# Dynamical Manipulation of Surface Plasmon Polaritons
## 5 Nondiffracting SPP Beams  
Besides the attenuation caused by absorption of metal, the propagation of SPP also suffer from the scattering because of the rough surface and inherent diffraction. Nondiffracting SPP beams with the diffraction-free and self-healing properties can effectively overcome these effects and lengthen the propagating distance of SPP. Inspired by the generation of nondiffracting beam in the 3D free space, 2D plasmonic Airy beams and Bessel beams have been accomplished and extensively studied [25; 26; 28; 29; 30]. Actively controlling the trajectory, position, propagation direction, and profile of the nondiffracting SPP beams is realized as well. Figure 6a schematically exhibits the experiment setup used to dynamically manipulate the trajectory of SPP Airy beam [42]. 1D Airy beam which is generated through the Fourier transform of a Gaussian beam with a cubic phase is impinged on to a metallic grating and then the excited SPPs take on the profile of incident Airy beams. Mechanical displacements of objective lens O\({}_{1}\) along the transversal or longitudinal direction can change the incident angle of the Airy beam, and an oblique phase is imprinted on the SPP Airy beam. Thus, the propagation direction of the SPP Airy beam can be adjusted by changing the incident angle. Likewise, controlling the displacements of the input Gaussian beam and the cubic phase can modulate the trajectory of the SPP Airy beam. With subwavelength nanoslits, the position of SPP Airy beam can be controlled by the incident polarization [74], as shown in Figure 6b. To generate SPP Airy beam, the length of the slits are designed according to the Airy function and a binary phase (0 and \(\pi\)) modulation is adopted. The orientation angles of the slits are set to be \(\alpha=-\pi/4\) and \(\alpha=\pi/4\), which leads to a dynamical PB phase \(2\sigma_{\pm}\alpha\). A geometrical phase \(k_{spS}\) which is independent of incident polarization is introduced by spacing the slits a distance \(s=A_{sp}/4\) apart. Thus, the phase of leftward and rightward SPP are \(\varphi_{sp}^{l}=2\sigma_{\pm}\alpha+k_{sp}s\) and \(\varphi_{sp}^{r}=2\sigma_{\pm}\alpha-k_{sp}s\), respectively. For LCP incident light, only the SPP propagating to the left satisfies the required phase modulation and SPP Airy beam is generated on the left side. When the incident light is switched to RCP, the SPP Airy beam is only observed on the right side. Figure 5: For Archimedes spiral slits, the topological charge of SPP vortex can be modulated by the polarization (**a**) or topological charge (**b**) of the incident light [21; 44]. (**c**) For SPP vortex generator consisting of nanoslits, dynamically reversing the topological charge of the high-order SPP vortex can be realized [73]. Reproduced with permissions from: [21], ACS, 2010, [44], OSA, 2012, [73], Wiley-VCH, 2018. Compared with the parabolic profile of the SPP Airy beam, the trajectory of SPP Bessel beam is linear. Initial generations of SPP Bessel beam took advantage of intersecting grating structures which can excite two plane SPP waves with an inclined wavefront [28; 30]. Such a SPP phase distribution can also be achieved by projecting a designed hologram onto a simple metallic grating [41]. Schematic diagram of the experimental setup is presented in Figure 6c. To excite SPP Bessel beam, a pure phase distribution \(\varphi(x,y)=-k_{0}(\left|y\right|\sin\alpha+y\sin\beta)\) is addressed on the SLM. The width of the main lobe and the propagation direction of SPP Bessel beam can be manipulated by varying the parameters \(\alpha\) and \(\beta\), respectively. Breaking the intersecting grating into subwavelength slits, SPP Bessel beam with different profiles can be obtained by changing incident polarization [75]. As shown in Figure 6d, the orientation angles of upper and lower slits are \(\alpha=\pi/4\) and \(\alpha=-\pi/4\), repetitively. There also exists a \(\lambda_{sp}/4\) distance between the upper and lower slits.