## 4 Simulation of Practical Spin Routing Device  
In this section, we demonstrate an application example of routing optical signals to single or multiple subwavelength waveguides using nondiffracting SPP-beam launching. For this, we added a PMMA film with 250 nm thickness to the original metal/dielectric interface. In addition, we chose the communication wavelength window at 980 nm as the working wavelength to design the geometric parameters. First, we changed the structure parameters of the single nano-slot to realize the highest SPP excitation efficiency at an incident wavelength of 980 nm. The optimized width and length of the single nano-slot was chosen to be 40 and 220 nm, respectively. In the optimization, we set \(h=120\) nm  
Figure 8: (**a**) The SPP intensity contrast ratio between the points (\(-11\) μm, 0) and (\(11\) μm, 0) under LCP incident light in the wavelength range of 500 to 1000 nm. (**b**) The SPP intensity distribution on the metal/air interface under LCP incident light when the wavelength is 565 nm. (**c**) The SPP intensity distribution on the metal/air interface under LCP incident light when the wavelength is 875 nm. Figure 7: The intensity distribution of nondiffracting SPP beams when there is a cylinder obstacle on the SPP beam’s transmission path. (**a,c**) The self-healing ability of the side lobe SPP beam. (**b**) The self-healing ability of the main lobe SPP beam. and the refractive index of the PMMA to be 1.49. The simulated relationship between the excitation efficiency and the incident wavelength under these parameters is shown in Figure 9. In the simulation, the incident wavelength ranged from 0.7 to 1.2 mm and the electric field polarization direction is perpendicular to the long side of the nano-slot. The SPP intensity at the point \(O\) located on the center point of the nano-slot edge was chosen to evaluate the excitation efficiency. The simulation result shows that the structural parameters can meet our requirement; thus, we used the nano-slot with these geometric parameters to design practical spin-routing devices. For incident light of 980 nm, the dielectric constant of the gold is \(-\)39.938 + 2.75855i, so the wavelength of the SPPs is 967.65 nm. We hence set \(S=242\) nm and \(D=400\) nm in our design. To connect the routing device to the second-order on-chip photonic functional element, we designed strip waveguides to transmit the SPP signal. The detailed device arrangement is shown in the inset of Figure 10a. The brown area presents the PMMA and the orange area presents the gold film. The strip waveguides with width of 150 nm and thickness of 250 nm were fabricated on the gold film. In order to couple the nondiffracting SPP beam to different waveguides under the different incidence angles and provide high coupling efficiency between the strip waveguides and the nondiffracting SPPs beam, the strip waveguides have the same slant angle as the nondiffracting SPP beams' propagation directions. Therefore, we can realize on-chip nondiffracting signal routing by controlling the incidence inclined angle and the spin state. We demonstrated this by FDTD simulation. In the simulation, we designed three strip PMMA waveguides which can couple the nondiffracting signal with the inclined incidence angles of \(-\)7.5\({}^{\circ}\), 0\({}^{\circ}\), and 7.5\({}^{\circ}\); the distance between the two subarrays on the different sides of y-axis is \(\delta=5\) um; and every column has 12 nano-rectangular slots. The lengths of the three strip PMMA waveguides are all 5 um in the horizontal direction. Due to the significantly different transmission losses of the SPPs between metal/air and metal/PMMA interfaces, the nondiffracting SPP signal can only enable stable transmission in the PMMA strip waveguides, which can be seen in Figure 10a-c. Therefore, there is high coupling efficiency between the strip PMMA waveguides and the nondiffracting SPP signals. Moreover, the nondiffracting SPPS beams excited by different inclined angles will couple to different PMMA strip waveguides.