 2b) between the left and right symmetric structures is \(\delta=5\) um and the other parameters are that same as those used in Figure 2a. We then chose the transversal electric field intensity distributions at \(x=\pm 13\) um, shown in Figure 2c, to observe the intensity distribution of the nondiffracting SPP beam. It can be found that the transversal electric field intensity distributions are similar to the cosine-Gauss-like beam [30]. We found that the intensity distribution is slightly asymmetrical with the x-axis. This is because the subarrays are not symmetrical with the x-axis. The key point of a nondiffracting SPP beam in improving the anti-interference ability of photonic devices is that when there is an obstacle on the propagation path, the SPP beam can effectively bypass the obstacle and continue to propagate. This self-healing ability of our device is demonstrated by the FDTD simulation result of Figure 2d, in which a gold cylinder with a radius of 150 nm is set on the propagation path at the point of coordinate (\(-13\) um, \(0\)) as an obstacle. Obviously, although the obstacle causes the SPPs to diverge, the SPP beam will return to being nondiffracting behind the obstacle. Thus, the proposed structure can improve the anti-interference ability of the photonic device. In addition, the tunability of a device is very important in practical applications. Hence, realizing tunable nondiffracting SPP-beam launching is expected in our device. For this, we investigated the influence of the incident angle on the SPP launching direction. If the light is incident at an inclined angle \(\gamma\) with the z-axis in the y-z plane, it carries an in-plane wave vector \(k_{in}=k_{0}\cdot\sin(\gamma)\), where \(k_{0}\) is the free-space wave vector of the incident light. This extra wave vector will change the SPP-beam launching direction [31; 32]. Figure 3 illustrates how \(k_{in}\) influences the nondiffracting SPP-beam launching direction when the incident light has an inclined angle with the z-axis in the y-z plane. In the figure, 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 SPP-beam launching direction when \(\gamma=0\); and OF\({}^{\prime}\) is the nondiffracting SPP-beam launching direction when \(\gamma\
eq 0\).