## 2 Principle and Simulation Results  
The 3D structure diagram of our device is shown in Figure 1a and the 2D structure diagram is shown in Figure 1b. To realize the polarization-controlled SPP launching, the basic structure of the device consists of two parallel columns of a nano-rectangular slot with width \(W\) and length \(L\), which are etched on a gold film. The distance between the center points of the two adjacent slots on different columns is \(\sqrt{S^{2}+\left(D/2\right)^{2}}\), where \(S\) is the perpendicular distance of the two columns and \(D\) is the distance between the center points of the two adjacent slots on one column. When \(D\) is shorter than the effective wavelength of the SPPs (\(\lambda_{spp}\)), the columns will generate a quasi-plane SPP wave. For the case of plane wave incidence, only the component polarized perpendicular to the long side of the nano-rectangular slot can significantly excite the SPPs. Therefore, the initial phase of the SPPs generated by a single rectangle slot depends on its orientation angle \(\alpha\) and the handedness of the incident light. This is the so-called Pancharatnam-Berry (PB) phase [29], which is given by \(\phi(\alpha)=\sigma_{\pm}\left[\alpha-sgn(\alpha)\cdot\frac{\pi}{2}\right]\), where \(\sigma_{\pm}\) is the spin quantum number, i.e., \(\sigma_{+}=1\) represents LCP and \(\sigma_{-}=-1\) represents RCP; \(sgn()\) is the sign function; and \(\alpha\in(-\pi,\pi)\) is the polar angle of the orientation direction of the nano-rectangular slot in the local coordinate system \((x^{\prime},y^{\prime})\) (see Figure 1b). Thus, under LCP incidence and slot parameters of \(\alpha_{1}=\frac{\pi}{4}\) and \(\alpha_{2}=\frac{-\pi}{4}\), for the SPP waves propagating to the left side of the columns, the phase difference between the SPPs exited on column 1 and column 2 is \(\Delta\phi_{left}=k_{spp}\cdot S-\frac{\pi}{2}\), whereas for the SPP waves propagating to the right side of the columns, the phase difference between the SPPs exited on column 1 and column 2 is \(\Delta\phi_{right}=k_{spp}\cdot S+\frac{\pi}{2}\), where \(k_{spp}\) represents the wavevector of the SPP, and \(k_{spp}=\frac{2\pi}{\lambda_{spp}}\). If we design \(S=\frac{\lambda_{spp}}{4}\), the phase difference will be \(\Delta\phi_{left}=0\) and \(\Delta\phi_{right}=\pi\). This means that the SPPs wave will generate constructive interference on the left side of the columns and destructive interference on the right side. Similarly, when the incident light is RCP, the opposite happens. In this way, we can realize different directions of SPP launching under different circular polarization excitations. If the columns have a slant angle \(\theta\) with the y-axis, the propagation direction of the SPP plane wave will have the same angle with the x-axis. To realize nondiffracting SPP-beam excitation, an aperture structure consisting of an upper subarray with slant angle \(\theta\) and a lower subarray with the slant angle \(-\theta\) was designed, as shown in the inset of Figure 2a. The structure can generate a cosine-Gauss SPP beam [30], which is a kind of novel nondiffracting beam. This is demonstrated by the FDTDsimulation result given in Figure 2a, which shows a nondiffracting SPP beam launching along the negative x-axis under LCP incidence. This is because, when the incident light is LCP, the SPP beams excited on the upper and lower subarray launch toward the left side and converge on the negative x-axis. Then, the constructive interference of the two converging SPP beams generates the nondiffracting SPP beam. In the simulation, the incident light is a plane wave with LCP, the light wavelength (\(\lambda_{0}\)) is 633 nm, and the dielectric constant of the gold is \(-11.8351+1.24102\). Hence, the wavelength of the SPPs is \(\lambda_{spp}=\lambda_{0}\sqrt{(e_{m}^{\prime}+\varepsilon_{d})/(e_{m}^{ \prime}\varepsilon_{d})}=605.67\)nm, where \(e_{m}^{\prime}\) is the real part of the permittivity of metal and \(\varepsilon_{d}\) is the permittivity of the dielectric medium (i.e., air).